Dual Prototype-Enhanced Contrastive Framework for Class-Imbalanced Graph Domain Adaptation
Authors: Xin Ma
Yifan Wang
Siyu Yi
Wei Ju
Junyu Luo
Yusheng Zhao
Xiao Luo
Jiancheng Lv
Venue: NeurIPS 2025 poster ()
Keywords: Graph Domain Adaption
Class-Imbalanced Learning
Primary area: general_machine_learning

Abstract: Graph transfer learning, especially in unsupervised domain adaptation, aims to transfer knowledge from a label-abundant source graph to an unlabeled target graph. However, most existing approaches overlook the common issue of label imbalance in the source domain, typically assuming a balanced label distribution that rarely holds in practice. Moreover, they face challenges arising from biased knowledge in the source graph and substantial domain distribution shifts. To remedy the above challenges, we propose a dual-branch prototype-enhanced contrastive framework for class-imbalanced graph domain adaptation in this paper. Specifically, we introduce a dual-branch graph encoder to capture both local and global information, generating class-specific prototypes from a distilled anchor set. Then, a prototype-enhanced contrastive learning framework is introduced. On the one hand, we encourage class alignment between the two branches based on constructed prototypes to alleviate the bias introduced by class imbalance. On the other hand, we infer the pseudo-labels for the target domain and align sample pairs across domains that share similar semantics to reduce domain discrepancies. Experimental results show that our ImGDA outperforms the state-of-the-art methods across multiple datasets and settings. The code is available at: https://github.com/maxin88scu/ImGDA.

Dual Prototype-Enhanced Contrastive Framework for Class-Imbalanced Graph Domain Adaptation
Xin Ma'; Yifan Wang", Siyu Yr, Wei Ju ft Junyu Luo", Yusheng Zhao Xiao Luo Jiancheng Lv
Colleeg of Computer Science, Sichuan University Schooo of Information Technology Management, University of International Business and Economics
'College Mathematics, Sichuan University *Peking University SUCLA
maxin88estu. edu. cn, juwei web.cu..euucc..
Abstract
Graph transfer learning, especially in unsupervised domain adaptation, aims transfer knowledge from label-abundant source graph to unlabeled target graph. However, most existing approaches overlook the common issue of label imbalance in the source domain, typically assuming a balanced label distribution that rarely holds in practice. Moreover, they face challenges arising from biased knowledge the source graph and substantial domain distribution shifts. To remedy the above challenges, we propose dual-branch prototype-enhancer enhanced contrastive framework for graph domain adaptation under class- clas--ibbllanced scenario. Specifically, we introduce dual-branch graph encoder to capture both local and global information, generating class-specific prototypes from distilled anchor set. Then, prototype- enhanced contrastive learning framework is introduced. On the one hand, we en- courage class alignment between the two branches based constructed prototypes to alleviate the bias introduced by class imbalance. On the other hand, we infer the pseudo-labels for the target domain and align sample pairs across domains that share similar semantics to reduce domain discrepancies. Experimental results show that our ImGDA outperforms the state-of-the-art methods across multiple datasets and settings. The code is available at: httpp:://gthhb..oom// httss///ttbbboom/mmmamns/u/////
Introduction
Graph serves as a versatile data structure to represent complex relationships [2 47 in number of
fields such social networks (2). molecular biology [13 55 and recommender systems [20] 44).
One fundamental task for graph-structured data is node classification, which endeavors to predict the category of each node within the graph and is widely applied in various applications, i.e.,
community detection (51), smart city (58] and knowledge graph [49]. Nevertheless, the effectiveness of this task heavily relies label information, which is time-consuming and costly [9]. Graph transfer learning [19 61 has emerged as an effective framework for tackling this problem by leveraging labeled information from source graph faciliiate learning
unlabeled target graph, significantly enhancing the model's ability to generalize on the target graph.
Actually, there several approaches that apply graph transfer lcarning for domain adaptation in the node classification task. Thanks to the powerful capabilities of graph neural networks (GNNs), unsupervised graph domain adaptation focuses reducing the distribution discrepancy between
'Equal Contributions Corresponding Author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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target and source graphs within the latent representation space induced by GNNs 23
53
56
eestance-based methods minimize divergence measure between their distributions to learn invariant representations, such maximum mean discrepancy [4 and graph subtree discrepancy 45 to align domains. Adversarial-bant methods incorporate a discriminator to distinguish between the two domains and produce invariant features to confound the discriminator 32).
Despite the promising performance of graph transfer learning, it often relies on the unrealistic assumption that the source domain graph exhibits a balanced label distribution. In practice, however, real-world graphs usually exhibit long-tailed structures, where most classes contain only a few labeled nodes (tail classes) and a small number of classes dominate with many labeled samples (head classes) [T],4] resulting in severe class imbalance. For example, in the NCI dataset, which consists of graphs of chemical compounds [40], only around 5% of compounds exhibit anti-cancer activity, with the overwhelming remainder are labeled as inactive. Therefore, this class-imbalanced issue inevitably leads to the knowlede extraction bias [59] in the source graph which in turn adversely affects the graph domain adaptation. This naturally spurs question: How can label semantics the larget graph be effectively inferred under domain shifts and severe source imbalance?
However, designing an effective framework for graph domain adaptation under class im- balance remains challenging due to several critical obstacles: O How to sufficiently al- leviate the class imbalance for extracting knowledge from the source graph? The latent space formed by imbalanced train- ing data is highly skewed, with minor sub- spaces being compressed by the dominant ones. This imbalance forces the model to focus primarily on the head class, which re- sults in insufficient learning of the tail class to extract unbiased knowledge. @ How to effectively reduce the domain discrepancy to make accurate predictions on the target graph? Since the target graph is entirely unlabeled, existing methods primarily focus entire domain alignment, overlooking class-level distributions. Therefore, as the result shown in Figure 1 existing graph domain adaptation methods struggle to transfer the correct semantic knowledge, leading to poor performance, particularly for tail classes.
o Class Class 3lass
Source
100
Aocussy Loss
7,077
30
Gruph
(00
80
72:85
24
Cross crutppy los
Aonurayy
Class-inbslaned
Dumain Adaptation
02207
Unlabeled Nodes
Target Gruph
4:36
Hene
Figure 1: Illustration of class-imbalanced graph do-
main adaptation. The unsupervised domain adaptation method GDA -SeecReg suffers from an imbalanced class of source graphs, particularly for the tail class.
Towards this end, in this paper, we propose a holistic method termed ImGDA, a dual-branch prototype- enhanced contrastive framework for Glas--Imallanced Graph Domain Adaption, which facilitates the transfer of class-imbalanced label information from the source graph to the unlabeled target graph. Specifically, we develop dual graph encoder that jointly captures local and global information to learn generalized node representations. Building on this, a prototype for each class is generated from distilled anchor set. Then, introduce prototype-aware contrastive learning framework that integrates cross-branch and cross-domain contrastive learning to enhance adaptation performance. To rebalance the feature space, the brass-branch prototype contrast encourages class alignment between the two branches. To further reduce domain discrepancy, we infer pseudo-labels of nodes from the target domain graph in a non-parametric manner and align sample pairs across domains that exhibit the same semantic meaning. Additionally, we treat temperature as a rebalancing parameter to mitigate class imbalance during training. Extensive experimental results validate the effectiveness of our proposed ImGDA for class-imbalanced graph domain adaptation.
2 Related Work
Unsupervised Domain Adaptation (UDA). UDA focuses on learning domain-invariant represen- tations between labeled source domain and an unlabeled target domain to transfer cross pross-domain information [24 26 43). Recently, graph UDA methods have included adversarial learning and reducing domain discrepancies based on certain metrics (e.g., MMD [7], subtree discrepancy [45]). Among adversarial methods, RNA (25 adversarially extracts domain-invariant subgraphs to address domain shift, while leveraging spectral seriation for robust alignment under label scarcity. In the metric-based category, GDASpecReg [33] leverages spectral smoothness and maximum frequency response regularizations to enhance GNN transferability across node and link transfer scenarios,
2

