TFGDA: Exploring Topology and Feature Alignment in Semi-supervised Graph Domain Adaptation through Robust Clustering
Authors: Jun Dan
Weiming Liu
Chunfeng Xie
Hua Yu
Shunjie Dong
Yanchao Tan
Venue: NeurIPS 2024 poster (2024)
Keywords: Graph Transfer Learning
Graph Domain Adaptatipn
Graphs Semi-supervised Learning
Graph Node Classification
Primary area: graph_neural_networks
TL;DR: A nove graph transfer learning framework for semi-supervised graph domain adaptation.

Abstract: Semi-supervised graph domain adaptation, as a branch of graph transfer learning, aims to annotate unlabeled target graph nodes by utilizing transferable knowledge learned from a label-scarce source graph. However, most existing studies primarily concentrate on aligning feature distributions directly to extract domain-invariant features, while ignoring the utilization of the intrinsic structure information in graphs. Inspired by the significance of data structure information in enhancing models' generalization performance, this paper aims to investigate how to leverage the structure information to assist graph transfer learning. To this end, we propose an innovative framework called TFGDA. Specially, TFGDA employs a structure alignment strategy named STSA to encode graphs' topological structure information into the latent space, greatly facilitating the learning of transferable features. To achieve a stable alignment of feature distributions, we also introduce a SDA strategy to mitigate domain discrepancy on the sphere. Moreover, to address the overfitting issue caused by label scarcity, a simple but effective RNC strategy is devised to guide the discriminative clustering of unlabeled nodes. Experiments on various benchmarks demonstrate the superiority of TFGDA over SOTA methods.

TFGDA: Exploring Topology and Feature Alignment in Semi-supervised Graph Domain Adaptation through Robust Clustering
Jun Dan'", Weiming Liu"", Chunfeng Xie², Hua Yu', Shunjie Dong', Yanchao 5.6.7
'Zhejiang University PQueen Mary University of London Dalian University of Technology *Shanghai Jiao Tong University FFuzhou University 'Eggneeriig Research Center of Big Data Intelligence, Ministry of Education Fuujian Key Laboratory of Network Computing and Intelligent Information Processing danjunEzju. edu. en, 218310108zju.eda cn, c. c.xie@qmulacc yhiced@mail, dlutt edu. en, sjdong@sj tu. edu.cn, yctanêfzu. edu. cn
Abstract
Semi-supervised graph domain adaptation, branch of graph transfer learning, aims to annotate unlabeled target graph nodes by utilizing transferable knowledge learned from a label-scarce source graph. However, most existing studies primarily concentrate on aligning feature distributions directly to extract domain-invarian features, while ignoring the utilization of the intrinsic structure information in graphs. Inspired by the significance of data structure information in enhancing models' generalization performance, this paper aims investigate how to leverage the structure information to assist graph transfer learning. To this end, we propose innovative framework called TFGDA. Specially, TFGDA employs structure alignment strategy named STSA to encode graphs' topological structure informa- tion into the latent space, greatly facilitating the learning of transferable features. To achieve a stable alignment feature distributions, we also introduce a SDA strategy mitigate domain discrepancy the sphere. Moreover, to address the overfitting issue caused by label scarcity, simple but effective RNC strategy is devised to guide the discriminative clustering of unlabeled nodes. Experiments on various benchmarks demonstrate the superiority of TFGDA over SOTA methods]
1 Introduction
With the rise of deep learning, node classification techniques have made significant progress in diverse fields. However, due the distribution shift issue, well-trained models often suffer severe performance degradation when applied directly to a new domain. Graph transfer learning (GTL) [ has been proposed to tackle this issue by transferring domain-invariant features from labeled source graph to an unlabeled target graph, effectively boosting the model's performance on the target graph.
Although current studies on GTL have made significant strides, they often rely on the assumption that all nodes in the source graph are labeled. However, this ideal assumption does not hold true in many scenarios. annotating the entire source graph time-consin tome-consuming, especially for large-scale networks. Therefore, in this paper, we focus on a more realistic application scenario known as semi-supervised graph domain adaptation (SGDA) (2). where the source graph only has few labeled nodes. Utilizing the transferable knowledge acquired from the label-scarce source graph to enhance the model's adaptation performance the target graph the most crucial challenge for SGDA.
Equal Contribution, Corresponding Author.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

---

tend to focus on directly aligning feature distributions across domains to extract domain-invarian node features, while overlooking the utilization of the intrinsic structure information in graphs. Notably, the recent advancements in unsupervised learning have showcased the significance of data structure information in enhancing models' generalization. Considering the complex topological structure information presented in the graph, this paper seek to leverage these critical structure information to assist the transfer of shared node knowledge. To this end, we propose innovative SGDA framework named TFGDA that employs a Subgraph Topological Structure Alignment (STSA) strategy to encode structure information into latent space. Specially, STSA utilizes persistent homology (PH) [10] to extract the topological structure information of the input and latent spaces, and then align the topological structures of two space. significantly improving the model's transfer performance. Furthermore, current works 1 4 primarily utilize adversarial training to reduce domain discrepancy. However, adversarial training is an unstable process that may destroy the discriminative details hidden in features [[2], thereby affecting the transfer of shared knowledge. To remedy this issue, we propose a Sphere-guided Domain Alignment (SDA) strategy, aiming to achieve more stable domain alignment. Concretely, SDA initially maps node features to the spherical space. Then, geodesic projection [13] is utilized to project spherical features onto multiple great circles, where the spherical
However, most existing studies B 4
5 7 9
(SSW) distance [4] is employed to quantify the feature distributions discrepancy across domains.
More importantly, in the SGDA scenarios, due the label scarcity of source graph, well-trained model on only a few labeled source nodes is likely to encounter overfitting. Consequently. it may make ambiguous or even incorrect predictions for certain target graph nodes located near the decision boundaries or far from their corresponding class centers. To address this overfitting issue, we devise Robustness-guide Node Clustering (RNC) strategy effectively enhance the model's robustness. RNC aims to guide the discriminative clustering of unlabeled nodes by maximizing the mutual information between the soft cluster assignment of the original node and its perturbed version, significantly improving the model's generalization performance on the target graph.
In summary, the main contributions are listed as follows:
(1) To the best of our knowledge, this is first attempt to utilize the intrinsic topological structure information hidden in graphs to assist GTL. A novel STSA strategy is proposed to preserve the topological structure information in latent space.
(2) A strategy named SDA is introduced to stably align the node feature distributions across domains.
(3) To address the overfitting issue, simple but effective RNC strategy is devised to guide the discriminative clustering of unlabeled nodes.
(4) Experimental results show that our TFGDA outperforms SOTA methods on various benchmarks.
2 Related Works
Graph Transfer Learning. GTL [6] has gained widespread attention for relieving the burden of collecting labeled data for new tasks. Early studies usually source nodes to pre-train expressive models for related tasks in target domain 11 [8] 19 20 21). To enhance model's generalization, recent studies have shifted their emphasis to domain adaptation
22 23 There are two main ways to extract domain- invariant node features: (1) Using adversarial training to enforce domain confusion
[66 24: (2) Minimizing the statistical distance between two domains [25] 26 27 28 29)
However, existing works tend to focus on domain alignment while overlooking the utilization of structure information in graphs.
Semi-supervised Learning on Graphs. Semi-supervised learning on graphs addresses node clas- sification with small fraction of labeled nodes. Previous works [30 31
32 commonly adopt the message passing paradigm to extract discriminative features. Recent studies have explored various techniques, including adversarial training
[33 34], data augmentation 33 36). continuous graph
37.. contrastive learning (27 and meta learning 38 39 to further enhance model's generalization.
Persistent Homology (PH). PH is an essential method in topology for extracting structure infor- mation from point clouds [40 41. Recently, PH has shown significant advantages in various areas,
including signal processing 42 shape matching(43), and design of network [44] Some studies have
investigated its differentiability
45 46). Recent works have also explored its potential in image
segmentation [7 48), action/image recognition 49 50 5
52 53), and evaluation of GANs [54.

---

3 Preliminaries: Persistent Homology (PH)
PH is method used to capture the topological structure of complex point clouds scale parameter p is varied. this section, we briefly introduce some key concepts. Further details on PH can be found in [10 40).
Notation. X {-:)==1 denotes a point cloud and w is a distance metric over X.
Vietoris-Rips (VR) Complex. The VR complex [55] is a unique simplicial complex constructed from set of points, providing approximation of the underlying space's topology. The VR complex of X' at scale p. denoted as (2))), contains all simplices of X. Each component of X satisfies the distance constraint: wxxi, 2z)) S p for any i, Additionally, the VR complex exhibits a nesting property: Vp, S Vp, for any pi S Pj. which enables us to track the evolution progress of simplical complex p increases.
Persistence Diagram (PD). The PD dgm is a multi-set of points (g1, 92) in the Cartesian plane I?, encoding lifespan information of topological features. Concretely, it summarizes the birth time 91 and death time 92 information of each topological feature with a homology group. The birth time 9i indicates the scale of feature creation and death time 92 refers to the scale of feature destruction.
4 Methodology
4.1 Problem Definition
The source graph is defined as G* = (Vod, Vo,u yol, A X²), where ya. is the labeled node set, and vs." is the remaining unlabeled node set in G.. y E R |xk denotes the label matrix of Vo. where K is the number of node classes. If node nē Vad belongs the k-th class, vi,
Source Domain Graph:
otherwise, Vi, 0. A RN*NN" is an adjacency matrix, where N = |oo|| + [ is the number of nodes in 9 If there is an edge between nodes n, and ny, the value of Ai, is set to I; otherwise, it is set to 0. X E N xe indicates an attribute matrix, where e is the dimension of node attributes. Notably, | is much smaller than V in the SGDA setting.
Target Domain Graph: Similarly, the target graph represented as g' (V* A"; Af,)), which is completely unlabeled graph with an unlabeled node set V A' E R N" is an adjacency matrix, and X E R xe is node attribute matrix, where N = | denotes the number of nodes in G..
Semi-Supervised Graph Domain Adaptation (SGDA): Given partially labeled source graph g and an unlabeled target graph g', the goal of SGDA is to precisely annotate target graph nodes by utilizing transferable knowledge learned from the limited labeled source nodes [2 [6).
4.2 Network Architecture
The architecture of our TFGDA model is depicted in Figure 1 It consists of two components: graph convolutional network (GCN)-based feature extractor and a node classifier C. Mathematically, given an input graph G AV
A, X), the node features extracted by F is denoted Hl = F(G) e R xd and it is further normalized map onto spherical space S to obtain spherical features Z E RR VVld where d is the feature dimension, r is the radius and V denotes the number of nodes in G. The classification probability predicted by C is denoted V C(Z) E k
To capture more precise adjacency relationships of graph G. we compute the positive posnt-wise mutual information (PPIM) between nodes following 2]. Specially, for given graph g = (V, X). we utilize random walk to sample a collection of paths on A and generate frequency matrix R. Based on R, we can compute the PPIM matrix P as follows:
Ri
E,Ro,
E. Rij
Pij
P...
P.j.
Eig Roj
Ens
Rij
Ei,
Raj
(1)
Pij
P.j max max(log(
Pi, x P..j ),
3

---

Death
dgmn
Doyth
dgm (2))
(99)
Hirth
Bärth
mms (Q')
Z
g
Co
Conuf33
Classifier C
Lets
Feature Extractor FF
Geodesic Projection
Eda
2
Conu
Con
Sd-1
Classifier C
Spherical Space
mi (Q9)
Deach
dgm (g")
Death
dgm(Z*
L Str (gt)
Birth
Barth
Figure 1: Global overview of the TEGDA model. STSA strategy encodes critical structure information of graphs into spherical space (Letsa (9t) Let greatly improving the model's generalization. SDA strategy aims to extract iamaain-nnvariatt node features by minimizing domain discrepancy on sphere (Leda). Moreover, to effectively solve the overfitting issue, RNC strategy is introduced to guide the discriminative clustering of unlabeled nodes (Crnc Lya (Q²)) ) + L.ss
where P.j denotes the positive mutual information between nodes nı and nj. which quantifies the topological proximity between nodes. higher value of Pey indicates a strong connection between n, and ny. Then, the output of the I-th GCN layer Conv(" is defined as:
H Conv (P, H(-1)) o PD H(-DW())
where D is the diagonal degree matrix of P, and P= P 7 (T is identity matrix). W refer the trainable parameters of the (-th layer, a--) is activation function, and ( = X. Thus, the feature extractor F can be constructed by sequentially stacking L layers of GCN Co 2, L). Given the source labeled node set ys., the classification loss on the source graph g is defined as:
Cets
Σ (c((C((()))) v2). B.EVo
(3)
where Lee represents the standard cross- ensropy loss.
4.3 Subgraph Topological Structure Alignment
As mentioned in Section 1, the graph consists of numerous nodes (e.g., ACMr9 has over 9000 nodes), thereby containing rich structure information. Inspired by the significance of data structure information in enhancing models' generalization (T] seek leverage such critical structure information to facilitate the learning of domain-invariant features.
To achieve this goal, we treat the graph as point cloud and attempt directly capture its underlying topological structure using PH. However, we inevitably encounter huge computational burden due to the complex attributes and adjacency relationships of graph. Fortunately, Refs. [57] 58 have indicated that the properties of graph can be well preserved its multiple local subgraphs. To this end, propose Subgraph Topological Structure Alignment (STSA) strategy to encode structure information input space into the latent space. For a given graph G = AV, X)). STSA first sample
a subgraphs { S.... ... using random walk, and then employ PH to capture the intrinsic topological structure information of each subgraph Gi-
Specially, for each subgraph G. represent its spherical features extracted by F as 2, E gldd which are obtained by indexing the local nodes features from the complete nodes features Z E RR xd Here D denotes the number of nodes in each subgraph. Then we construct the VR complexes