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while A2GNN [23] improves cross-domain transfer by adjusting GNN propagation layers using Lipschitz bounds. However, our ImGDA studies a novel yet practical scenario of imbalanced source data, and introduces a dual prototype-ane powootype-aware.ee contrastive framework to reduce source graph bias and align the semantic space between source and target for cross-domain knowledge transfer.
Learning on Graphs. It is well recognized that class imbalance on graphs can degrade classification performance. To address this problem, there are typically three approaches: (a) Modifying the loss function to prioritize underrepresented classes 3 29
36 50 (b) Post-hoc correc-
tion modify logits for the tail class TO I6]. (c) Re-aamiing techniques that augment or generate
tail class data [27 42 [77) For instance, GraphSHA [22 expands tail class decision boundaries by creating more challenging samples, while ImGCL (54] addresses class imbalance by employing bal- anced sampling and explicitly accounting for node centrality within contrastive learning paradigm. Extending these strategies to graph-level tasks, C*GNN [14] addresses paassimmbllance graph clas- sification by clustering majority classes and applying Mixup to learn hierarchical representations, while KDEX (28] transfers head-to-tail knowledge and trains diverse experts that are adaptively combined via self-supervised router. Additionally, Qin et al. [33 further propose comprehensive benchmark IGL-Bench for imbalanced graph learning, which evaluate the effectiveness, robustness, and efficiency of various algorithms within unified framework. However, distribution shifts in graphs further complicate caassimmallnnee learning on graphs. To address this, our proposed ImGDA introduces cross- booscbbanchh prototype contrast to reduce class imbalance bias and cross-domain prototype contrast to align domain discrepancies, effectively generating domain-invariinl representations.
3 Notations and Problem Definition
Source Domain Graph. Denote G = (V", "e, the source domain graph with the labeled node V and edge sets 8 The node feature matrix can be represented X E R|V"Ixd where entry a. E Rd is associated with a feature vector of node e with dimension d. We use the adjacency matrix A e R [=*"""" to describe the structure information of the graph, where A; = if an edge exists between U; and By. i.e., (U; U3) E E otherwise, A = 0. The degree matrix is denoted as D = diag( DI...., Dx) with a degree of each node D; = Σ)ー Aij. We denote the node label matrix of the source domain graph as Y RRV*IX,, where C' corresponds to the total classes.
Target Domain Graph. The target domain graph is denoted as g³ [V* "', x*) with unlabeled node set V and edge set Et. Similarly, the adjacency matrix A E ex"1 indicates the node connectivity information in the target domain graph. And the feature matrix can be represented as The attribute sets of the source and target domain graph could exhibit significant differences. Here, we construct unified attribute set across both domains align the dimensions.
Problem Definition. We consider G" as a fully labeled source graph and G as an unlabeled target graph. Each e-th class in G contains No nodes, ordered such that No 2 N22 2 ... 2 No. The source domain graph is assumed to be class-imbalanced, with the degree of imbalance quantified by the factor N//Ne. The objective of the task is to mitigate this class imbalance while transferring knowledge from the source graph to the target domain graph to achieve accurate node label prediction. Figure] provides schematic overview of our proposed framework in the following.
4 Methodology
4.1
Dual-Branch Embedding Generalization
Generalized node embeddings are crucial for effective graph domain adaptation. Therefore, we introduce a dual-branch graph encoder to fully capture both local and global structure information of the graph [3 62).
Local Consistency Encoder. To capture local consistency knowledge (i.e., neighboring samples are prone to share the same semantics), we directly utilize the Graph Convolutional Network (GCN) [18] as the encoder. Given the adjacency matrix A" and feature matrix X (* E (s,t)) of both source and target domain graphs, the output of the (-th layer is defined as:
Z (1) focal =D Ā. Zz 2,coal w=))),
(1-1)
(I)
3

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iaassiimbllacced
Source Graph
Local View
Clas- Prisispa
Fambeddings
Spall
Aarbur
Nogelives
Looal View
Crusc
Labcied
FORD
Cross
Posilives
Glohal View
Beanch
Anthors
Aatber
Negatives
Tokobal Vieu
GCN Encoder
Positives
Spuch
Target
Pronotrpes
Souree
Node- Anchar
Ameriio leacd Fuiio
Saniluit
pull
Posttives
Liccal View
Andhar Grandh:
Nade
Pseudda Labels
Cross
Embeddings
tunh rabels
Domsuin
Negalives
Target Gruph
Figure 2: A schematic overview of our proposed ImGDA framework.
where A IM.11 A is the adjacency matrix containing self-loop, D* is the corresponding degree matrix accordingly. W serves as the learnable filter in I-th layer and the initial feature matrix is local = Xx. Here a--) denotes the activation function. By stacking L graph convolutional layers, the extracted local consistency knowledge can be expressed as Z ((L)
(0)
"local
Global Consistency Encoder. Furthermore, we utilize a graph encoding strategy based on positive pointwise mutual information (PPMI) [6 62). We represent the state at current time t. s(t) Us with the probability transit from the node to any of its neighbors vy expressed as:
P.j p(s(t + 1) sy)s(t) 0²) /
(2)
We apply the random walk guided by P to generate collection of node paths on A". From these paths, we construct co-occurrence frequency matrix F* E ""'''>/>"" where F, records how often node U appears within predefined window around v; The PPMI between nodes is calculated as:
P Σ P P P. Σ., P P
P. P P
Σ,
P.P. Pi P
P P.. x Pj
P P
M2 max
).0),
(3)
where P the probability that v appears the v;'s context, P and P are the estimated proba- bility of node v; and context v respectively. Mī₃ captures the high-order topological relationship between nodes. Thus, nodes that frequently co-occur high frequency will have larger M,, values compared independent nodes. By treating the PPMI matrix M as new adjacency matrix, we can effectively extract global consistency knowledge as:
Z (1) gloobal D'DD'
! (').
x.global
4
where D = Mú and (-()) is shared learnable parameters used with the local consistency encoder. Similarly, the global structural consistency can be also extracted by stacking I. graph convolutional layers, namely, Zttobal (L)
"ggibball
Attention-Basee Consistency Fusion. To fuse the extracted local and global consistency knowledge,
we leverage the attention mechanism 388 and the attention coefficients can be obtained
Sij = (ol Zi.locat> W gloobaa)))
(5)
where W is the shared parameter matrix, 0(z,, LeakyRelu( W [z,||æ,]) denotes the attention function with parameter Wi. The fused consistency knowledge of both domains can be:
Z Sis Ziocal + - ( Zytobel.
(6)
4.2 Anchor-Based Prototype Construction
In contrast to directly using cross-entropy loss on class-imbalanced data, supervised contrastive learning (SCL.) tends to achieve better results imbalanced, the feature space remains dominated by head class. To avoid overemphasis head
17 60). However, when the dataset is highly