---

Vp(),) and (2,) for point clouds G. and 2,, employ PH to extract their topological structures, and obtain their corresponding PDs dgi and dgm( (2,) respectively. To align the topological structures of the input and latent spherical spaces, we adopt the 1-Wasserstein distance Wi to measure the discrepancy between two PDs (i.e., dgm for input space and dgm (2.) for spherical space), which aims to seek the optimal transport plan y between two PDs:
X" = arg min W1 (iddm((G)) dgm((2,) 2,))
7
Σ ||a - 8
arg min (a.9)
7
where dgm(Gi), 3 E dgm 2,), and || is the Lo distance. After obtaining y", the local structure diserepancy Sar (9:) between two spaces of Ô, can be calculated as:
Caub (G:)
Σ
||a 311
(S)
(o.8))y"
Hence, we can estimate the global structure discrepancy between the input and spherical spaces of graph 9 by aggregating the local structure discrepancy of subgraphs:
Catr(S)
Σ
Caub (G:)
(6)
In the SGDA scenario, the STSA strategy will be applied to both the G and G³, and its loss function is defined as:
Cstea = (9") + (9rr
(7)
Notably, preserving topological structure information has the potential guide unlabeled nodes towards achieving discriminative clustering, thereby promoting the learning of transferable node features, verified in Section 5.3.
Although many GCNs-based methods have already been proposed to exploit graph structure infor- mation to promote the learning of features, these methods are not effective in addressing the SGDA task. Specifically, these GCNs-based methods [59] 60 61
62 typically mine the graph structure information in the deep feature space by designing well crafted GCN architectures or introducing some complex modules. However, recent studies [27 633
64 16 have pointed out that GCNs are insufficient in capturing the sophisticated structure information in graph, which means that the graph structure information may be lost or destroyed after passing through the GCNs-based feature extrac- tors. Thus, directly mining graph structure information from the deep feature space is suboptimal way, which affects the learning of transferable node features in our SGDA setting.
The proposed STSA strategy aims to extract the graph structure information directly from the input space and encode these powerful information into the latent spherical space by aligning the topological structures of the two spaces. This method does not lose or destroy the graph structure information during training. Furthermore, our STSA strategy does not introduce any changes to the network architecture, effectively avoiding an increase in model's complexity and ensuring its adaptability to integration with other methods.
4.4 Sphere-guided Domain Alignment
As mentioned in Section 1, adversarial training has been widely adopted by existing GTL models to reduce domain discrepancy. However, it an unstable process that may destroy the discriminative information hidden in node features, thereby impacting the learning of shared features.
To tackle this issue, we propose stable alignment of cross-domain node features distributions in the spherical space. Our SDA strategy mainly comprises three steps: (1) Map node features onto the sphere space S (2) Use geodesic projection [13 project node features from S to multiple great circles. (3) Compute the feature distributions discrepancy on great circles and minimize it during training.
sahere-guided Domain Alignment (SDA) strategy that achieves
Step (1): Motivated by the effectiveness of spherical features in improving model's transfer perfor- mance 65 we first normalize node features H E R extracted by F with by to obtain
-
5

---

the spherical features Z E R in the sphere space - = 22 2, is the i-th row of H and Z. respectively. Notably, Ref. [66] has proved that a proper radius is lower bounded by parameters т and K:
IR ||21|22 =r), where h2 and
K K
K 1)
(8)
where denotes the expected minimal classification probability of class center and K is the number of classes. In this work, 7 is set to 0.999, and radius r is set to the lower bound.
Step (2): Previous studies 67 68, 69 77 have shown the superiority of optimal transport in aligning feature distributions. Let Q be a probability space and μt, v be two probability measures in P(Q). For any 1, the g-Wasserstein distance between j and is defined as:
(g, = inf vETI(a.))
L.S. (2(2,g)d7(z.
where M(,,,)) {r E P(Ω x 1 μ4 #2# the two marginal projections Q Q # denotes the push-forward operator, and M x Ω + Rt is geodesic metric. However, find that directly using the classical Wasserstein distance to compute features distributions discrepancy on the sphere s is computationally expensive, due to numerous nodes in the graph.
/ is the set of couplings, and ma denote
For more efficient calculations, we utilize geodesic projection ll to project node features lying on s to b great circles (C1, C..... C.,. On the hypersphere, great circles [71] are circles whose diameter equal that of the sphere, and they correspond to the geodesics. Specially, the geodesic projection 16 is determined by U:
1 (2) T
arg min DEspan(UUTT)a)
M Mag- (2.9) arg min M (2) Va,, E S DEB
(10)
where Mga- (2,-1(2,)) (2.g) arccos( (2, g)), and Va UU E d U = 12] is the Stiefel manifold 72
Step (3): Next, we utilize the spherical sliced- Wasserstein (SSW) distance [4] to measure the feature distributions discrepancy of two domain multiple great circles, which can be formulated as:
SSW v)
W ( (U))(((
(11)
JVa.
where a is the uniform distribution over Va In SSW, the geodesic metric MM g) in Wasserstein distance Wz i)) is defined as the geodesic distance (71) Ma; (z.g) = min( gl, r |z 9l).
In practice, it's common approximate the source and target feature distributions using sam- plcs (2)) and (z)))= (i.c., through the empirical approximations j = N - deg and i = No Σ 8zz), where å is the Dirac function. As result, the node features distributions discrepancy between two domains can be measured as:
Cada SSWP R 1 Em W7(
(12)
where is the number of projections. As training progresses, SDA strategy gradually reduces domain discrepancy, making the learning of domain-invariant features easier.
4.5 Robustness-guided Node Clustering
Due to the label scarcity in Go, the model is prone to overfitting when solely relying on Lets for optimization, severely degrading the model's 's generalization performance on G'. To alleviate this overfitting issue, we devise novel Robustness-guidee Node Clustering (RNC) strategy to enhance the
model's 's robustness by guiding the discriminative clustering of unlaheled nodes. Specially, RNC first
introduces trainable shift parameters & = {s!") _.!)).... ...)...))))) and & = (c()),))
(L) to
perturbs the source and target node features respectively, at each layer of F:
(o pps/t, x*/1) + 59/0
cl)
1=1
(13)
(o (( (pa/t, H0/1,(1-1)) + (0)
SofD 1 1<l.

---

where H=&s, and H'&lol) denotes the perturbed source and target node features encoded by Conv()) respectively, and each <./1 specific the output Convl" The shift parameters and & are defined as randomly initialized multi-layer parameter matrices. After perturbation, based on H*.E,.(L) and HF*&&,(L) we can obtain the perturbed source node spherical features z and the perturbed target node spherical features Z respectively.
For brevity, we will omit domain -peciffc notations in the following text. Ideally, regardless of how the node feature is perturbed, the model's prediction for it should remain unchanged because its class label has not changed. To achieve this goal, RNC aims maximize the mutual information between the soft cluster assignment (i.e., classification prediction of classifier C) of the spherical features Z and its perturbed version Z5, capturing their intrinsic invariant information between Z and ZS.
Concretely, given a node spherical feature 2,, the classification probability predicted by is denoted as V (2,) Rx that can be viewed as the distribution of discrete random variable over K classes: r( = k/2) = (2z). Let Φ and of denote the cluster assignment variables of 2; and 2.. respectively, Then, their conditional joint distribution defined as: r( = k, of Re |,, 25) = x W (2.). After marginalization, the joint probability distribution can be formulated as a matrix Q E R K
V ΣM
1 M ((z)) (T
(14)
where QLAE l( = k, k5), Qk l( k), and Qua r( = 15). To preserve the equivalence between pairs (2,, 25) and (2f, 2,), matrix Q is typically symmetrized using (Q+QQ )/2.
In this way, the mutual information 773 [4] between the soft cluster assignment of Z and z can be computed as:
Qukt s.t., |15 S w. VE Eg.
Lmi ( = Σ OLkS In
(15)
Qu Que
1=
where is coefficient that controls the scale of feature perturbation.
In the SGDA scenario, all target domain nodes V; and source domain nodes V U Var" are used to calculate matrices Q² and Q*, respectively. Therefore, the objective function Crne of RNC can be expressed as:
Lyne (Q)" + (Q'), s.t., IIt., S V. E E",
(16)
1,,,115t-0) 115t.000 s, E
Notably, we leverage source labeled nodes you in RNC as they can significantly guide the discrimi- native clustering unlabeled nodes in the right direction. With the help of RNC, more and more intrinsic invariant features of nodes are extracted, which greatly promotes the learning of transferable features. Moreover, unlike previous studies that employ pseudo-labels strategy [2] conditional entropy term 775 to guide the learning of unlabeled nodes, our RNC strategy does not involve any pseudo-labels and naturally avoids degenerate clustering solutions (see Figure for further analysis).
4.6 Model Optimization
In summary, the total objective of TEGDA can be expressed as follows:
min Lats + nLado +Lsssa XCyne F,C.E*
(17)
s.t., 1I5 I w, vE* E 5*, 1 (1 S v, E e
where dyper-parametert 7) e and are used to balance the contributions of the corresponding term.
4.7 Theoretical Analysis
The theoretical analysis of our method is based on the theory of domain adaptation (DA) 776 77
Formally, let H be the hypothesis space. Given two domains S and T, the probabilistic bound of error of hypothesis on the target domain is defined as: (h(h) S s + [dHHH T) μ², where the expected error on the target domain u (h) are bounded by three terms: (1) the expected
7

---

between the source and target domains (S T): (3) the combined error of ideal joint hypothesis μ min 4ss (h') + (h").
error on source domain (h); (2) the
The goal of DA is to lower the upper bound of the expected target domain error 1hT (h). Note that in unsupervised domain adaptation (UDA), minimizing (h) can be easily achieved with source label information, as source domain samples are completely annotated. However, in our SGDA setting, due to the label scarcity of source domain, the model is prone overfitting when solely relying on the source domain classification loss Cets for optimization. Therefore, we introduce the RNC strategy (Crne) to address the overfitting issue, with the aim of guiding G5g (h) towards further minimization.
Most DA methods mainly focus on reducing the domain discrepancy duAn (S, T), such as utilizing techniques like adversarial learning, MMD, optimal transport [78
79 80 8I]. and CORAL. In comparison to these methods, our SDA strategy (Leda) effectively eliminates the feature norm discrepancy in spherical space S and guide a more stable alignment of feature distributions. Furthermore, considering that graph data contains rich structure information that encodes complex relationships among nodes and edges, and existing GTL methods usually adopt GCNs-based feature extractors to learn domain-invariant node features. However, recent studies [27 63 64 [6] have pointed out that GCNs are insufficient in capturing the sophisticated structure information in graph, which seriously affects the transfer of domain-invariant knowledge and consequently limits the model's 's generalization ability. To solve this problem, we thus propose the STSA strategy (Catsa) to align the topological structures of the input space and the spherical space, in order to facilitate the GCNs-based feature extractors to capture more commin--nnvariin node features. Consequently, the combination of SDA (Leda) and STSA (Lstsa) strategies further promotes the minimization of the domain discrepancy (S.
Notably, μ is expected to be extremely small, and therefore it is often neglected by previous methods. However, it possible that μ tends to be large when the cross-domain category distributions are not well aligned [82 883 In this paper, we leverage the RNC strategy (Cyne) to guide both labeled nodes and unlabeled nodes toward achieving robust clustering, effectively promoting the fine-grained alignment of category distributions and ensuring that μ² remains at relatively small value.
In summarry our proposed method not only minimizes the source expected error ths and domain discrepancy dHAH(S,7 T), but also keeps '² at a small value, thereby ensuring a low upper bound.
5
Experiments
5.1 Setup
Datasets.
Our experiments involve three real-world graphs: ACMv9 (A), Citationv/ (C), and DBLPv7 (D), obtained from AretMinnrr [84). Since these graphs have varying sets of node attributes, we union their attribute sets and adjust the attribute dimension to 6775 following (2]. Each node is assigned five-class label, determined by its relevant research areas. Six typical transfer tasks are considered in our experiments: C, A-D, C-AA, C-DD D A and D- Due to the page size limitation, more settings and implementation details are placed on Appendix.
Compared Methods. We compare TFGDA with several SOTA (1) graph semi- suprrvipe learning methods and (2) graph domain adaptation methods as Ref. (2: (1) GCN (30. GSAGE 31,, GAT 32
GIN 85 (2) DANN 86), CDAN 12), UDA-GCN 775, AdaGCN 0. CoCo 27), StruRW 22
and SGDA 2 DANNGCN and CDANGCN are two variants that adopt GCN-based feature extractor.
5.2 Results and Discussion
to showcase the superiority of our TFGDA, we report its performance on the challeng- ing scenario, where only 5% of the nodes in the source graph are labeled. Micro-Fl and Macro-F1 are employed as evaluation metrics, and the classification results on the target graph are gathered in [T] For all transfer tasks, we run each experiment times and record the average accuracy with standard deviation. And we sample different label sets each time to mitigate the randomness. As can be seen, our model obtains the overall best results on all transfer tasks. Specially, TFGDA greatly surpasses the SOTA method SGDA 2 by +7.3% and +100% on "Micro-F1" and "Macro-F1" respectively for the C-A task, implying the superiority in extracting domain-invariant features. Notably, TFGDA enhances performance substantially two hard transfer tasks, C-AA and D D-A.
Following (2).
8

---

Table 1: Transfer performance (%) six transfer tasks with source graph label rate of 5% for semi sumi--upervieed graph domain adaptation.
Medhocs
Micro-Fi
Macro Ft
Micro-Fi
Macro-FF
Micro-Fi
Maam Fl
Macro-Fi
Macco-F1
Micro-FI
Macro
Micro-Fi
Macro-FI
MLP
a1.3a
35.8.
12.8
36.5
39 194_
43.7
16.7s
37.5.330
12.8
OCN 20
$2.0...
56.912.3
53.4.14
$6.1.1.0
523uuse
58.9
54,51155
50.1.214
48.0u1
56.0
11.91.
GSAGE 33
49.
51.8
42.43.42
363
45.0
51.7
48.1a1.7
41.72217
37.4
45.4
39.3
GAT X2
58.1
40
58.3
51.8,2
50.0...
6566ase
55.4223
49.245.m
4684294
38.
50.4
42.0.cm
GIN
63
64/6144
00.01...9
51.3,3.0
57.3.1.0
54.4
02.0.1:
56.811.0
51.92m
45.4ua
502
53.01100
DANN
56
46.3
39.3
44.0...:
38.7
41 81
57.
45.5
19.5
33.2aass
41.7a233
35.611::
CDAN
44.61.0
45.5
424
36.21.1
46771177
29.210.06
32.3.100
41.741.5
34.811.9
DANNGUK
630
62.211.0
57.7.3.05
56.7.a33
55.2100
66.31224
19,011.0
523:100
58.11275
52A13.4
CDANoCK
66.0
61.3219
16.3
53.
58.84..8
53...:::
48.7a
59.021.0
53.3.1
UDA-IIN
25
72.4.390
65.2.0
68.0)..3
64.347.0
62.9ua.0
02.2a14
714422
67.545:3i
558.1.0
12.4.
66.2.44
60.7aca
A
70
68.5.035
68.2
64.21..1
61.5.a.0
6044.115
00.1.
65.843.07
56.1aim
64.1aom
62.81.59
CoCa 27
22.7
648
61
44
62.7gam
01
71.62171
67.3g113
56.721
54.1.1
66,020
64Ag111
SmoRW DX
22.9
68.5n
644-111
63621
11
71.8a
67 67.645-.
570
54.221
66.720m
63 12.1
SCIDA
75
714
60.24635
64.7g3.3)
66 66
62.3gm
72.9
68.94194
68/2)
73.2405
60.3.
SEGDA
558g
33.6-1
11
58.2.1 44
48
57.021
46.341mm
49.8.>
41.0ga
45.9
45.2.123
TEGDA-T
12
65.920ss
6244..3)
64 84
6182m16
65.61201)
54.74::3
16.2.1
53.4
67420
TEGDA-D
758
707.0
71.2
67.5
68.5_ast
6372110
7222nus
68.1
63
58.5.mm
73,4003
TEGDA-R
74
68.81044
64.7.1:44
656_am
6244.1
63.3
627729
568.0
72.1a0
TEGDA-TD
78
72.92044
31
68.9ms
73
71.1a:m1
648-10
62.6.mm
75.2
724
TEGDA-TR
62.3
68.3-11
69
73.4209
70.841.0
642.19
618.0s1
7633011
72.6
TEGDA-DR
774.0
73.2
71
12.0.355
714400
74551113
71.5
653
630mm
77.1
12.
IEGDA
31
78,3
134.3m
72.300
76.0:3.1
64.3mmm
789
744.so
and achieves outstanding results in some easy transfer scenarios, such as A- and D-+C, implying that TFGDA can successfully minimize domain discrepancy. More importantly, the results with a smaller fluctuation range indicate not only the stability of our framework, but also its robustness in the face of different scenarios. Furthermore, we find that most competitors, such as CDANGON. UCN,GCN, and AdaGCN, exhibit poor performance due to their limited ability to align domains and ineffective utilization of unlabeled nodes. In contrast, TFGDA effectively solves these challenges.
5.3 Analysis and Ablation Study
Due to the limitation of page size, more experiments and analysis are placed on the Appendix.
1) Ablation Study:
To investigate the contribution of each component in TFGDA, we compare TFGDA and its 7 variants on various tasks. The variants of TFGDA are shown in Table and the detailed ablation study results are gathered in Table
Table 2: Variants of TEGDA.
Variant
Eyte
Exten
Lats
Lyne
T
IFGDA-T
TEGDA-D
Contribution of Each Component: The results in Table ! reflect the following observations: (1) TFGDA-S (baseline) performs poorly on all tasks because it encounters overfitting problem. (2) Compared to TFGDA-S, variants TFGDA-T, TFGDA-D and TFGDA-R achieve significant performance gains, indicating that preserving topological structure informa- tion, reducing domain discrepancy on the sphere, and guiding discriminative clustering of unlabeled nodes all facilitate the learning of comain-invariant node features.
TEGDA-R
TEGDA-TD
TEGDA-TR
IFGDA-DR
TFGDA
Correlation of Our Strategies: As shown in T the combination of different strategies improves the model's transfer performance, implying a clear complementary relationship among the STSA, SDA, and RNC strategies.
2) Visualization of Node Features:
To show the superior transfer ability of our model, we employ t-SNE to visualize node features on task A-C under the same 5% label rate setting, as depicted in Figure 2 Although the SOTA method SGDA reduces domain discrepancy to certain, there are some overlaps between different clusters, causing some
nodes to be easily misclassfied. In comparison, TFGDA achieves exactly 5 clusters with clean decision boundaries, indicating that our model can capture more fineinrained transferable features as well as align more complex distributions.
3) Effect of STSA: To showcase the effectiveness of preserving topological structure information in assisting GTL, we conduct in-depth experiments from both quantitative and visual aspects: (1) As depicted in Table [] TFGDA-TD and TFGDA-TR greatly outperform TFGDA-D and TFGDA-R respectively, indicating that aligning the topological structures of the input and latent spaces can effectively boost the model's generalization. (2) As shown in Figure compared to TFGDA-R.

---

(a) SGDA
(b) TFGDA-R
(c) TFGDA-TR
(d) TFGDA
SGDA
(f) TEGDA-R
(g) TFGDA-TR
(h) TFGDA
Figure 2: The t-SNE visualization of representations learned by SGDA, TEGDA and two variants on A- task with 5% label rate. In all subfigures, the marks and represent the source domain and target domain, respectively. Fig 2(a-d) depict category alignment (Different colors denotes different classes). Fig 2(e-h) depict domain alignment (Red: Source domain; Blue: Target domain).
A-C
EG04
2004
UON-OI
UDA-G0
Nümber Epoche
26
54
Number Spachs
Figure The trend Micro-F1 during training. Figure 4: Performance with different label rates.
variant TFGDA-TE exhibits better intra-class compactness and inter-class separability in feature space, implying that the incorporation of topological structure information helps guide the discriminative clustering of unlabeled nodes, thereby promoting the learning of domain- invariant nodes features.
4) Effect of RNC: To show the effectiveness of our RNC strategy, we compare it with existing node clustering strategies, including conditional entropy minimization strategy (CEM) 75 and the recently proposed re-weighted pseudo-labeling strategy (RPL.) 2 We investigate the trend of Micro-F1 score during training on tasks ACC and A-+D The curves Figure reffect the following observations: (1) TFGDA-R converges more smoothly and quickly, achieving higher transfer performance, which suggests that RNC strategy can effectively accelerate the learning of domain-invariant features. (2) Compared to TFGDA-S (baseline), TFGDA-S + CEM suffers from severe performance degradation, as CEM may enforce over-confident probability on some misclassified unlabeled nodes. (3) RPL strategy fails to achieve satisfactory performance as it's sensitive to pseudo-labe noise.
5) Effect of Label Rate: To verify the model's robustness under different label scarcity settings, evaluate the performance of different methods on tasks A-C and A-DD using the following label rates for the source graph: 1%, 5%, 7%, 9%, and 10% respectively, shown in Figure It can be observed that our TFGDA significantly outperforms other competitors, even in the most challenging environment of % label rate, indicating the superiority of TFGDA capturing transferable features.
Conclusion
In this paper, we develop novel model named TFGDA for SGDA. Specially, we propose a STSA strategy to encode critical structure information into latent space, significantly improving model's s transfer performance. Moreover, to stably reduce domain discrepancy, the SDA strategy is introduced to align features distributions sphere. We also devise the RNC strategy to guide the cluster- ing of unlaheled nodes to address the overfitting issue, greatly enhancing the model's robustness. Comprchensive experiments and analysis verify the superiority of our TFGDA.
10

---

7 Acknowledgements
This work was supported in part by the National Natural Science Foundation of China under Grants No.66302098, No.624013553 and the Start-up Program for New Young Teacher of Shanghai Jiao Tong University (KI330021-22-6344).
References
[1] Quanyu Dai, Xiao-Ming Wu, Jiaren Xiao, Xiao Shen, and Dan Wang. Graph transfer learning via adversarial domain adaptation with graph convolution. IEEE Transactions on Knowledge and Data Engineering, (5(5):490849925 2023.
[2] Ziyue Qiao, Xiao Luo, Meng Xiao, Hao Dong, Yuanchun Zhou, and Hui Xiong. Semi- supervised domain adaptation in graph transfer learming, In Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, pages 2279-2287, 2023.
[3] Xiao Shen, Quanyu Dai. Sitong Mao, Fu-Lai Chung, and Kup-Sze Choi. Network together: Node classification via cross-network deep network embedding. IEEE Transactions on Neural Networks and Learning Systems, 12355 2021.
[4] Xiaowen Zhang, Yuntao Du, Rongbiao Xie, and Chongjun Wang. Adversarial separation network for cross-network node classification. In Proceedings of the 30th ACM International Conference on Information Knowledge Management, pages 2626,, 2021.
[5] Leonardo Tadeu Lopes and Daniel Carlos Guimarães Pedronette. Self-supervised clustering based on manifold learning and graph convolutional networks. Proceedings of the IEEE/CVF Winter Conference Applications of Computer Vision (WACV), pages 5634-5643, January 2023.
[6] Michael Moor, Max Horn, Bastian Rieck, and Karsten Borgwardt. Topological autoencoders. In International conference on machine learning, pages 7045-7054 PMLR, 2020.
[7] Wenjie Zhu and Bo Peng. Manifold-basse aggregation clustering for unsupervised vehicle re-identiffiatton. Knowledge-Bond -asee Systems, 235:107624, 2022.
[8] Shunjie Dong, Zixuan Pan, Yu Fu, Dongwei Xu, Kuangyu Shi, Qianqian Yang, Yiyu Shi, and Cheng Zhuo Partial unbalanced feature transport for mrdal-tyy cardiac image segmentation. IEEE Transactions Medical Imaging, 1758-1175817771 2023.
[9] Mushui Liu, Yuhang Ma, Yang Zhen, Jun Dan, Yunlong Yu, Zeng Zhao, Zhipeng Hu, Bai Liu, and Changjie Fan. Llm4gen: Leveraging semantic representation of 1lms for text-to-image generation. In AAAI, 2025.
[10] Herbert Edelsbrunner, John Harer, et al. Persistent homology-a survey. Contemporary mathe- maticy, 253(2))227--28,, 2008.
[11] Xiao Shen, Quanyu Dai, Fu-lai Chung, Wei Lu, and Kup-Sze Choi. Adversarial deep network embedding for cross-network node classification. In Proceedings of the AAAI conference on artificial intelligence, volume 34, pages 2991- 2020.
[12] Mingsheng Long, ZHANGJIE CAO, Jianmin Wang, and Michael I Jordan. Conditional adversarial domain adaptation. In Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa- Bianchi, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018
[13] P Thomas Fletcher, Conglin Lu, Stephen M Pizer, and Sarang Joshi. Principal geodesic analysis for the study of nonlinear statistics of shape. IEFE transactions on medical imaging, 23(8)995510055 2004.
[14] Clément Bonet, Paul Berg, Nicolas Courty, François Septier, Lucas Drumetz, and Minh-Ta Pham. Spherical sliced-wasserstein arXiv preprint arXiv:2206.08744 2022.
11