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classes, a straightforward approach is to generate a set of uniformly distributed prototypes for all classes, ensuring that each contributes approximately equally during optimization. The subsequent analysis provides theoretical guarantees that this strategy can effectively alleviate the class imbalance.
Theorem 4.1. Let Z {z1,..... zx). }. || = points with label Y (.1..... VN The supervised contrastive loss for class in batch B is bounded by:
be the extracted consistency knowledge of N node
(2:Y, B,,) log(( - + 1B.l exp(
Σ
2, 2,)), (7)
B.
Be
eB
kEB
JEB
repulaton term
attraction term
where Be represents the subset within containing all samples of class e. and Be denotes its complement set.
The lower bound of SCL above is derived from and comprises two terms. The attraction term encourages intra-class instances to converge toward their prototypes regardless of the class distribution, while the repulsion term enforces uniform inter-class separation and is dominated by head classes
Theorem 4.2. Let CB. (Cl C denotes the set of classes that appears in B. The supervised contrastive loss for class after class averaging is bounded by:
(2 (Z;Y,B,C B,c) (),)2 2
Σ k
log(1 + (1Csl - 1)
(8)
X exp(
Σ QEC ((e)
Σ KEB
2i Zk:
Σ
21 z1)),
CB
|Bgl
B.
JEBAM(
repudsion term
attraction term.
Therefore, head classes no longer dominate the repulsion term. To fully train all classes in B, we learn the prototype of each class for prototype-aware contrastive learning. The proofs of the theorem are in Appendix A
In practice, we distill the original graph sample the anchor consisting of the most important nodes. Then, we calculate the prototype based on the anchor set to facilitate effective learning. Specifically, for each class e in source domain graph, the top & nodes ranked by the degree are selected to get the sub-graph of anchor nodes Gä. We calculate the prototype as the mean vector of each class, namely, Mc.g Σ zg.g Vi c. E {local, global].
4.3 Prototype-Enhanceed Contrastive Learning
Given the prototype sets of two branches for both source and target domain graphs, we formalize a prototype-aware contrastive learning framework, which integrates cross-branch and cross-domain prototype contrastive learning to mitigate class imbalance and effective domain adaptation.
Brass-Branch Prototype Contrast. Considering that the model extracts both the local and global consistency knowledge from both complementary branches, we contrast the consistency knowledge of the source domain graph between the two branches in prototype manner to mitigate the imbalance effect M. Specifically, we calculate the prototype of both local and global consistency knowledge from two branches as foctt ) ) and global je=1 For each query node vū e V*, we use the prototype with the same class label as the positive sample and the cross-branch prototype contrastive loss can be defined as:
Leb = 4/2
P.
Eiglobal
Σ
Mef globai
log exp(2+ M+/T) + EnEp, exp(2+ (app((+./7))) ) (9)
exp(2+ 11+/7)
Liooaal M4 Myg foomt
where P.- denote the prototype set excluding gy 9 E [Jocal.global] in two branches respectively, and r the temperature parameter for contrastive learning.
Pross-Dommin Prototype Contrast. To alleviate the domain shift in the graph space, seek to align the consistent knowledge of nodes in the source domain graph with nodes in the target domain graph that share the same semantics. To achieve this, infer pseudo-labels of nodes from the target
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domain graph in a non- between cross-domain pairs [52].
non--onnnaaen parametric manner and employ cross dross-domain prototype contrastive learning
The pseudo-label for node vj. in the target domain graph can be:
exp(2} 2(/r)
Σ
Σ
Eeeg exp(2) 2 21/T)
Y
(10)
(o) (e)e
where Y corresponds to the one-hot label of v.- The pseudo-label can be derived as 8/ arg max(;)). ). Then, for each query node vf E V*, we pull semantically similar prototypes close compared to those with different semantics:
IV
exp(x) Haj) Mgj + MEP; (xp((2--1))
Led
log
(11)
exp(22)
where Pj denotes the prototype set of fused consistency knowledge excluding Ma; in the source domain graph. Note that the cross-domain contrastive learning process can be interpreted as an Expectation Maximization (EM) scheme, where the aligned semantics between the source and target domain nodes are inferred in the E-step, and the log- ligelikd of the nodes in the target domain graph is maximized in the M-step. The proof can be seen in Appendix B
Adaptive Temperature Formulation. The temperature parameter T in contrastive learning controls the penalty on hard negative samples [41]. However, for tail classes, where node samples are fewer, increasing т has a negligible impact but reduces their gradients, worsening class imbalance. We propose an adaptive mechanism in which the temperature for each class is adjusted according to the number of samples within that class:
To = 7 (1 7) Ne/Nc,
(12)
where To is the temperature of class c, and here denotes the minimum value of temperature.
4.4 Overall Optimization
To further reduce the impact of class imbalance in the source domain graph, we employ logit compensation strategy to correct the consistency knowledge [26 29 59], summarized as follows:
Lie -> exp(1x + dc)
(13)
2o expl (z,) + 6w)
where (-)) is the classification function that outputs the logit for each label, x represents the contribution weight for class y. and & denotes the compensation value for class Here, we have A = and d- = log Ne, following the previous work (29]. Finally, the objective can be:
== Les + Led + Lic-
(14)
Typically, the dynamic weight hyperparameters can be used to balance these losses during training, but we find in practice that simple addition already yields effective results.
Experiment
5.1 Experimental Settings
Benehmark Datasets. This study conducts experiments on three publicly accessible network datasets from the ArnetMiner [37]: ACMv9 (A), Citationv (C), and DBLPv7 (D). These datasets are derived from different sources and cover distinct time periods: ACM (post-2010), Microsoft Academic Graph (pre-2008), and DBLP (2004-2008) resulting diverse domain characteristies. All datasets model academic papers as nodes and construct undirected edges to represent citation relationships. To realistically simulate real-world class imbalance scenarios, we employ the operation proposed by 31 for preprocessing source domain data. This involves iteratively adjusting the number of nodes within classes in the source domain to achieve specified imbalance factors (IF). The imbalance factor is defined as p N₁ NNN,, where class populations follow N; 2 N₂ 2 ... 2 Nc. with N,, denoting the node count for class e in the source graph. The experiments on more metries of imbalanced distribution can be found in Appendix E