---

[15] Jaekoo Lee, Hyunjae Kim, Jongsun Lee, and Sungroh Yoon. Transfer learning for deep learning on graph-structured data. In Proceedings of the AAAI Conference on Artificial Intelligence. volume 31, 2017.
[16] Jun Dan. Weiming Liu, Mushui Liu, Chunfeng Xie, Shunjie Dong, Guofang Ma, Yanchao Tan. and Jiazheng Xing. Hogda: Boosting semi- supe-supe graph domain adaptation via high-order structure- guided adaptive feature alignment. In Proceedings of the 32nd ACM International Conference on Multimedia, MM '24, page 11109-11118, New York, NY, USA, 2024. Association for Computing Machinery.
[17] Jiezhong Qiu, Qibin Chen, Yuxiao Dong, Jing Zhang, Hongxia Yang, Ming Ding, Kuansan Wang, and Jie Tang. Gee: Graph contrastive coding for graph neural network pre-training, In Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining, pages 1150-1160, 2020.
[18] Ziyue Qiao, Yanjie Fu, Pengyang Wang, Meng Xiao, Zhiyuan Ning, Denghui Zhang, Yi Du, and Yuanchun Zhou. Rpt: toward transferable model on heterogeneous researcher data via pre-training. IEEE Transactions Big Data, 9(1):186-199, 2022.
[19] Ziniu Hu, Yuxiao Dong, Kuansan Wang, Kai-Wei Chang, and Yizhou Sun. Gpt-gnn: Generative pre-training of graph neural networks. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 1857-1867, 2020.
[20] Weiming Liu, Chaochao Chen, Xinting Liao, Mengling Hu, Jianwei Yin, Yanchao Tan, and Longfei Zheng. Federated probabilistic preference distribution modelling with compactness co- clustering for privacy- preservin multi-domain recommendation. In IJCAI, pages 2214-2,,, 2023.
[21] Weiming Liu, Xiaolin Zheng, Mengling Hu, and Chaochao Chen. Collaborative filtering with attribution alignment for review-basee non-overlapped cross domain recommendation. In Proceedings of the ACM web conference 2022, pages 181-1199, 2022.
[22] Shikun Liu, Tianchun Li, Yongbin Feng, Nhan Tran, Han Zhao, Qiang Qiu, and Pan Li. Structural re-weighting improves graph domain adaptation. In International Conference Machine Learning, pages 21778-21793. PMLR, 2023.
[23] Ziqian Lu, Fengli Shen, Mushui Liu, Yunlong Yu, and Xi Li. Improving zero-shot generalization for clip with variational adapter. ECCV, 2024.
[24] Jun Dan, Tao Jin, Hao Chi, Shunjie Dong, Haoran Xie, Keying Cao, and Xinjing Yang. Trust- aware conditional adversarial domain adaptation with feature norm alignment. Neural Networks, 168:518-520
2023.
[25] Xiao Shen, Quanyu Dai, Sitong Mao, Fu-lai Chung, and Kup-Sze Choi. Network together: Node classification via cross-network deep network embedding. IEEE Transactions on Neural Networks and Learning Systems, 52(5):1935-199) 2020.
[26] Gaoyang Guo, Chaokun Wang, Bencheng Yan, Yunkai Lou, Hao Feng, Junchao Zhu, Jun Chen, Fei He, and Philip Yu. Learning adaptive node embeddings across graphs. IEEE Transactions on Knowledge and Data Engineering, 2022.
[27] Nan Yin, Li Shen, Mengzhu Wang, Long Lan, Zeyu Ma, Chong Chen, Xian-Sheng Hua, and Xiao Luo. Coco: A coupled contrastive framework for unsupervised domain adaptive graph classification. In International Conference Machine Learning, pages 40040-40053, PMLR, 2023.
[28) Jun Dan, Tao Jin, Hao Chi, Yixuan Shen, Jiawang Yu, and Jinhai Zhou. Homda: High-order moment-basee domain alignment for unsupervised domain adaptation. Knowledge-Bast Systems, 261:1 10205, 2023.
[29] Jun Dan, Tao Jin, Hao Chi, Shunjie Dong, and Yixuan Shen. Uncertainty- joint unbal- anced optimal transport for unsupervised domain adaptation. Neural Computing and Applica- tions, 35(7):5351-536) 2023.
12

---

[30] Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. International Conference Learning Representations, 2016.
[31] Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. Advances in neural information processing systems, 30, 2017.
[32] Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. Graph attention networks. In International Conference on Learning Representations, 2018.
[33] Jiarong Xu, Yang Yang, Junru Chen, Xin Jiang, Chunping Wang, Jiangang Lu, and Yizhou Sun. Unsupervised adversarially robust representation learning on graphs. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 36, pages
2022.
[34] Wei Jin, Yaxing Li, Han Xu, Yiqi Wang, Shuiwang Ji, Charu Aggarwal, and Jiliang Tang. Adversarial attacks and defenses on graphs. ACM SIGKDD Explorations Newsletter, 22(2):19 34, 2021.
[35] Yiwei Wang, Wei Wang, Yuxuan Liang, Yujun Cai, Juncheng Liu, and Bryan Hooi. Nodeaug: Semi-supervised node classification with data augmentation. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 207-217, 2020.
[36] Yongduo Sui, Qitian Wu, Jiancan Wu, Qing Cui, Longfei Li, Jun Zhou, Xiang Wang, and Xiangnan He. Unleashing the power of graph data augmentation on covariate distribution shift. Advances Neural Information Processing Systems, 36, 2024.
[37] Louis-Pascal Xhonneux, Meng Qu, and Jian Tang. Continuous graph neural networks. In International Conference Machine Learning, pages 10432-1044 PMLR, 2020.
[38] Ziyue Qiao, Pengyang Wang, Pengfei Wang, Zhiyuan Ning, Yanjie Fu, Yi Du Yuanchun Zhou, Jianqiang Huang, Xian-Sheng Hua, and Hui Xiong. A dual-channel supervise learning framework on graphs via knowledge transfer and eeta-learnnng. ACM Transactions on the Web, 2023.
[39] Ziyue Qiao, Pengyang Wang, Pengfei Wang. Zhiyuan Ning, Yanjie Fu, Yi Du, Yuanchun Zhou, Jianqiang Huang, Xian-Sheng Hua, and Hui Xiong. A dual-channel semi-supervised learning framework on graphs via knowledge transfer and meta-learming ACM Transactions on the Web, 18(2):1-26, 2024.
[40] Afra Zomorodian and Gunnar Carlsson. Computing persistent homology. In Proceedings of the twentieth annual symposium on Computational geometry, pages 347-356, 2004.
[41] Chi Seng Pun, Si Xian Lee, and Kelin Xia. Persistent-homoloyy-ben machine learning: survey and a comparative study. Artificial Intelligence Review, 55(7):5169-522 5213, 2022.
[42] Jose A Perea and John Harer. Sliding windows and persistence: An application of topological methods signal analysis. Foundations of Computational Mathematics, 15:799-838, 2015.
[43] Adrien Poulenard, Primoz Skraba, and Maks Ovsjanikov. Topological function optimization for continuous shape matching. In Computer Graphics Forum, volume 37, pages 13-25, Wiley Online Library, 2018
[44] Gunnar Carlsson and Rickard Brüel Gabrielsson. Topological approaches to deep learning. In Topological Data Analysis: The Abel Symposium 2018, pages 119-146. Springer, 2020.
[45] Rickard Brüel Gabrielsson, Bradley J Nelson, Anjan Dwaraknath, and Primoz Skraba. A topology layer for machine learning. In International Conference Artificial Intelligence and Statistics, pages 1553-1563. PMLR, 2020.
[46] Christoph Hofer, Florian Graf, Bastian Rieck, Marc Niethammer, and Roland Kwitt, Graph filtration learning. International Conference on Machine Learning, pages 4314-4323, PMLR, 2020.
13

---

[47] James R Clough, Nicholas Byrne, Ilkky Oksuz, Veronika A Zimmer, Julia A Schnabel, and Andrew P King. topological loss function for deep-learing based image segmentation using persistent homology. IEEE transactions pattern analysis and machine intelligence, 44(12))8766-8777, 2020.
[48] Mushui Liu, Jun Dan, Ziqian Lu, Yunlong Yu, Yingming Li, and Xi Li. Cm-unet: Hybrid cnn- mamba unet for remote sensing image semantic segmentation. arXiv preprint arXiv:2405.10530 2024.
[49] Ekaterina Khramtsova, Guido Zuccon, Xi Wang, and Mahsa Baktashmotlagh. Rethinking persistent homology for visual recognition. In Topological, Algebraic and Geometric Learning Workshops 2022, pages 206-215. PMLR, 2022.
[50] Vinay Venkataraman, Karthikeyan Natesan Ramamurthy, and Pavan Turaga. Persistent ho- mology of attractors for action recognition. In 2016 IEEE international conference on image processing (ICIP), pages 4150-4154. IEEE, 2016.
[51] Jun Dan, Yang Liu, Jiankang Deng, Haoyu Xie, Siyuan Li, Baigui Sun, and Shan Luo. Topofr: closer look at topology alignment on face recognition. arXiv preprint arXiv:2410. 105877 2024.
[52] Mushui Liu, Fangtai Wu, Bozheng Li, Ziqian Lu, Yunlong Yu, and Xi Li. Envisioning class entity reasoning by large language models for few-shot learning. In AAAI, 2025.
[53] Bozheng Li, Mushui Liu, Gaoang Wang, and Yunlong Yu. Frame order matters: A temporal sequence-aware model for few-shot action recognition. In AAAI, 2025.
[54] Danijela Horak, Simiao Yu, and Gholamreza based approach for evaluating generative adversarial networks. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 7721-7728, 2021.
Topology distance: A topology-
[55] Afra Zomorodian. Fast construction of the vietoris-rips complex. Computers Graphics 34(3):263-277 271, 2010.
[56] Chi-Chong Wong and Chi-Man Vong. Persistent homology based graph convolution network for fine aie-ggriied 3d shape segmentation. In Proceedings of the IEEE/CVF international conference on computer vision, pages 7098-7107, 2021.
[57] Yuning You, Tianlong Chen, Yongduo Sui, Ting Chen, Zhangyang Wang, and Yang Shen. Graph contrastive learning with augmentations. Advances in neural information processing systems, 33:5812-5823, 2020.
[58] Yanbei Liu, Yu Zhao, Xiao Wang. Lei Geng, and Zhitao Xiao. Multi-scale subgraph contrastive learning. In Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, pages 2215-2223 2023.
[59] Yiding Yang, Jiayan Qiu, Mingli Song, Dacheng Tao, and Xinchao Wang. Distilling knowledge from graph convolutional networks. In Proceedings of the IEEF/CVF conference on computer vision and pattern recognition, pages 7074-7083, 2020.
[60] Sen Jia, Shuguo Jiang, Shuyu Zhang, Meng Xu, and Xiuping Jia. Graph-in in in-graph convolutional network for hyperspectral image classification. IEEE Transactions on Neural Networks and Learning Systems, 35(1):1157-11
2022.
[61] Jiangzhang Gan, Rongyao Hu, Yujie Mo, Zhao Kang, Liang Peng, Yonghua Zhu, and Xiaofeng Zhu. Multigraph fusion for dynamic graph convolutional network. IEEE Transactions on Neural Networks and Learning Systems, 3561):196-207, 2022.
[62] Yimeng Min, Frederik Wenkel, and Guy Wolf. Scattering gen: Overcoming oversmoothness in graph convolutional networks. Advances in neural information processing systems, 33:14498. 14508, 2020.
[63] Luca Cosmo, Giorgia Minello, Alessandro Bicciato, Michael M Bronstein, Emanuele Rodolà, Luca Rossi, and Andrea Torsello. Graph kernel neural networks. IEEE Transactions on Neural Networks and Learning Systems, 2024.
14

---

[64] Qingqing Long, Yilun Jin, Yi Wu, and Guojie Song. Theoretically improving graph neural networks via anonymous walk graph kernels. In Proceedings of the Web Conference 2021, pages 1204-1214, 2021.
[65] Ruijia Xu, Guanbin Li, Jihan Yang, and Liang Lin. Larger norm more transferable: An adaptive feature norm approach for unsupervised domain adaptation. In Proceedings of the IEEE/CVF international conference computer vision, pages 1426-1435, 2019.
[66] Xiang Gu, Jian Sun, and Zongben Xu. Unsupervised and semi-supervised robust spherical space domain adaptation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022.
[67] Weiming Liu, Xiaolin Zheng, Chaochao Chen, Jiahe Xu, Xinting Liao, Fan Wang, Yanchao Tan, and Yew-Soon Ong. Reducing item discrepancy via diffcrentially private robust embedding alignment for privacy-preseriing cross domain recommendation. In Forty-first International Conference on Machine Learning.
[68] Weiming Liu, Chaochao Chen, Xinting Liao, Mengling Hu. Yanchao Tan, Fan Wang, Xiaolin Zheng, and Yew Soon Ong. Learning accurate and bidirectional transformation via dynamic embedding transportation for cross-domain recommendation. In Proceedings of the AAAI Conference Artificial Intelligence, volume 38, pages 8815-8823, 2024.
[69] Weiming Liu, Xiaolin Zheng, Chaochao Chen, Jiajie Su, Xinting Liao, Mengling Hu, and Yanchao Tan. Joint internal multi-interest exploration and external domain alignment for cross domain sequential recommendation. In Proceedings of the ACM Web Conference 2023, pages 383-394, 2023.
[70] Xinting Liao, Weiming Liu, Chaochao Chen, Pengyang Zhou, Fengyuan Yu, Huabin Zhu, Binhui Yao, Tao Wang, Xiaolin Zheng, and Yanchao Tan. Rethinking the representation in federated unsupervised learning with non-iid data. In Proceedings of the IEEF/CV Conference on Computer Vision and Pattern Recognition, pages 22841-228500 2024.
[71] Julien Rabin, Julie Delon, and Yann Gousseau. Transportation distances on the circle. Journal of Mathematical Imaging and Vision, 41(1-2):17-1167, 2011.
[72] Thomas Bendokat, Ralf Zimmermann, and P-A Absil. A grassmann manifold handbook: Basic geometry and computational aspects. arXiv preprint arXiv:2011.13699 2020.
[73] Erik G Learned-Miller. Entropy and mutual information. Department of Computer Science, University of Massachusetts, Amherst, 4, 2013.
[74] Xu Ji, Joao F Henriques, and Andrea Vedaldi. Invariant information clustering for unsuper- vised image classification and segmentation. In Proceedings of the IEEE/CVF international conference on computer vision, pages 9865-9874 2019.
[75] Man Wu, Shirui Pan, Chuan Zhou, Xiaojun Chang, and Xingquan Zhu. Unsupervised domain adaptive graph convolutional networks. In Proceedings of The Web Conference 2020, pages 1457-1467, 2020.
[76] Shai Ben-David. John Blitzer, Koby Crammer, Alex Kulesza, Fernando Pereira, and Jen- nifer Wortman Vaughan. theory of learning from different domains. Machine learning. 79:151-175, 2010.
[77] Shai Ben-David, John Blitzer, Koby Crammer, and Fernando Pereira. Analysis of representations for domain adaptation. Advances in neural information processing systems, 19, 2006.
[78] Bharath Bhushan Damodaran, Benjamin Kellenberger, Rémi Flamary, Devis Tuia, and Nicolas Courty. Deepjdot: Deep joint distribution optimal transport for unsupervised domain adaptation. In Proceedings of the European conference on computer vision (ECCV), pages 447-463, 2018.
[79] Weiming Liu, Xiaolin Zheng, Chaochao Chen, Mengling Hu, Xinting Liao, Fan Wang, Yanchao Tan, Dan Meng, and Jun Wang. Differentially private sparse mapping for privacy-preservie cross domain recommendation. Multimedia, pages 0243-6252, 2023.
Proceedings of the 31 ACM International Conference on
15

---

[80] Weiming Liu, Xiaolin Zheng, Jiajie Su, Mengling Hu, Yanchao Tan, and Chaochao Chen. Exploiting variational domain-invariant user embedding for partially overlapped cross domain recommendation. In Proceedings of the 45th International ACM SIGIR conference on research and development information retrieval, pages 312-321, 2022.
[81] Fan Wang, Chaochao Chen, Weiming Liu, Tianhao Fan, Xinting Liao, Yanchao Tan, Lianyong Qi, and Xiaolin Zheng. Ce-rcfi: Robust counterfactual regression for consensus-enabled treatment effect estimation. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 3013-3023, 2024.
[82] Chaoqi Chen, Weiping Xie, Wenbing Huang, Yu Rong, Xinghao Ding, Yue Huang, Tingyang Xu, and Junzhou Huang. Progressive feature alignment for unsupervised domain adaptation. In P Proceedings of the IEEF/CVF conference computer vision and paltern recognition, pages 627-636, 2019.
[83] Jun Dan, Mushui Liu, Chunfeng Xie, Jiawang Yu, Haoran Xie, Ruokun Li, and Shunjie Dong. Similar norm more transferable: Rethinking feature norms discrepancy adversarial domain adaptation. Knowledge-Baie Bassed Systems, 296:11 1 1908, 2024.
[84] Jie Tang, Jing Zhang, Limin Yao, Juanzi Li, Li Zhang, and Zhong Su. Ametminer: extraction and mining academic social networks. Proceedings of the 14th ACM SIGKDD international conference Knowledge discovery and data mining, pages 990-998, 2008.
[85] Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? In International Conference on Learning Representations, 2018.
[86] Yaroslav Ganin, Evgeniya Ustinova, Hana Ajakan, Pascal Germain, Hugo Larochelle, François Laviolette, Mario March, and Victor Lempitsky. aomaaraadversarial training of neural networks. Journal of machine learning research, 17(59):1 2016.
[87] Chen- Yu Lee, Tanmay Batra, Mohammad Haris Baig, and Daniel Ulbricht. Sliced wasserstein discrepancy for unsupervised domain adaptation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10285-10295, 2019.
16

---

A Appendix
A.1
Datasets
We run experiments on three real-world graphs: ACMv9 (A), Citationv (C), and DBLPv7 (D). In these graphs, every node refers to paper, and the attribute of each paper is represented as a sparse bag-of-words vector derived from its title. The edges in these graphs depict citation relationships among the papers. Each node is assigned a five-class label, determined by its relevant research areas, including Artificial Intelligence, Computer Vision, Databuse, Information Security, and Networking.
Table 3 displays various statistical information of three graphs, including graph scale, attributes, average degree, and label proportion. We can observe substantial intrinsic discrepancy among these graphs. In this paper, we adopt an alternating approach where we select one of these graphs as the source domain, while considering the remaining two the target domains.
Table 3: The statistics of three real- world graphs. Note that '#' means 'the number of". 'Attr' refer to "Attributes'. 'Avg.' represents 'Average".
Graph
#Nodes
#Edges
#Attr.
Avg. Degree
Label Proportion (%)
ACMv9 (A)
9,360
15,602
5,571
1,667
Citationv (C)
8,935
15,113
5,379
1.691
DBLPv7 (D)
5,484
8,130
4,412
1.482
21.7/33,,0223.86..0155
A.2 Implementation Details
Our experiments implemented using Pytorch library. Following previous work (2), choose two-layer GCN as the feature extractor F of TFGDA model. We randomly initialize the shift parame- ter 5 and 5 using uniform distributions (-,(-, c) and U4(-c, respectively. In all experiments, we set the value of e to 0.5. For all transfer tasks, we perform each random experiment 5 times and record the average accuracy with standard deviation. And sample different label sets for each experiment to mitigate the randomness.
To optimize the network, employ Adam optimizer with weight decay of 0.001 for better convergence. The base learning rate is set to 0.002 for all tasks. terms of the balanced coefficients and 77, we choose s 0.3 and 7 = for all transfer tasks. Furthermore, instead of fixing the trade-off parameter À of RNC strategy, we adopt a progressive schedule as (2 to dynamically adjust from 0 to 1 by multiplying by & to more stably guide the discriminative clustering unlabeled nodes, where is the current epoch and θ is the maximum epoch. Parameter 7 in Eq.(8) is set to 0.999, and the spherical radius is set the lower bound.
In our STSA strategy, we choose to retain O-dimensional topological information in PDs. This because some preliminary experiments have shown that using higher-dimension topological information does not lead to clear accuracy improvements but noticeably increases the model's s training time. For the subgraph sampling operation, we the number of subgraphs 10 and the number of nodes in each subgraph to 800 to strike a balance between model performance and training efficiency. During the inference process, we disable the shift parameters branch in our RNC strategy. Notably, for all methods (including the compared methods), the dimension of node features is set to 512.
A.3 More Experiments and Analysis
A.3.1 More Ablation Study
To demonstrate the effectiveness of SDA strategy, we compare it with existing domain alignment strategies, including adversarial training alignment strategy (AT) [.] sliced Wasserstein distance-based alignment strategy (SWD) 87], class-conditional MMD strategy (CMMD) R. and the recently proposed shifting- grrtinngggiiedd adversarial training alignment strategy (SAT)
Effectiveness of SDA:
We employ variant TFGDA-S as the baseline and evaluate the performance gains brought by these strategies two typical transfer tasks: A and D.
[2.
17

---

A-C
A-D
75
TFODAS SWO
TEGDNS +
70
TFGDA + SWD
TFGDAS 1 AT
TRODWS CHMD
TEGDA- CHMD
TRODA
TFGDA-O
65
TFGDMO
TTGDA-
65
60
60
55
50
Micro-F1 (%)
Macro-F1 (%)
Micro-F1 (%)
Macro-F1 (%)
Figure 5: Transfer performance with different domain alignment strategies A A and D.
Table 4: Notations.
Notation
Description
number of sampled subgraphs (9,
Sa
a
b
number of great circles projections
a coefficient for controling the scale feature perturbation balance parameters of loss terms Lada Latsa and Lyne number of nodes in each subgraph
17 A
[
The results shown in Figure the following observations: (1) Compared to adversarial training- based strategies such as AT and SAT, our SDA strategy can bring greater performance improvements to the model, especially in the hard transfer task AD This is because SDA implements more stable distributions alignment process, which promotes the model to capture more transferable features. (2) The proposed SDA strategy works better than the SWD strategy, SDA takes into account the manifold structure of the data in the spherical space, while SWD primarily focuses on the distribution discrepancy the Euclidean space. (3) TFGDA-D significantly outperforms all compared strategies, which indicates the superiority of our SDA strategy in mitigating domain discrepancy and extracting Nomain-invarian features.
A.3.2 Parameter Sensitivity
The key parameters and notations in our TFGDA model are summarized in Table
7) Effect of Subgraphs: As depicted in Figure 6 we investigate the effect of different numbers of sampled subgraphs a and different subgraph sizes |b on the model's transfer performance, respectively.
can obtain the following observations: (1) As the number of sampled subgraphs a increases, the model's transfer performance gradually improves until it converges. However, large number of subgraphs can lead to slow model training. Therefore, in our model, we set the number subgraphs to 10 to balance model's 's accuracy and training efficiency; (2) Similarly, the size of the subgraphs | increases, the model's 's accuracy gradually improves until converges. However, excessively large subgraphs also significantly increase training time. Hence, to strike balance between performance and training efficiency, we set the number of nodes in each subgraph to 800. (3) When the number or size [V,] of the subgraphs set too small, the model's performance becomes less robust, exhibiting a higher standard deviation. This is because, in such cases, the subgraphs struggle to capture the structure information present in the original graph sufficiently.
8) Effect of Feature Perturbation Scale:
The constraint coefficient w of shift parameters & and is responsible for controlling the scale of node feature perturbation. To investigate the effect of coefficient w in our framework, we train our TEGDA models with different w and evaluate their performance two tasks: A C and AD
The results are illustrated Figure 7 As to increase, the model's 's accuracy first rises and then falls, which implies that properly perturbing the node feature can effectively enhance the model's robustness.
18

---

C-A
C-A
D-4
Mirooe PS)
Mico-1 PR
35
15
10
102
121
400
11.3
2003
121
152
300
LVd 250
Sampled Subgraphs
Subgraph
Figure 6: Transfer performance with subgraphs at different scales on C-A and D-A tasks.
80
Micro-F1 (%)
Micro-F1
0.01 0.03
0.05
0.1
0.3
5
0.01
0.03
0.05
0.1
0.3
0.5
5
Perturbation Scale
Perturbation Scale
Figure 7: Transfer performance with different feature perturbation scale A A and A D- tasks.
A-C
A-4C
A-CC
A-D
MicroF11 (99
Micro-F1 1%)
82
80
78-
78
78
76
76
74-
74
72
0.1
0.3
0.5
0.01
0.05
0.1
0.3
0.5
10
25
50
80
100
Ballnce parameter
Balance parameter
Number of projections D
Figure Parameter sensitivity analyses of parameters v,, E, and on A-+Can and A-D tasks.
Specially, when wo E [0.05, 0.5]. our model can achieve stable transfer performance with a very small standard deviation. However, when the coefficient is set to large value, unlabeled nodes struggle cluster the correct direction, leading
significant degradation in model performance.
9) Effeet of Hyper-parameter: Figure 8 depicts our evaluation of the sensitivity of several hyper- parameters transfer tasks A-C and A-D. The evaluated hyper-parameters include balance parameters and e, and the number of projections For the parameter v), we find that selecting an appropriate value adjust the SDA loss Leda can effectively decrease domain discrepancy. Moreover, we can observe that our model is robust to changes in parameter E, indicating the stability of our STSA strategy. The results also implies that our SDA strategy maintains stability when aligning feature distributions across domains, regardless of variations in the specific value of the parameter b. When b extremely small, accurately approximating the SSW distance (i.e. domain discrepancy (12)) in the SDA strategy becomes difficult, leading to slight decrease in model's transfer performance.
A.3.3 More Analysis
10) Why our RNC strategy can avoid degenerate clustering solutions ?: The mutual information
(6, (MI) objective function (m) Eq. 15 can be expanded to: Cms (Q) Lmi (Ø, df) = E(Ø)
(((ld)) 73 74.. Therefore, maximizing this objective Lmi involves trade-off between minimizing the conditional cluster assignment entropy E'(lØF) and maximizing the entropy of individual cluster assignments E()). Specially, the minimum value of E(ØlØ5) is O. which is achieved when the cluster assignments can be precisely predicted from each other. The maximum value of E(ω) is In K, achieved when all clusters have an equal probability of being selected, where K is the number of classes. This situation arises when the data is evenly distributed among the clusters, resulting in an equal distribution of their masses. Hence, the loss function cannot minimized when all
19

---

samples are assigned to the same cluster. In such case, maximizing MI naturally achieves a balance between reinforeing predictions and equalizing the cluster masses, thereby avoiding the occurrence of degenerate clustering solutions. The t-SNE node features visualization results in the main text also validate this viewpoint.
A.3.4 Limitation
Our model might has the following two limitations:
(i) As depicted in of the Appendix, the effectiveness of our STSA strategy depends on the quality of the subgraphs (i.e., subgraph size V/51 and the number of subgraphs a). As result, the model's 's transfer performance may decrease if the subgraph size is small or the number of subgraphs small, as these local subgraphs are difficult sufficiently capture the properties of the original graph.
(ii) As depicted in Figure 7 of the Appendix, the transfer ability of the model affected by the feature perturbation scale wo in the RNC strategy. Specially, when the feature perturbation scale w set to large value, it is difficult for the RNC strategy accurately capture the intrinsic invariant features of nodes, which affects the discriminative clustering of unlabeled nodes and leads to a decline in model's generalization performance.
20

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification:
The abstract and introduction section include the main claims made in the paper.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals as motivation long is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: We have discussed the limitations of this work. Please refer to the Section A.3.4 in the Appendix.
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (c.g.. independence assumptions, noiseless settings, model sell-speciiiatiinn asymptotic approximations only holding locally). ). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-tex, system might not be used reliably to provide closed captions for online lectures because it fails handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and faimesss.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community, Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory Assumptions and Proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
21