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Table I: Results of methods across varying imbalance factors (p). Here A=C represents using A as the source graph and C as the target graph. Scores are reported as miero-average (%) and -narro-vverage (%) The top- performnngn method is shown in bold with the runner-up is underlined.
Medoods
Micro
ArsC
Marmo
Micro
AnD
Macro
Micro
Cr
Macro
Micro
Cre
Miao
DeWA
Mazro
Mizo
DesC
Macro
60.00..1
61 23
38.25
63.39
5547
61.68
CKN
50
20
62.28
55.4
4244
40 M0.5
56.25
4338as0
51.80.1.
St. 5t.17
4434
12 32
Sullless
530
48.22
500
45 48.12
St. St.10
42:38
54.02
58.3
55.10
6087
52.9
GAT
43.0
41.07
52.29
28 28.8
45.18am
10
62.12
55.08
54.30..
54.
50.89..
00.00;: xs
46:27am
50.38
4.02
10
40.7
StAlasms
45.54amm
52.7
47.07
3637a
CDV SpecRes
20
(050gs es
40.8
16
35.82.u
30.20
38
51.4
35.1511
43.86mm
41.55g
2625
31.89232
4653mm
45.83g
41.70amm
A2GNN
50
35.05
32
45.38a1.
25.3
17.0
15.10.00
15.1aam
46
24
56.1asst
5033aas
42
31
4131aam
31.27
14
41.00am
131
St Mta
GaptENS
(2.74
15.5
10
72
22. 63
61.52
63.40a1
16.20
55.36
5666
TAM
20
WiW2z:00 as
000121 m
30
1700g
51.1221
25
10
20,43 23.20
61 MLaa
56 56.09...
66.0
56.25
56.9 6305
63.36
54
21.11
00.0
GugtSHA
50
30
11
6097g3 99
33.99 4
M.
68
47.37as
34.07
50.5
0277aam
14.72 39
5000
57.5
2631.1
50.3,2
IsGDA (Oun)
50
73
73.92.00
07.42.121
0614.L
41.37
66387
65.45:1
68.48114
70557.315
63.42..1
66.32
6867
63.45
21.9
71,99
66.07
08.38:100
62.722111
Compared Baselines. For our study on graph domain adaptation under class imbalanced scenario, we employ three GNNs baselines: GCN [18), GAT [39], and GIN [48). Meanwhile, we incorporate two baselines that are specifically developed for domain adaptation: GDA-SpecReg [53] and A2GNN [23].
In addition, include three methods recognized for their effectiveness in handling imbalanced graph
learning: GraphENS B1), TAM (35). and GraphSHA [22).
Implementation Details. We conduct extensive experiments by alternately setting one domain as the source and the other two as targets. The source imbalance factor p E { {10, 20, 50) covers mild to severe imbalance levels. For our ImGDA, we adopt GCN 18 as the backbone with 512-dimensional feature space. The hyperparameters are set as: 7 = 0.5, K = 200, and a = 3 1. For fair comparison, all baselines employ the same GNN encoder and are fine-tuned for optimal performance. Each method is evaluated on the target domain graph w.r.t. micro-F1 and macro-FI scores, and the final results is averaged over five runs.
5.2 Performance Comparison
Table 1 presents our results for م = 10, 20, 50J. while additional results for 0 {5. 100} are provided in Appendix D.1 From the table, our ImGDA consistently achieves the best performance. And the comparison shows that our approach sig- nificantly outperforms all other methods in class-imbalanced domain adaptation tasks. Additionally, when using DBLP dataset as the source domain with fewer samples, baseline methods generally perform worse
ASC
A2D
21 Irshabance Sutce
Epocls
(a) Different P on A2C
(b) Training loss (p 50)
Figure 3: Imppac of p and convergence analysis.
than with other datasets. However, our ImGDA mitigates this issue by effectively capturing intrin- sic semantics via a prototype-enbaned contrastive framework. Furthermore, Figure 3a shows the performance trend across different p values in the A=C experiment, where p ranges from 5 to 100. When is small (e.g.. 5), performance gaps between methods are minor. As p increases, all methods degrade due to rising imbalance. However, our ImGDA shows the smallest decline, maintaining stable results even under severe imbalance. Notably. as p increases, domain adaptation-speciin methods (GDA-SpecReg, A2GNN) drop sharply, while imbalance-handlnng methods (GraphENS, TAM, GraphSHA) outperform others. This indicates that addressing source-domain imbalance has a greater impact than mitigating domain shifts. Figure 3b also shows the rapid convergence of our method within few epochs.
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5.3 Ablation study
To evaluate the contribution of each compo- nent in our method, we conduct ablation study. We remove three loss terms (w/ Lior w/o Leb, w/o Lea). the global branch (w/o global, i.e., two branches are local branches), the local branch (w/o local, i.e., two branches are global branches), and the dynamic tem- perature (w/o 7), and assess the performance under = 50. The results for the Micro score shown in Figure 4 while the results for the
160
El Widry
100
Menuhh
Figure 4: Results of ablation study all data pairs
(p = 50, Micro score (%) with standard deviation).
We can clearly see that excluding any component causes the performance degradation, especially the removal of Lob (cross-branch prototype contrastive loss). This emphasizes the importance of addressing data imbalance in the source domain and enforcing consistency, Also, eliminating Lid (cross-domain prototype contrastive loss) leads to some decline, but the impact is less severe, supporting the argument that mitigating data imbalance is more crucial than domain adaptation. Additionally, removing the Lie, global and local branches or switching to fixed temperature reduces performance, particularly when DBLP is the source domain. The macro score drops after fixing the temperature emphasizes the importance of dynamic temperature in contrastive learning, where adjusting it based on class distribution alleviates data imbalance. These results validate the necessity and effectiveness of each component within our framework.
Macro score can be found in Appendix [D.2]
5.4
Sensitivity Study
Effect of k. We here study the impact of the number of anchor nodes k where k
C2A
A2D
-50
1100-200
C2A
A2D
+0.50
-0.25
takes values from {50, 100, 200, 300, 400, 500). as shown in Figure Sa Both small and large values of & degrade performance, with the impact more pronounced for small k. A small & samples too few nodes, ig- noring useful information and hindering learning. On the other hand, for large k; while the number of head class nodes sam- pled remains unaffected, the number of tail class nodes sampled decreases due to the limited number of such nodes, leading to a data imbalance phenomenon similar to that in the source domain, which also drops performance. Hence, selecting an appropriate number of anchor nodes k is critical for effective prototype learning.
-20 500
-0.75
+100
CID
A2C
D2A
D2C
DZA
D2C
(a) le
(b) Y
Figure 5: Impact of and 7 (p 50). The distance between the points on each line and the center point
represents the magnitude of the Micro score (%).
Effect of 7. We explore the impact of dynamic temperature 7 in Eq. 122. where y represents the minimum temperature associated with the tail class. It can be observed that as decreases, the tail temperature lowers and the gradients increase, making 7 weight parameter related the gradients. We experiment with in {0.25, 0.50, 0.75, 1.00], as shown in Figure (5b] Compared to the default y = 0.5, both high and low temperatures degrade performance, with lower temperatures slightly better. This highlights that smaller temperatures help alleviate data imbalance, but overly small values disproportionately increase the gradient of tail class, harming the training of other classes.
5.5 Capability to Mitigate the Imbalance Issue
We evaluate our ImGDA's 's capability to handle data imbalance by examining cross-entropy loss and accuracy across tail and head classes under p= 20. To enhance comparability, we normalize these metrics for each method and visualize the results in Figure The results show that for head classes, all three methods achieve similar accuracy and cross-entropy loss ratios, indicating comparable effectiveness when abundant training data is available. However, for tail classes, the other two methods degrade significantly, revealing difficulty in handling imbalance. It can be observed that GraphENS performs better than GDA-SpecReg. likely due its design advantages in dealing with imbalanced data. In comparison, our ImGDA consistently performs well in both the head and tail classes, underscoring its ability to mitigate class imbalance while ensuring robust generalization.
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020
030
D20
020
C20
C29
A28
A70
Grpatii
Coplli
Coplltt
(a) Accuracy (Head)
(b) Accuracy (Tail)
(c) CE Loss (Head)
(d) CE Loss (Tail)
Figure 6: Comparison of head and tail class performance terms of accuracy and cross-entropy (CE) loss. The horizontal axis here indicates the relative contribution of each compared method, normalized across all the three methods.
(a) GDe-SpeeReg
(b) ImGDA (Ours)
Figure 1-SNE visualization of node embeddings from the baseline GDA-SpecReg and our proposed ImGDA. In each panel we sequentially present the balanced source domain graph, the imbalanced source domain graph, and the target domain graph, respectively.
5.6 Visualization
To further evaluate our ImGDA from qualitative perspective, we compare its t-SNE visualizations with GDA-SpecReg. With p=20, node features learned by the encoder are projected into a 2D space to visualize three cases: a balanced source domain graph, an imbalanced source domain graph, and target domain graph (Figure (). As for the baseline, we can find that class boundaries appear blurred in both source domains, and the target domain shows clear shift, indicating challenges in transferring domain-invariant features, In contrast, our ImGDA maintains well-separated class boundaries even though the source domain suffers from severe imbalance, and its target domain closely resembles that of the balanced source domain. This indicates that ImGDA effectively learns class structures and remains robust in the presence of imbalanced training data.
5.7 Different Sampling Strategies
To examine the impact of different anchor node sampling strategies on prototype com- putation, we compare three strategies: sam- pling based on node degree (Deg.), sam- pling based on inverse degree probability (Inv.), and random sampling (Rand.), We visualize the results for p 50 in Figure 7 with additional results available the Appendix D.4 From the figure, it can be observed that random sampling performs worse compared to the graph-structur based sampling strategies, while the degree-based strategy employed by our method achieves the best performance. Additionally, our experiments reveal that inverse degree sampling significantly reduces training speed, further demonstrating the effectiveness of our selected sampling strategy.
Deg
Inv.
Rand
Deg.
Inv
Rand.
75.0
Mocech
75.0
50.0
30.0
0.0
A3C A3D
C2A
C10
D7A
000
0.0
A30
A30
C3A
CTD
62A
100
Figure 7: Results of sampling strategies (p 50).
6 Conclusion
This paper tackles the challenge of class- inbbllnned graphs by introducing a dual prototype-enhanced contrastive framework for graph domain adaptation. We use dual graph encoder to capture local and global information and generate class-specifi prototypes from a distilled anchor set. A prototype- aware contrastive learning module is introduced, combining cross-branch and cross-domain contrast. It mitigates source-domain imbalance via class alignment and reduces domain discrepancy by generating pseudo-labels to align semantically similar cross-domain pairs. Extensive experiments demonstrate the effectiveness of ImGDA compared state-of-the-at methods.