---

Answer:
[NA]
Justification:
This work does not involve any novel theoretical findings.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
The proof's can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental Result Reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided not)?
Question:
Answer: [Yes]
Justification: We have provided detailed implementation details in Section A.2 of the Appendix.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, descríbing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g.. g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) the contribution is primarily a new algorithm, the paper should make clear how reproduce that algorithm. (b) If the contribution is primarily new model architecture, the paper should describe the architecture clearly and fully.
(c) the contribution is new model (e-g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should possible for other researchers to have some path to reproducing verifying the results.
5. Open access to data and code
22

---

The authors should provide scripts to reproduce all experimental results for the new reproducible, they Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, as described in supplemental material?
Question:
Answer: [No]
Justification: We have provided publicly available dataset information in Section A. Appendix.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips.c cc/
for more details.
While we encourage the release of code and data, we understand that this might be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https
/ https/ccpppllligggddeeeeeeeeeeee Cotee//mdeeeSbmmmcia ssi onPolicy) for more details.
The authors should provide instructions data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
proposed method and baselines. only subset of experiments should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code is permitted.
6. Experimental Setting/Details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: We have provided detailed implementation details and training settings in Section A.2 of the Appendix.
Guidelines:
The answer NA means that the paper does include experiments.
The experimental setting should be presented in the core the paper to level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment Statistical Significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
Justification:
Our experimental results already include error bars.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, or statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall with given experimental conditions).
23

---

The method for calculating the error bars should be explained (closed form formula, call a library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
It should be clear whether the error bar is the standard deviation the standard error of the mean.
It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful figures symmetric error bars that would yield results that are out of range (e.g. negative rates).
show in tables or
If error bars are reported in tables or plots, The authors should explain the text how they were calculated and reference the corresponding figures tables in the text.
8. Experiments Compute Resources
For each experiment, does the paper provide sufficient information on the puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Question:
Answer: [Yes]
Justification:
We have provided detailed experiment settings in Section A.2 of the Appendix.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary failed experiments that didn't I make it into the paper).
9. Code Of Ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics
Answer: [Yes]
The research conducted the paper fully adheres to the NeurIPS Code of Ethics.
Justification:
Guidelines:
The answer NA means that the authors have reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., there a special consid- eration due to laws or regulations in their jurisdiction).
10. Broader Impacts
Question: Does the paper discuss both potential positive socictal impacts and negative societal impacts of the work performed?
Answer: [NA]
Justification:
All the datasets involved in this paper are publicly available.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact why the paper does not address societal impact.

---

Examples of negative societal impacts include potential malicious unintended uses (e.g., disinformation, generating fake profiles, surveillance), faireess considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms monitor how system learns from feedback over time, improving the efficiency and accessibility of ML).
11. Safeguards
Does the paper deseribe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: The paper poses no such risks.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: [Yes]
Justification: The data and code used in this paper have obtained legal permissions.
Guidelines:
The answer NA means that the paper does use existing assets.
The authors should cite the original paper that produced the code package dataset.
The authors should state which version of the asset used and, possible, include URL.
The name of the license (e.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g., website). the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms use in package should be provided. For popular datasets, paperswithcone com/ datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
25

---

For existing datasets that are re-packaged, both the original license and the license of the derived asset (if has changed) should be provided.
If this information is not available online, the authors are encouraged to reach out to the asset's s creators.
13. New Assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [NA]
Justification:
The paper does not release new assets.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details the dataset/code/moodl as part their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsoureing and Research with Human Subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification: The paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included the main paper.
According the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based the requirements of your country or institution) were obtained?
Answer: [NA]
Justification: The paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Depending the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
26