---

Acknowledgements
Jiancheng Lv and Xin Ma are supported in part by the National Major Scientific Instruments and Equipments Development Project of National Natural Science Foundation of China under Grant 62427820, the Fundamental Research Funds for the Central Universities under Grant 10822041 12364. Wei Ju is supported by the National Natural Science Foundation of China under Grant 62306014, the Postdoctoral Fellowship Program (Grade A) of CPSF under Grant BX20250376, the Sichuan Science and Technology Program under Grant 2025ZNSESC1506, the Fundamental Research Funds for the Central Universities under Grant 1082204 12K97, and the Sichuan University Interdisciplinary Innovation Fund 10822041 122774 Siyu Yi is supported by the National Natural Science Foundation of China under Grant 12501 344, the Postdoctoral Fellowship Program (Grade A) of CPSF under Grant BX20240239, the China Postdoctoral Science Foundation under Grant No. 2024M762201, and the Sichuan Science and Technology Program under Grant 20252NSFSC0808.
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14

---

A Proof of Theorem 4.2
The supervised contrastive loss for a class c a batch can be re-written as the following form 660
Lscr (,;
Σ SEB
log
exp 2 xp)
B
exp(z; 2x))
PEBAA)
B
JEYB
REB;
Σ
exp (zi 21)
B
Σ
log
jECB
KEBj
exp( 2p) 1/18:1-1
(15)
PEBA)()
Σ
exp(z; 2k)
B
Σ BEB
log
JECB
KEB
exp
21 =p)
PEB.
We divide the sum in the numerator into the positive and negative terms and since the exponential function is convex, we apply Jensen's 's inequality to get the lower bound of two terms as follows:
Σ jeCs
exp(z: 2x)
Σ
exp(z: 2x)+
exp(z; #*),
Bj
B.
B
kEB,
KCB. MD
JECB
k
positive term
negativc terms
Σ
exp(z =4) exp
26 2c221)
[B&l
[B.l
(C)
KcB. (+))
Σ JECB 3PC
exp(z,
Σ
exp
Zi Zk
2(1E) - exp
2
24
B
CB
B
KEB
JECg 3PC
REB
SECB s
REB
(16)
And the lower bound of the numerator can be written as:
Σ
Σ
exp(z;
#x) exp
Σ
#/) (ICsl - 1) exp [cal-1
Σ
Σ
B
|551-1
[8,]
JECs
REB
kEB.
KEB;
(17)
Thus, the lower bound supervised contrastive loss can written as:
Escr (2, Eies, log 1 + ((Cs) exp
22
Σ
# 22,
C6
B
B.
OEC
keB,
repulsion
term
(18)
Thus, the proof of Theorem 4.2 is complete.
B Proof of Expectation-Maximization Perspective
In unsupervised graph domain adaptation, aim learn the graph encoder with parameter 0 to maximize the log-likelihood of nodes in target graph G with source graphs Go, written as:
V Σ log Σ
arg max
(19)
My E
m1=1
We introduce surrogate function Q(of) EE Q(v:) = 1) to estimate the lower-bound via Jensen's
inequality 21 52
D Σ log Σ oEEV
p(o 09:
p(ug of:0)
pluf, 0f:0)= Σ log
Q(
Σ Σ
Q(1)) log
Q(1))
Q(v²)
1=1
i=1
EEV 1=1
(20)
15