Reviews:
[{"review_id": "kxzKriFrKr", "reviewer": "Reviewer_9hdx", "summary": "This paper introduces a graph transfer learning framework called TFGDA, which leverages the structure information to enhance model’s generalization performance. The TFGDA framework includes the structure alignment strategy STSA, the feature distribution alignment strategy SDA, and the RNC strategy to address the overfitting caused by label scarcity. Experiments are conducted various benchmarks.", "questions": "See Weaknesses", "limitations": "The authors should further clarify the motivation behind using spherical features of their proposed method.", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.This paper is first attempt to utilize the intrinsic topological structure information hidden in graphs to assist graph transfer learning, which is well-motivated and novel.\n\n2. This paper is well-written and well-organized. The figures are clear and the text is easy to follow.\n\n3.The experiments are comprehensive. The experimental results demonstrate the superiority of the proposed framework.", "weaknesses": "1. This paper proposes to extract spherical features of subgraphs in Subgraph Topological Structure Alignment strategy. Please further explain the reasons for using spherical features and analyze the necessity.\n\n2. The interplay between loss functions could affect the extracted features and model performance. It would be beneficial if the authors could provide a thorough analysis for the combination of loss functions and theoretically explanation of the success.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to express our gratitude to Reviewer 9hdx for their comprehensive evaluation of the manuscript and the insightful feedback provided, which will greatly contribute to the improvement of our paper. Kindly refer to our specific responses outlined below.\n\n**W1: This paper proposes to extract spherical features of subgraphs in STSA strategy. Please further explain the reasons for using spherical features and analyze the necessity. The authors should further clarify the motivation behind using spherical features of their proposed method.**  \n**A1:** Thanks for your valuable advice.\n\n**1) explain the reasons:** Notably, several studies [Y1] in transfer learning have demonstrated that the domain shifts are mainly caused by the feature norm discrepancy between the source and target domains, and the model degradation on the target domain is primarily caused by its excessively smaller feature norms than the source domain. To eliminate the negative effects of feature norm differences, we map features into the spherical space to guide the alignment of feature distribution (as stated in lines 170-173), which can significantly facilitate the learning of domain-invariant features and improve the model's transfer performance.\n\nFurthermore, Refs.[Y1-Y2] have pointed out that highly informative features typically display more significant feature norms, and task-specific features with larger norms are more transferable.\nHowever, due to the large parameter search space, it is difficult to find the optimal spherical radius for different transfer tasks.\nTo address this issue, we follow the lower bound theorem from Ref.[Y3] to set an appropriate radius $r$ for the spherical space $\\mathbb{S}_{r}^{d-1}$, as mentioned in lines 173-176 of the manuscript.\n\nRef.[Y1] Larger Norm More Transferable: An Adaptive Feature Norm Approach for\nUnsupervised Domain Adaptation. ICCV 2019. \\\nRef.[Y2] Rethinking the Smaller-Norm-Less-Informative Assumption in Channel Pruning of Convolution Layers. ICLR 2018.\\\nRef.[Y3] Unsupervised and Semi-supervised Robust Spherical Space Domain Adaptation. TPAMI 2022.\n\n**2) analyze the necessity**:\nAccording to your advice, we conduct additional ablation experiments to validate this point.  As described in Table 2 of the paper, variant TFGDA-T ($\\mathcal{L}\\_\\{cls}+\\mathcal{L}\\_\\{stsa}$) implements the STSA strategy in spherical space $\\mathbb{S}\\_\\{r}^{d-1}$. \nBased on variant TFGDA-T, we remove the spherical space $\\mathbb{S}\\_\\{r}^{d-1}$ and implement the STSA strategy in regular space, resulting in a new variant called TFGDA-T (w/o sphere).\nThe experimental results are shown in the **Table A** of the global response PDF file.\nWe can observe that the introduction of spherical space $\\mathbb{S}\\_\\{r}^{d-1}$ can effectively enhance the model's transfer ability, which is consistent with the aforementioned analysis.\n\n\n**W2: The interplay between loss functions could affect the extracted features and model performance. It would be beneficial if the authors could provide a thorough analysis for the combination of loss functions and theoretically explanation of the success.**  \n**A2:** Thanks for your valuable suggestion.\nIt is worth noting that our ablation study results in Section 5.3 (lines 271-285) have validated the contribution of each loss term and the complementary relationship among different loss terms (i.e., different combinations of loss terms).  Moreover, the t-SNE visualization results in Figure 2 have also confirmed the importance the combination of loss terms $\\mathcal{L}\\_\\{rnc}$, $\\mathcal{L}\\_\\{stsa}$ and $\\mathcal{L}\\_\\{sda}$.\nWe have also conducted a sensitivity analysis on the trade-off parameters of these loss terms in Section A.3.2 of the Appendix (lines 557-565). \n\n**Theoretically Explanation:** Based on your insightful advice, we provide a theoretical analysis of our method. Due to the characters limit, we will present this theoretical analysis in the **global rebuttal area**.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "zQBs3xPFRh", "reviewer": "Reviewer_aMJG", "summary": "This paper presents a framework called TFGDA for semi-supervised graph domain adaptation (SGDA). It addresses the challenge of annotating unlabeled target graph nodes by utilizing knowledge from a source graph with limited labels. The framework incorporates three key strategies: Subgraph Topological Structure Alignment (STSA), Sphere-guided Domain Alignment (SDA), and Robustness-guided Node Clustering (RNC). These strategies collectively aim to encode topological structure information, stably align feature distributions, and guide the clustering of unlabeled nodes, thereby enhancing the model's transfer performance.", "questions": "please refer to Weaknesses", "limitations": "please refer to Weaknesses", "rating": 4, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "1. Interesting Topic: Graph domain adaptation (GDA) is a compelling topic with significant potential for advancing the field of graph-based learning.\n2. SOTA Performance: The experimental results indicate that the proposed methods achieve state-of-the-art (SOTA) performance across various benchmarks.\n3. Theoretical Foundation: The paper is supported by a solid theoretical foundation, leveraging topological data analysis and domain adaptation principles.", "weaknesses": "1. Limited Innovation: The innovation in the paper is limited. While the authors claim to be the first to consider graph structure, similar approaches have been explored in previous work that also utilize graph structural information.\n2. Overly Optimistic Results: The experimental results seem excessively positive, with improvements of 5-10 points on certain datasets, which is highly challenging. The absence of open-source code makes it difficult to verify these results.\n3. Lack of Code Availability: The paper does not provide open-source code, which hinders reproducibility and further validation of the proposed methods by the research community.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We extend our heartfelt gratitude to Reviewer aMJG for the careful reading of the manuscript and the valuable feedback provided, which are helpful to improve our paper. Our detailed point-by-point responses are provided below.\n\n**W1: While the authors claim to be the first to consider graph structure, similar approaches have been explored in previous work that also utilize graph structural information.**  \n**A1:** Thanks for the valuable comment. We primarily showcase the innovation of our method through the following three aspects:\n\n**1):** Although many graph convolutional networks (GCNs)-based methods have already been proposed to exploit graph structure information to promote the learning of features, these methods heavily rely on a large amount of labeled data.\nMoreover, these methods overlook the substantial domain discrepancy between training and testing datasets in real-world scenarios, making them unsuitable for semi-supervised graph domain adaptation (SGDA) scenario.\nSpecifically, these GCNs-based models trained only with the limited source labeled nodes (i.e., SGDA task scenario) will suffer severe performance degradation when directly applied to a new target domain.\n\n**2):** In addition, these GCNs-based methods [X1-X6] typically mine the graph structure information in the deep feature space by designing well-crafted GCN architectures or introducing  some complex modules. However, recent studies [X6-X8] have pointed out that GCNs are insufficient in capturing the sophisticated structure information in graph, which means that the graph structure information may be lost or destroyed after passing through the GCNs-based feature extractor. Thus, directly mining graph structure information from the deep feature space is a suboptimal way, which affects the learning of transferable node features in our SGDA setting.\n\nThe proposed STSA strategy aims to extract the graph structure information directly from the input space and encode these powerful information into the latent spherical space by aligning the topological structures of the two spaces. This method does not lose or destroy the graph structure information during training.  Furthermore, our STSA strategy does not introduce any changes to the network architecture, effectively avoiding an increase in model's complexity and ensuring its adaptability to integration with other methods.\n\n**3):** What's more, these GCN-based methods typically model graph structure by considering the similarity between features of adjacent nodes, making it difficult to capture the sophisticated high-order structure information in graph [X5,X6].\nIn contrast, our work attempts, for the first time, to model the graph structure information from a persistent homology (i.e., topological data analysis) perspective, enabling a more precise capture of the complex structures inherent in graph. \n\nIn summary, our proposed STSA strategy is an innovative solution for mining graph structure information and facilitating graph transfer learning.\n\nRef.[X1] Distilling Knowledge From Graph Convolutional Networks. CVPR 2020.\\\nRef.[X2] Graph-in-Graph Convolutional Network for Hyperspectral Image Classification. TNNLS 2022.\\\nRef.[X3] Multigraph Fusion for Dynamic Graph Convolutional Network. TNNLS 2022.\\\nRef.[X4] Knowledge Embedding Based Graph Convolutional Network. WWW 2021.\\\nRef.[X5] Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networks. NIPS 2020.\\\nRef.[X6] Coco: A Coupled Contrastive Framework for Unsupervised Domain Adaptive Graph Classification. ICML 2023.\\\nRef.[X7] Graph Kernel Neural Networks. TNNLS 2024.\\\nRef.[X8] Theoretically Improving Graph Neural Networks via Anonymous Walk Graph Kernels. WWW 2021.\n\n**W2&W3: The experimental results seem excessively positive. The paper does not provide open-source code.**  \n**A2&A3:**\\\n**1):** It is worth noting that semi-supervised graph domain adaptation (SGDA) is a relatively novel task scenario in graph transfer learning, first introduced in Ref.[X9]. Currently, there has been little exploration in this field. As stated in lines 248-251, the main compared methods adopted in Table 1 are some semi-supervised methods and graph domain adaptation methods.\nDue to the label scarcity of source graph and the huge domain discrepancy in the SGDA scenario, these semi-supervised methods are unable to tackle these challenges, resulting in severe performance degradation on the target domain.\n\nAlthough graph domain adaptation can alleviate domain discrepancy, they inevitably encounter the overfitting issue. Because these methods typically assume that the source domain is fully labeled, making it difficult to effectively utilize a large number of unlabeled nodes, as stated in lines 265-267.\nOur method effectively addresses these challenges, thus achieving SOTA performance.\n\n**2):** Regarding the pioneering work SGDA [X9], it struggles to achieve superior performance because it simply utilizes the classical adversarial learning to reduce domain discrepancy, and its clustering strategy inevitably introduces pseudo-label noise into the model (as verified in lines 307-308 and 518-532).\n\nRef.[X9] Semi-supervised Domain Adaptation in Graph Transfer Learning. IJCAI 2023.\n\n**3) Source code:** \nBased on your valuable suggestion, we will provide AC with the source code of our method in order to validate the authority of our work. We commit to publicly release the code after the paper is accepted.\n\nIf you have additional concerns, please let us know and we will do our best to address them. We appreciate your time and efforts in reviewing our work.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "I9d9L0Lv3a", "reviewer": "Reviewer_byDA", "summary": "This paper focus on the semi-supervised graph domain adaptation, and introduces a new framework called TFGDA. Graph usually contains complex structure information, while existing GTL studies often overlooks the importance of structure information when extracting transferable node features. TFGDA thus proposes a novel STSA strategy to utilize the topological structures information between input and latent spaces to assist GTL. To solve the instability caused by adversarial training-based domain adaptation methods, this paper also presents an SDA strategy to reduce cross-domain node feature distributions discrepancy in the spherical space. Furthermore, an innovative mutual information-based RNC strategy is proposed to address the overfitting issue by guiding the robust clustering of unlabeled target graph nodes. Extensive experimental results show that TFGDA outperforms existing state-of-the-art methods across various transfer learning tasks, indicating its superiority and stability.", "questions": "I have some doubts and hope the authors to clarify them.\n(1)\tWhen the model performs inference on the target domain graph, is the shift parameter perturbation branch $\\xi$ of RNC activated? Does the graph data flow through the regular branch or the perturbation branch before being fed into the classifier \\mathcal{C} for inference?\n\n(2)\tWhat is the intrinsic reason for the need to introduce structure information in graph transfer learning frameworks? Is it because the structure information of the data tends to be lost as the network layers go deeper?\n\n(3)\tSome previous images based-transfer learning works [2-4] have utilized the wasserstein or the sliced wasserstein as distance metrics to minimize domain discrepancy. In the SDA strategy, why is the SSW distance better than these two distance in measuring domain differences? \n\nReference:\n[2] Sliced wasserstein discrepancy for unsupervised domain adaptation. (CVPR 2019).\n[3] Reliable weighted optimal transport for unsupervised domain adaptation. (CVPR 2020).\n[4] Deepjdot: Deep joint distribution optimal transport for unsupervised domain adaptation. (ECCV 2018).", "limitations": "The authors have provided clear explanations of the limitations that the proposed method may encounter in the supplementary materials. This article does not have any potential negative societal impact.", "rating": 7, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "(1) The paper is well-written and has a clear structure. Compared to the widely studied unsupervised domain adaptation in GTL, the semi-supervised domain adaptation is more relevant to real-world application scenarios. Therefore, it is meaningful to explore effective solutions to address the challenges faced by semi-supervised domain adaptation. In general, the paper is quite novel and worth reading.\n\n(2) The introduction of the STSA strategy is well-motivated. Leveraging the graph structure information to facilitate graph transfer learning is indeed an innovative attempt and shows significant transfer performance gains on multiple tasks.\n\n(3) The SDA strategy exhibits significant superiority over existing methods in reducing node feature distributions difference. Additionally, it is an interesting idea to devise a node clustering strategy RNC from the view of mutual information. Detailed experimental results demonstrate the effectiveness of RNC in addressing the overfitting problem and enhancing model robustness. \n\n(4) The paper provides comprehensive experiment on multiple benchmark datasets to validate the superior transfer performance over existing state-of-the-art methods.", "weaknesses": "To make this paper more comprehensive, there are some concerns that I would like the authors to address.\n(1)\tThis paper mainly utilizes multiple real-world academic graphs as datasets. Further exploration can be conducted on other types of graph datasets (such as real-world graph datasets), which can more effectively validate the generalizability of the proposed method.\n(2)\tFurthermore, I recommend the authors to include a discussion and comparison of the model’s inference efficiency in the paper. \n(3)\t[Minor comment:] While the t-SNE visualization results in Figure 2 clearly show the advantage of TFGDA in reducing feature distribution discrepancy, I recommend the authors to include additional quantitative metrics to better demonstrate the transfer ability of the method, such as the {A}-distance [1].\n(4)\t[Minor comment:] Since the SDA strategy contains some complex mathematical details, it is recommended to add a high-level algorithm table to summarize it.\n\nReference:\n[1] Analysis of representations for domain adaptation. (Neurips 2006).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the Reviewer byDA for the careful reading of the manuscript and the related comments, which are helpful to improve our paper.\n\n**W1: Further exploration can be conducted on other types of graph datasets.**  \n**A1:** Based on your suggestion, we conduct additional experiments on a real-world recommender systems graph dataset called AliCVR to validate the generalizability of our method. Please refer to the answer **A5** to Reviewer **R5oT**.\n\n**W2: Include a discussion and comparison of the model’s inference efficiency.**  \n**A2:** We compare model's inference time on the transfer task **A**$\\rightarrow$**C** in the following Table R3. Due to the addition of the spherical space $\\mathbb{S}\\_\\{r}^{d-1}$, our TFGDA exhibits a slightly longer inference time (1.02x) than the SOTA competitor SGDA [S1], which does not significantly increase the inference time but brings a clear performance gain. \nAdditionally, it is worth mentioning that if the spherical space $\\mathbb{S}\\_\\{r}^{d-1}$ is removed, during inference the network architecture of our TFGDA is almost identical to that of SGDA, as we will disable the shift parameters perturbation branch $\\xi\\_\\{s}$ and $\\xi\\_\\{t}$.\n\n**Table R3: Model's Inference time on Citationv1 (C).**\n| Transfer Task | Method | Inference Time on **C** | Micro-F1 |\n| ------ | ------ | ------ | ------ |\n| **A**$\\rightarrow$**C** | SGDA | 5.46s | 75.6$\\_\\{\\pm0.57}$ |\n|  | **TFGDA** | 5.58s | 81.0$\\_\\{\\pm0.34}$ |\n\nRef. [S1] Semi-supervised Domain Adaptation in Graph Transfer Learning. IJCAI 2023.\n\n**W3: Include additional quantitative metrics to better demonstrate the transfer ability of the method, such as the  $\\mathcal{A}$-distance.**  \n**A3:** Following your advice, we utilize the $\\mathcal{A}$-distance as a metric to evaluate the transfer ability of different methods in Figure 2. Table R4 shows the results of the $\\mathcal{A}$-distance on **A**$\\rightarrow$**C** task. Since our method can accurately align feature distributions of two domains at the class-level, it achieves the smallest $\\mathcal{A}$-distance. \n\n**Table R4: $\\mathcal{A}$-distance on A$\\rightarrow$C task.**\n| Method | $\\mathcal{A}$-distance |\n| ------ | ------ |\n| TFGDA-R | 1.67 |\n| SGDA | 1.54 |\n| TFGDA-TR | 1.48 |\n| **TFGDA** | 1.36 |\n\n**W4: Add a high-level algorithm table to summarize the SDA strategy.**  \n**A4:** Thanks for the valuable advice. We will include a a high-level algorithm table for the SDA strategy in the revised version to make the paper more comprehensive. \n\n**Q1: During inference, is the shift parameter perturbation branch $\\xi$ of RNC activated? Does the graph data flow through the regular branch or the perturbation branch before being fed into the classifier $\\mathcal{C}$ for inference?**  \n**A5:** As mentioned in Section A.2 of the Appendix (line 513), during the inference process, we will disable the shift parameters perturbation branches $\\xi_{s}$ and $\\xi_{t}$. \nThus, during the inference process, the graph data will be fed through the regular branch (i.e., without any feature perturbation) into the classifier $\\mathcal{C}$ for the final prediction.\n\n**Q2: What is the intrinsic reason for the need to introduce structure information in graph transfer learning frameworks? Is it because the structure information of the data tends to be lost as the network layers go deeper?**  \n**A6:** Notably, unlike images and time series data, graph data usually contains rich structure information that encodes complex relationships among nodes and edges. Most existing graph transfer learning works  directly use graph convolutional networks (GCNs)-based feature extractors to learn transferable node features. However, recent studies [S2-S4] have indicated that GCNs are insufficient in capturing the sophisticated structure information in graph, which means that the graph structure information may be lost or destroyed after passing through the GCNs-based feature extractor. Therefore, we propose the STSA strategy to encode these intrinsic structure information in graph (i.e., from the input space) into the latent space by aligning the topological structures of the input space and the latent space, effectively improving the model's transfer performance.\n\nRef. [S2] Coco: A coupled contrastive framework for unsupervised domain adaptive graph classification. ICML 2023.\\\nRef. [S3] Graph Kernel Neural Networks. TNNLS 2024.\\\nRef. [S4] Theoretically improving graph neural networks via anonymous walk graph kernels. WWW 2021.\n\n**Q3: In the SDA strategy, why is the SSW distance better than the wasserstein and the sliced wasserstein distance metrics in measuring domain differences?**  \n**A3:** **1)** As described in lines 182-184, due to numerous nodes in the graph (e.g., ACMv9 dataset has over 9000 nodes), directly using the classical Wasserstein distance to compute feature distributions discrepancy is computationally expensive, rendering it impractical for graph transfer learning task.\n\n**2)** To eliminate the negative influence of feature norm discrepancy on the learning of transferable node features, our SDA strategy thus guides feature distributions alignment in spherical space.  As described in lines 528-530, the sliced Wasserstein distance focuses on calculating discrepancy between distributions in Euclidean space [S5], making it difficult to precisely measure feature distributions discrepancy in spherical space. While our SSW distance fully considers the manifold structure of data in spherical space when assessing distribution discrepancy [S6], thereby facilitating a more precise quantification of difference in feature distributions. Furthermore, the detailed ablative experiments results in Figure 5 of the Appendix (lines 518-532) have already validated that our SSW distance is superior to the sliced Wasserstein distance in measuring domain discrepancy.\n\nRef.[S5] Sliced Wasserstein Kernels for Probability Distributions. CVPR 2016.\\\nRef.[S6] Spherical Sliced-Wasserstein. ICLR 2023.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "MNjDCP3ozl", "reviewer": "Reviewer_R5oT", "summary": "This paper proposes a novel framework named TFGDA for the semi-supervised graph domain adaptation. Considering that existing graph domain adaptation works overlook the utilization of graph structure information, this paper innovatively proposes a STSA strategy that fully leverages graph structure information to promote the learning of domain-invariant node features. Moreover, TFGDA also devises a SDA strategy to achieve a fine-grained feature distributions alignment, which maps node features onto multiple great circles and utilizes the spherical sliced-Wasserstein distance to quantify the domain discrepancy. To remedy the overfitting phenomenon caused by limited source labeled nodes, a novel RNC strategy is proposed to guide the discriminative clustering of unlabeled nodes. Comprehensive experiments on various benchmarks demonstrate that the proposed TFGDA outperforms state-of-the-art methods in semi-supervised graph domain adaptation tasks.", "questions": "See Weakness.", "limitations": "See Weakness. If the authors address all my concerns, I am pleased to improve the final score.", "rating": 7, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1) This paper is well-motivated and easy-to-follow. The overall structure is clear. Source graph label scarcity is indeed a common challenge encountered in real-world applications.\n\n2) Preserving the graph structure from a topological perspective to promote the extraction of transferable node feature is a novel idea. It effectively utilizes the inherent properties of the graph to enhance model’s transfer performance, which can shed some light on future research on graph transfer learning.\n\n3) It is a novel attempt to utilize the SDA strategy to achieve fine-grained feature distribution alignment in spherical space. \n\n4) The motivation behind the RNC strategy is clear. The experimental results also validate that the RNC strategy effectively mitigates overfitting issues and significantly  outperforms other strategies.\n\n5) The effectiveness and SOTA transfer performance of TFGDA has been confirmed through extensive ablation studies, visualization results, and comparative experiments.", "weaknesses": "I have several concerns and questions as below:\n\n[About writing]\n1) It is suggested to include some discussions on practical applications of graph transfer learning in the Sec 1, which may better emphasize the significance of the research.\n \n[About the proposed method]\n2) The proposed STSA strategy employ persistent homology to extract the topological structures of both graphs. In topological theory, topological features of different dimensions capture the structure of the underling space from different perspectives. What dimensions of topological features did the authors use in STSA strategy to align the topological structures of the input space and latent space? How was this determined?\n\n3) What distance metric was used when constructing the Vietoris-Rips simplicial complex in the STSA strategy?\n\n4) Previous domain adaptation works [1] have used the K-means algorithm to guide unlabeled nodes clustering. What advantages does the RNC strategy have compared to K-means? \n\n[About the experiments]\n5) Although the authors conducted detailed experiments on mainstream graph domain adaptation datasets (i.e., ACMv9, Citationv1 and DBLPv7), I hope they discuss the scalability of TFGDA on larger graph datasets, such as the recommender systems dataset AliCVR [2]. \n\n6) It is suggested to compare and discuss the proposed TFGDA with the recently introduced GIFI method [3].\n\nRef [1] Deng W, Liao Q, Zhao L, et al. Joint clustering and discriminative feature alignment for unsupervised domain adaptation[J]. IEEE Transactions on Image Processing, 2021, 30: 7842-7855.\nRef [2] Guo G, Wang C, Yan B, et al. Learning adaptive node embeddings across graphs[J]. IEEE Transactions on Knowledge and Data Engineering, 2022, 35(6): 6028-6042.\nRef [3] Qiao Z, Xiao M, Guo W, et al. Information filtering and interpolating for semi-supervised graph domain adaptation[J]. Pattern Recognition, 2024, 153: 110498.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate Reviewer R5oT for the thorough review of the manuscript and the valuable comments that will aid in enhancing our paper. \n\n**Q1: Include some discussions on practical applications of graph transfer learning in the Sec.1.**  \n**A1:** Graph Transfer Learning can be applied in various practical scenarios, such as recommender systems [K1], molecular property prediction [K2], social and academic networks analysis [K3], cross-modal retrieval [K4], and human parsing [K5].\n\nRef.[K1] Learning adaptive node embeddings across graphs. TKDE 2022.\\\nRef.[K2] Transfer learning with graph neural networks for improved molecular property prediction. NC, 2024.\\\nRef.[K3] A comprehensive survey on graph neural networks. TNNLS, 2020.\\\nRef.[K4] Cross-Domain Transfer Hashing for Efficient Cross-modal Retrieval. TCSVT, 2024.\\\nRef.[K5] Graphonomy: Universal Human Parsing via Graph Transfer Learning. CVPR 2019.\n\n**Q2: What dimensions of topological features did the authors use in STSA strategy? How was this determined?**  \n**A2:** As described in Section A.2 of the Appendix (lines 508-511), we use 0-dimensional topological features in our STSA strategy to align the topological structures of the input and latent spaces. Because some preliminary experiments have shown that using higher-dimension topological information does not lead to clear accuracy improvements but noticeably increases the model’s training time.\\\nAdditionally, the topological theory [K6-K7] has demonstrated that low-dimensional topological features (e.g., 0-dimensional) can roughly reflect the topological structure of the data, while high-dimensional topological features (e.g., 3-dimensional and 4-dimensional) are responsible for capturing some complex details of topological structure.\nThus, to balance computational efficiency and model performance, we choose to retain 0-dimensional topological features in our STSA strategy.\n\nRef.[K6] Computing persistent homology. 2004.\\\nRef.[K7] Persistent homology-a survey. 2008.\n\n**Q3: What distance metric was used when constructing the Vietoris-Rips simplicial complex in the STSA strategy?**  \n**A3:** We use Euclidean distance as the distance metric to construct the Vietoris-Rips simplicial complex in our STSA strategy.\n\n**Q4: What advantages does the RNC strategy have compared to the K-means algorithm?**  \n**A4:** Compared to the K-means clustering algorithm, our RNC strategy has two main advantages:\n\n**1)** Using the K-means algorithm in neural networks results in a two-stage clustering process [K8]. Specifically, the deep features extracted by the network are first clustered using the K-means algorithm to generate pseudo-labels. These pseudo-labels are then used to guide the model training. This clustering process inevitably introduces pseudo-labels noise into the model during training, limiting the model's generalization ability. On the contrary, our proposed RNC strategy is an end-to-end clustering method that does not involve any pseudo-labels, thereby enhancing the model's robustness in face of different transfer scenarios.\n\n**2)** When combined with representation learning, the K-means algorithm is prone to degenerate clustering solutions [K8-K10], where all unlabeled nodes are assigned to the same cluster, severely affecting the construction of decision boundaries.\nThe proposed RNC strategy is designed based on the mutual information theory, which effectively guides unlabeled nodes toward robust clustering and naturally avoids degenerate clustering solutions. As shown in Section A.3.3 of the Appendix (lines 566-579), we have provided a detailed theoretical analysis that explains how our RNC strategy can avoid degenerate clustering solutions. Furthermore, as mentioned in Section 4.5 (lines 234-236), the experimental results in Figure 2 and Figure 3 have also validated this point.\n\nRef. [K8] Deep Clustering for Unsupervised Learning of Visual Features. ECCV 2018.\\\nRef. [K9] On strategies to fix degenerate k-means solutions. Journal of Classification 2017.\\\nRef. [K10] How to Use K-means for Big Data Clustering. PR 2023.\n\n**Q5: Discuss the scalability of TFGDA on larger graph datasets, such as the AliCVR dataset.**  \n**A5:** Based on your valuable suggestion, we follow Ref.[K1] to utilize a real-world large-scale recommender systems dataset Ali-CVR to conduct additional experiments. Specially, Ali-CVR can be divided into 3 large-scale graphs: **AN**, **A11** and **AB11**.\nWe report the node classification accuracy in the target graph, and the results in Table R1 demonstrate the scalability and stability of our method.\n\n**Table R1: Node classification accuracy (%) in the target graph. Source graph label rate: 10\\%. [Source graph $\\rightarrow$ Target graph]**\n| Method | **AN**$\\rightarrow $**A11** | **AN**$\\rightarrow $**AB11** | **A11**$\\rightarrow $**AN** |\n| ------ | ------ | ------ | ------ |\n| UDA-GCN | 20.66$\\_\\{\\pm2.41}$ | 23.47$\\_\\{\\pm3.07}$ | 21.29$\\_\\{\\pm1.75}$ |\n| GraphAE | 23.80$\\_\\{\\pm2.06}$ | 27.19$\\_\\{\\pm2.53}$ | 25.04$\\_\\{\\pm1.58}$ |\n| SGDA | 27.42$\\_\\{\\pm1.83}$ | 31.25$\\_\\{\\pm2.20}$ | 28.36$\\_\\{\\pm1.34}$ |\n| **TFGDA** | **33.67**$\\_\\{\\pm1.42}$ | **35.82**$\\_\\{\\pm1.73}$ | **34.15**$\\_\\{\\pm1.09}$ |\n\n**Q6: It is suggested to compare and discuss the TFGDA with the GIFI method.**  \n**A6:** Following your suggestion, we compare the transfer performance of our method with the GIFI on the challenging transfer scenario, where only 5% of the source graph nodes are labeled.  The results in the Table R2 demonstrate the effectivenss of our method.\n\n**Table R2: Transfer performance (%) measured by Macro-F1 on some transfer tasks. Source graph label rate: 5%.**\n| Method | **A**$\\rightarrow $**C** | **C**$\\rightarrow $**D**  | **D**$\\rightarrow $**A** |\n| ------ | ------ | ------ | ------ |\n| GIFI | 73.7$\\_\\{\\pm0.69}$ | 69.0$\\_\\{\\pm2.05}$ | 64.1$\\_\\{\\pm1.08}$ |\n| **TFGDA** | **78.9**$\\_\\{\\pm0.46}$ | **72.6**$\\_\\{\\pm1.35}$ | **64.3**$\\_\\{\\pm0.72}$ |", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
**1) To Reviewer 9hdx:** Dear Reviewer 9hdx, based on your insightful advice, we provide a **theoretical analysis** of our method.