---

Note that the equality holds when Q(vz)/p(u( of:0) 0) is constant. Thus, we have Q(x²) p(uf; eg. 0).
Since - En En= Q(uf) log ((²²) does not influence the optimization process, we objective can be re-written as:
y p(uf:o), of 0) log plof, vf:
Led 2
E Σ OE
(21)
Here optimize the objective via an EM algorithm. In the E-step, infer the posterior probability pluf; uf. ()) TOT [vy). vf") where indicator T(,), of) = 1 if they has the same label and [TT()
Σ Me,. vf). In the M-step, aim to optimize the lower-bound, which can be defined as:
V
exp(z) ma;)) i(o) vf) log exp(2) MØ;)+ + EnEp; exp(z) wi) (
0 = arg max
Σ
E
(22)
which is equivalent to our cross-domain contrastive learning objective in Eq.
C Complexity Analysis
For the time complexity, let No and |8|| represent the number of nodes and edges in the source domain graph, and | and | represent the number of nodes and edges in the target domain graph. Assuming L-layer GCN encoder with feature dimension of d, the computational complexity of feature encoding is O L E + LN*d²) for the source domain, and O(L)E|d + LN*d²) for the target domain. When E > n. this simplifies to (( and ((E)) d). respectively. For anchor node sampling, we sort nodes based on their degree and select m nodes per class. Since m & N the complexity is (N log N*) For prototype computation, the Mean prototype computation per class takes (mnd). the Fross-branch prototype contrastive loss takes (md). the Cross-domain prototype contrastive loss takes (NN)) d) and the Supervised loss computation in the source domain takes O (N*d), Thus, the total time complexity is (O(E* ( [E*|d+ | No log N + which can be approximated as: O(max [E*| |E"), No log N NNd)..
N*d).
As for the space complexity: storing node features incurs a complexity of O(N)); storing the sparse adjacency matrix requires O(EE):: the PPMI matrix has a space complexity of O(N2); the model parameters require ((²)): and storing the prototypes and pseudo-labels requires (CC)) and ((NC) respectively, and C denotes the number of classes. In summary, the main space cost of our method arises from the PPMI matrix, which is ((N3).
D Supplement of Experiments
D.1 Performance Experiment
To provide comprehensive evaluation of our ImGDA class-imbalanced domain adaptation tasks, we consider additional scenarios beyond the main experiments presented in the body of the paper. Specifically, presented in Table [ in the Appendix. At p = 5, the source graph is relatively less imbalanced, and the performance of all methods similar, with generally good results. As p increases, the advantages of our ImGDA become more pronounced. Even when 100, where the data is highly imbalanced, our ImGDA still maintains stable performance and significantly outperforms other competitive baselines. This highlights the robustness and effectiveness of our proposed ImGDA in addressing class- inballandd domain adaptation tasks.
explore
extreme settings with p values in (5, 100). All results
D.2 Ablation Study
To better validate which parts of our method ImGDA are effective and how much they contribute to the improvement model performance, we conduct ablation experiments based on the full experiments. Specifically, we evaluate the effects of the three loss terms (Lie, Leb, Loa), the two branches (local and global), and the dynamic temperature (7). Figure | and Table i the Appendix show the macro score performance from the ablation study, which follows a trend similar to that of the micro scores.
16

---

Table 1: The complete experiment results of approaches on glas--imbalanced domain adaptation with P rangee from 5 to 100. The best are highlighted in bold and the second besond-best are underlined.
Marhodk
Miano
Mazro
Micro
AnD
Marro
Micro
Manoo
Mizro
Macro
Miero
Maamo
Micro
DesC
Macro
69.51
46.33ua33 2222
60.20.0.0
64.7
64.65 1s
58 ua
63.56...a
60.04.1.7
60.00 a0.00
66.88
66 18.181
53.30a
m2.00amm
58 23.3
53,07ase
43.35
53
42.28a30e
100
45.54
34
51.44
3695
41.5420m7
26.75
49 49.
21.25
22 22
38.40aam
25
Ma
17
06.48 uo77
58.37.1344
1335
11.4
11
16.8
42.20
53.31
62.07
55.6
41.02aas4
40 40.76as::
12.59.a.1
38.89
45.36am
54
100
38.52
25.13
45.19 25.19
29.49
38.35
22 22
26.59 45
55
g0
31.91gm
1855
63.36
58.75
56
1000
50.88
48337.000
90 10.34.5m
55 13
6642
47
11.00
51477
448)
50
54,39
64.2
41.50.200
41.261027
29 21
31.57
43.38
12.4
41.59.2.0
30 31.21111
100
45
45.82
27.42
50.15
35.91
22.75
25.90_..2
37.33
24.27am
4000
26.9
4:37
76.1.
AZGNN
20
15
54.72.233
18
46 1
53 39
15.4
11.44
41.00am
St
50
17 m3
17
50N
50
5100
14.20
1319
100
25.3720o1
12457.444
12:57
34
12.35
31.58
22
46.66
46
25.98
29.79
10.4
28.31.o1
1377
SiA-SppeRaa
20
4
51:37a1
36.44
50.70
5300
35.82
4087
51.641.. 38.30.4
57.41as
35.15
31.89
47:0
44.53.0s
4501.2
312
50
5509 344
43:44:15
29.36.0.
13
$2.69.250
25,46 co0
41.5110
28.38
100
45
46
17.08amn
41.0
50.8..
14.00.mm
33.0
75:01
15.26
09.1
66.6
72.0
GiaySHA
10
31.0
61
70433
61.0
$6.0
06.00
Mill
66.34
56.99 53.05
53.05
03.3
64.00
21 woo
0003
S6.13
4473 144
47.25 1ay
12.0
71:
01
0665
6M
GophENS
20
10
65, 65.12.11.0
70.40
64.57
$7.59
15 1k
53.0
63.55mm
60 (0
$1.961
65 65.5
67
63
63 63
29.76
610 65
54,09
45
50.40
72.17
68,20.153
64.37
63.21
67.28
71.83
68.92
63.99
63.39
63.19 a3.1
71.45une
10
TAM
10
68 8l1e
72 30
67.27
0000
$2.12.19
41.52.1
36
63 k3
6764g3
65.30
59.12
55.36a1
66.65.00
01:25
n0. 10.16
11.
1164
17.88
78.35
25.12
72/08
67.78.0.5
07 15
67 23
6166
48.13
74 24.4...1
InGDA ((am)
10
77.30
77.83 L10
73.98 1.1
21.34.11
46.2...0
65.06...2
61.7 c.
68.2
73,6
09A1
664
1392...
16.6
63.45 m0.
7472 ncs
71.99 11
7286
61.37.1
49.10.0
20
08.0
60.22:1
62.8
45
58.79.10
Generally, removing any part of the method leads to a certain degree of performance degradation. However, removing Les leads to significant drops, which clearly demonstrates the importance of utilizing source domain information and mitigating source domain data imbalance.
volo Cxp
to Ced
GDA
volo Cir
Cee
IMGDA
100.0
wio Cup
wolo global w/w
100.0
w/o C.p
wol global
wwo
80.0
Macro (%6)
80.0
Macro
40.0
40.0
20.0
20.0
0.0
A2C
A2D
C2A
0.0
C2D
DZA
DZC
Figure 1: The results of ablation study (p- 50, Macro score (%) with standard deviation).
Table 2: The complete results of ablation study (p = 50).
Mathoals
Mikro
A-C Mucro
Misto
D
Masro
Micro
C-eAA
Mazro
Mixso
C=D
Musto
Micro
D+AA
Macro
Micro
DesC
Macro
wio C..
66:2842.7
62. 12.17a
64.10-31
38
52.50
5800
66 66.35
60 60.
38
S8.2545 46.27am
wio C..
$2.63
43,54pm
30.3
40 40.36.11
56.32a
48.25
58.0
54.56
50.04am
l00k
33.43..
26.54.m
wio Eut
70.112m
63.57
65.4.122
29
13.00
64.50
67.11am
63.561124
49.75.13.
41.17 25
52.222x0
44.7512.0
wio glood
11.3
63.34
67.6
60
10:30100
61,612m
64.44..
26.3011.20
50.2611.57
45.27.24
31.61110
43.0011a7
who
67.4
59
65
60.90ges
14
63,0
46.09...
19
4884
who
72,07
65.14
67.59
60
65.15..e
63.34
68.3
63.85.x00
46.00.mm
4736.2m
57.774m
ImK0A
23,5,,mm
6742...
0914..4
61.77110
06.771m
08.552241
06.32..n
00.67.cmm
06.77am
62.77am
17

---

C2A
A2D
55
-300
A2D
-0,25
100-
00.50
200 500
-0.5
1.00
C2D
A2C
C2D
A2C
D2A
D2C
122
D2C
(a)
(b) Y
Figure 2: Visualization of the sensitivity analysis of (a) y and (b) k. (Macro score (%))
D.3 Sensitivity Study
In this section, we further present the sensitivity analysis results of two key hyperparameters con- cerning the Macro score, along with the complete numerical results for both metrics, to provide clearer understanding of their impact on model performance. The experiments are conducted under the setting of p 50.
Table 3: The impact of different values of k on performance.
A-C
C-D
D
Mixro
Mucco
Macro
Macro
Micro
Macro
12.1lar4
61.40,
26.38
54.44am
64.42_..0
58 38.83
70.45
60.99
38,
44.34..
4a.29
68.36.1
68.99...
57.77
66.10...0
70.79
63.25
48.55
20.53
41.50
25
67.421.
69:14...
61.771330
65.45-244
66.32.1.0
60.67.0.
58,963.2
66.07.100
62.77
300
22
65.63ax
65.35
$4.08.00
66.72_1m
62.4
64.62.
45.24
52,84_:
45
65.5
$7.75.30
62.33
70.31
52,56 17.
22 22.06aa
65.35
68.64,1.0
69.92...s
52.32,x.0
60.50..10
Effect of k. To explore the impact of different values of k (the number of anchor nodes) for ImGDA, we conduct a sensitivity analysis of k. The results are shown in Table 3 and Figure 2a provides visual analysis of the macro scores. It can be observed that both excessively small and large values of k affect the model's performance. As discussed in Section 5.4 the body of the paper, too-small value of k results in insufficient utilization of node information from the source domain, limiting the exploration of graph structural semantics. On the other hand, an excessively large k may introduce data imbalance, leading to negative feedback that ultimately affects model performance.
Effect of y. As discussed Section i.4]jn the body of the paper, the hyperparameter y can be viewed weight parameter associated with the gradient of the tail class. To evaluate the impact of different values of > on model performance, we conduct a sensitivity analysis of y. The results are shown in Table 4 in the Appendix, and Figure 2h provides visual analysis of the macro scores. Both excessively small and large values of lead to decline model performance, indicating that the gradient the tail class should maintain moderate weight during model training (i.e., too small a value affects the classification performance of other classes, while too large a value negatively impacts the classification of the tail class itself).
D.4 Analysis of Different Sampling Strategies
Different sampling strategies affect the quality of the sampled anchor nodes. investigate the impact of different sampling strategies on model performance, we conduct comparative analysis of three different sampling strategies. Table the Appendix presents the experiment results with {20, 50, 100). It can be observed that graph-structure-bee Inv.) significantly outperform random sampling (Rand.), highlighting the importance of structural information in learning meaningful node representations. Furthermore, compared to the inverse dasree-based strategy, our degree-based sampling approach achieves better performance, possibly because node's is local subgraph structure plays crucial role in its representation within the entire graph. While the inverse degree-based strategy balances sampling bias, inevitably leads to greater structural semantic loss by disregarding key graph information. Additionally, experiments show
sampling strategies (Deg, and
18

---

Table The impact of different values of on performance.
A-C
A-D
C-A
C-D
Day
D-CC
Micro
Macro
Micro
Mazro
Miem
Macro
Micro
Macro
Micro
Moem
Micm
Macro
0.25
66 68,70.1
68.59
60
61 61.46.34
68.38ss
38.34
48.40
43 43.98a2:1
55.64
50,26_2.0
0.50
73.53
67442
69.4421
61.222
66 66
65
70.575.09
66 32.
60.67
58 98.0111
66.0 86.02.00
62.77
0.75
72.06:3.40
63.50
67.91331
58.791222
64.001.
19.17.a
67.60.1.5
61.21
48.05
4100
1012211
99.40
1.00
63.76 76.
64.761337
55.9713.5
62.4
56 56.74_30
67 67.18
Sa. 58.461225
46.55,235
18.921211
49.28,330
40.73
that the inverse degree-based sampling strategy results in significantly longer training times. These factors collectively justify our choice of the degree-basee based sampling strategy.
Table 5: The results of different sampling strategies.
Samping Strangs p-
A-cC
Assi
CasA
Cin
D
DoCC
Micro
Micro
Macro
Macro
Deg.
71:25auaa
66.39 61.1agas
31,9
Ins
77,57
74.15g1
71,27
65.24
65 90
00.0
61 61.28
64.47
64.25.
71 71.00gm
69.18
Rand
72
71.68ge37
Mil1gg
to 15
61.51am7
0887g0
62 13g
6360g1
71.70g
65.93
sampling method p-
A-rC
A+D
CocA
D
DwC
Marm
Deg.
65.45
70.57
02.3
In
72 72.40.1-
66
68 19
56.99
56
63.8
69 60.0
62 2aaa
$7.09
$4.8
59
$1.38
Rand
73.55
06 87
68002
57.38
66
36.39.3
6100
70.3
63 23
5666
534122.0
60.68
55.12.377
satpling metiod
A-CC
ADD
C+rA Maroo
C-D
D Marm
DwC
y 100
Micm
Mino
Dep.
56.70
$2.8
In
58
46
$4.621
47 47.59
58.884m
48 302322
Rand
09.25
09.25
$7.04...5
67.541300
36.54
59.32 19.32
48.51120
64.2...
$1.931900
$4.88
47.61114
57,301311
46.23
D.5 Analysis of Different GNN Encoders
To explore the effect of different encoders in method, replace our encoder from GCN to GraphSAGE [8) a widely used classic GNN encoder, and conduct experiments under p = 50. The results shown in Table 6 It can be observed that in method, GCN outperforms GraphSAGE, possibly because GraphSAGE samples only a subset of a target node' neighbors, which limits the exploration of local graph structures and leads to performance drop. This highlights the importance of selecting an appropriate backbone encoder.
Table The results of different GNN encoders.
Encoder
Micro
A-C
Macro
Mixro
A-D
Macro
Micro
C=A
Macm
Micro
C-D
Mocro
Micm
Dey
Mazro
Micro
DeCC
Macro
73.53
67.42.
61.27
66.8
65.45
70.57 m
60.77
58.9611 to
02.77
GraphSAGE
36.77.211 m2
60.1311::
5003
53.06.14 1.4
30.00.00 Lea
30
48.221145
44.50.201
52.59 1..5
46.34.1.
Table 7: Detailed values of Standard Deviation, Mean/Median Ratio, Gini Coefficient with different imbalance factors of different Datasets.
Methods
IF(p)
628.79
1.17
0.31
ACMv9
10
714.46
1.36
0.41
762.39
50
798.08
2.25
0.57
100
814.47
2.92
0.62
525.18
1.17
0.31
Citationy
596.31
1.36
0141
20
636.40
1.66
0.39
666.23
100
679.81
2.92
0.62
420.95
1.17
0.31
DBLPv7
471.26
0.41
502.90
1.66
0.49
50
526.27
2.25
0.57
537.29
19