The theoretical analysis of our method is based on the theory of domain adaptation (DA) [Y4-Y5].

Formally, let $\mathcal{H}$ be the hypothesis space. Given two domains $\mathcal{S}$ and $\mathcal{T}$, the probabilistic bound of error of hypothesis $h$ on the target domain is defined as:
$\\psi\_\{\\mathcal{T}}(h) \\le \\psi \_\{\\mathcal{S}}(h) + \\frac{1}{2}d\_\{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathcal{S},\\mathcal{T})+\\mu^{\*\}$,
where the expected error on the target domain $\psi_{\mathcal{T}}(h)$ are bounded by three terms: **(1)** the expected error on source domain $\psi_{\mathcal{S}}(h)$; **(2)** the $\mathcal{H} \Delta \mathcal{H}$-divergence between the source and target domains $d_{\mathcal{H} \Delta \mathcal{H}}(\mathcal{S},\mathcal{T})$; **(3)** the combined error of ideal joint hypothesis $ \mu^{*} = \min_{h'\in \mathcal{H}} \psi_{\mathcal{S}}(h') + \psi_{\mathcal{T}}(h')$.

The goal of DA is to lower the upper bound of the expected target domain error $\psi_{\mathcal{T}}(h)$.
Note that in unsupervised domain adaptation (UDA), minimizing $\psi_{\mathcal{S}}(h)$ can be easily achieved with source label information, as source domain samples are completely annotated. 
However, in our semi-supervised graph domain adaptation (SGDA) setting, due to the label scarcity of source domain, the model is prone to overfitting when solely relying on the source domain classification loss $\mathcal{L}\_\{cls}$ for optimization. Therefore, we introduce the **RNC** strategy ($\mathcal{L}\_\{rnc}$) to address the overfitting issue, with the aim of guiding $\psi\_\{\mathcal{S}}(h)$ towards further minimization. 

Most DA methods mainly focus on reducing the domain discrepancy $d\_\{\mathcal{H} \Delta \mathcal{H}}(\mathcal{S},\mathcal{T})$, such as utilizing techniques like adversarial learning, MMD, and CORAL.
In comparison to these methods, our **SDA** strategy ($\mathcal{L}\_\{sda}$) effectively eliminates the feature norm discrepancy in spherical space $\mathbb{S}\_\{r}^{d-1}$ and guide a more stable alignment of feature distributions. Furthermore, considering that graph data contains rich structure information that encodes complex relationships among nodes and edges, and existing graph transfer learning (GTL) methods usually adopt graph convolutional networks (GCNs)-based feature extractor to learn domain-invariant node features. However, recent studies [Y6-Y8] have pointed out that GCNs are insufficient in capturing the sophisticated structure information in graph, which seriously affects the transfer of domain-invariant knowledge and consequently limits the model’s generalization ability. To solve this problem, we thus propose the **STSA** strategy ($\mathcal{L}\_\{cls}$) to align the topological structures of the input space and the spherical space, in order to facilitate the GCNs-based feature extractors to capture more domain-invariant node features.
Consequently, the combination of **SDA** ($\mathcal{L}\_\{sda}$) and **STSA** ($\mathcal{L}\_\{stsa}$) strategies further promotes the minimization of the domain discrepancy $d\_\{\mathcal{H} \Delta \mathcal{H}}(\mathcal{S},\mathcal{T})$.

Notably, $\\mu^{\*\}$ is expected to be extremely small, and therefore it is often neglected by previous methods.
However, it is possible that $\\mu^{\*\}$ tends to be large when the cross-domain category distributions are not well aligned [Y9].
In this paper, we leverage the **RNC** strategy ($\mathcal{L}\_\{rnc}$) to guide both labeled nodes and unlabeled nodes toward achieving robust clustering, effectively promoting the fine-grained alignment of category distributions and  ensuring that $\\mu^{\*\}$ remains at a relatively small value.

In summary, our proposed method not only minimizes the expected error on source domain $\psi\_\{\mathcal{S}}(h)$ and the domain discrepancy $d\_\{\mathcal{H} \Delta \mathcal{H}}(\mathcal{S},\mathcal{T})$, but also keeps $\\mu^{\*\}$ at a small value, thereby ensuring a low upper bound.

Ref.[Y4] A theory of learning from different domains. Machine learning. 2010.\
Ref.[Y5] Analysis of representations for domain adaptation. NIPS 2006.\
Ref.[Y6] Coco: A coupled contrastive framework for unsupervised domain adaptive graph classification. ICML 2023.\
Ref.[Y7] Graph Kernel Neural Networks. TNNLS 2024.\
Ref.[Y8] Theoretically improving graph neural networks via anonymous walk graph kernels. WWW 2021.\
Ref.[Y9] Progressive feature alignment for unsupervised domain adaptation. CVPR 2019.

**2) To Reviewer 9hdx:** The necessity analysis Table A mentioned in A1 is displayed in the global response PDF file.

**3) To All Reviewers:** Based on the valuable suggestion of Reviewer aMJG, we will provide AC with the source code of our method in order to validate the authority of our work. You can get the anonymous link of our source code from the AC.

Meta-review: **Summary**

This paper presents TFGDA, which addresses the challenges in semi-supervised graph domain adaptation. The reviewers provided a generally positive assessment of the paper, noting its novelty, clear motivation, and thorough experimental validation. The proposed methods were recognized for their ability to effectively utilize graph structure information to improve transfer performance, which is a contribution to the field of graph transfer learning. The extensive experiments demonstrated the superiority of TFGDA over existing state-of-the-art methods.

**Decision**

The decision to accept is based on the novelty of leveraging the topological structures of graphs of graph structure information for GDA. 
In the final version, the authors should incorporate the additional experiments conducted during the rebuttal period, particularly those involving the AliCVR dataset, and clarify the distinctions between your approach and existing works. Additionally, ensure that the practical applications of your method, as well as a summary of the SDA strategy in an algorithm table, are clearly presented. These enhancements will further strengthen the paper's contribution and clarity.
Decision: Accept (poster)