---

E Additional Metrics of Imbalanced Distributions
In our experiments, we employ the imbalance factor (p) to quantity the degree of class imbalance in the dataset, defined as:
max (Ni, N2. NNc// min (Ni, N2, ,Nch
(23)
where N; denotes the number of nodes belonging to class in the source graph. To provide more comprehensive assessment of imbalance across different datasets, we further introduce several additional metrics to evaluate the distributional skewness of the data.
Standard Deviation (o)): It is widely used in probability and statistics measure statistical disper- sion, and in some cases it can reflect sampling uncertainty, which is defined as:
Σ n4 m,)
(24)
where C' represents the number of classes, n, represents the instance number of class i, and ñū represents the average number of instances.
Mean/Median Ratio (c): The median a fundamental statistical measure widely applied in fields such economics, sociology, and medicine. Unlike the mean, is less sensitive extreme values and thus provides more robust representation of the data distribution. Consequently, the mean-to-median ratio serves as indicator of data skewness, defined
mean N1, No. Ne)
(25)
median N1, N2. Nc)
Gini Coefficient (o): It was originally introduced by Italian economist Gini [5], measures distribu- tional equality based on the Lorenz curve. Commonly used to quantify income or wealth inequality, it can similarly be applied as metric of imbalanced distribution, as class imbalance paralleis inequality across categories.
And we provide the corresponding Standard Deviation, Mean/Median Ratio, and Gini Coefficient values for each dataset under different imbalance factors in Table 7
F
Broader Impact and Limitations
Our method addresses class imbalance in graph domain adaptation and has the potential to benefit various applications such scientific discovery, recommender systems, and bioinformaties by improving the representation of underrepresented classes. However, it also has limitations: the performance depends the quality of the selected anchor set, the dual-branch design introduces additional computational overhead, and the pseudo-labeling process may suffer from noise under large domain shifts. Moreover, the framework requires the same label space across source and target domains, which could not be applied to open-set scenarios.
20

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Reviews:
[{"review_id": "c7xdfpE5x9", "reviewer": "Reviewer_MqCZ", "summary": "This paper addresses the problem of graph unsupervised domain adaptation and aims to address the problem of class imbalance, which has been overlooked by prior methods. To overcome this, the authors propose the Dual Prototype-Enhanced Contrastive Framework (ImGDA). ImGDA consists of (1) dual-branch embeddings that simultaneously learn local and global structure information, (2) anchor-based prototype construction that considers the balance between classes, and (3) prototype-aware contrastive learning that simultaneously performs class alignment and domain alignment, and aims to mitigate both class imbalance and domain difference problems.", "questions": "See the weakness section.", "limitations": "The limitations of the proposed method are described in the Appendix. E (Broader Impact and Limitations).", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1. The performance is very good overall, and it is especially impressive that the performance remains stable for a large imbalance factor ρ, with a large performance gap to the baseline.\n2. Visualizations and various ablation experiments are used to intuitively demonstrate the effectiveness of the proposed method.\n\nWeaknesses\n1. In Figure 2 (Main Framework), there is no alignment between the caption and the visual elements, making it difficult to intuitively understand which parts of the figure are referred to by the components described in the text.\n2. Section 4.3 claims that aligning prototypes between local and global branches contributes to performance improvements, but it lacks an explanation of how this alignment relates to mitigating the class imbalance problem. It would be better to see some rationale or intuitive interpretation of why simply aligning the two branches improves the tail class representation.\n3. In Figure 4, the w/o local and w/o global settings seem to remove one of the two branches required for computing L_{cb}; wouldn't this make the use of L_{cb} infeasible in those cases?  It is somewhat surprising that these settings outperform the w/o L_{cb}, and require further explanation of experimental conditions.\n4. While the degree of class imbalance in the source domain is clearly controlled by the imbalance factor ρ, it is not specified whether the target domain has a balanced or equally unbalanced distribution. To reflect a more practical scenario, the paper would benefit from a discussion or empirical results on whether the proposed method remains effective when the target domain is also class-imbalanced.", "was_revised": true, "final_justification": "I appreciate the author's thoughtful and detailed rebuttal. The reviewer's response clarified the concerns I had raised. Therefore, I will increase my score.", "rebuttal": "We sincerely appreciate your comments and valuable suggestions, and we will give detailed responses to your concerns below. \n\n>Q1: The Alignment between the Caption and the Visual Elements in the Main Framework Figure 2.\n\n**A1:** Thanks for the comment! Our main framework consists of three core components: Dual-Branch Embedding Generalization, Anchor-Based Prototype Construction, and Prototype-Enhanced Contrastive Learning. As shown in Figure 2, the left side illustrates the Dual-Branch Embedding Generalization module using global and local views to capture richer graph representations.  The upper-right and lower-right parts of Figure 2  represent the Anchor-Based Prototype Construction and Prototype-Enhanced Contrastive Learning modules. After selecting anchor nodes from the source domain, we perform cross-branch and cross-domain prototype contrastive learning, which simultaneously mitigates the issue of class imbalance in the source domain and facilitates effective cross-domain knowledge transfer. The contents of the framework are consistent with the textual description, and **we appreciate your highly constructive suggestion — we promise we will revise the figure in the revised version** to explicitly mark each component, aligning them more clearly with the figure caption to improve reader comprehension. We sincerely appreciate your thoughtful feedback.\n\n>Q2: Interpretation of Why Aligning Two Branches could Improve the Tail Class Representation.\n\n**A2:** Thanks for comments! In Section 4.2, we **theoretically** explain how the anchor-based prototype construction changes the lower bound of the supervised contrastive loss, shifting it from a head-class-dominated regime to a more balanced one. **This adjustment reduces the adverse impact of head classes,** which usually dominate the source domain, on the learning of other class semantics.\n\nAdditionally, we introduce a **dynamic temperature** in the contrastive loss, which is computed based on the class frequency. This temperature plays two roles: it penalizes hard negative samples and modulates the gradient magnitude for each class. For head classes, a larger temperature increases attention to hard negatives while reducing the gradient, thus lowering their influence. For tail classes, a smaller temperature has a limited effect on hard negative focus (due to the scarcity of samples) but increases their gradient, amplifying their contribution to the loss. As a result, **this mechanism effectively reduces head-class dominance while promoting tail-class learning, alleviating the data imbalance.**\n\nThe purpose of Cross-Branch Prototype Contrastive Learning is to align local and global semantic views, allowing the model to capture more class-representative features while addressing imbalance. In summary, the alignment of semantic information across branches integrates multiple techniques to jointly mitigate class imbalance and enhance the quality of learned representations. We hope this response clarifies your concerns.\n>Q3: Further Explanation of Ablation Study Experiments.\n\n**A3:** Thank you for your detailed comment and your attention to our method. In the ablation study, **w/o local** and **w/o global** refer to replacing the original local and global dual-branch prototype contrastive learning setup with global and global and local and local configurations, respectively. In such cases, **the cross-branch prototype contrastive learning essentially degenerates into single-branch prototype contrastive learning.**\n\nOur motivation for designing the dual-branch prototype contrastive learning is to fully leverage both the local and global information of the graph. When the dual branches are replaced with a single branch, the absence of the complementary view leads to the loss of additional semantic information, resulting in performance degradation. **However, compared to completely removing this module (i.e., w/o $\\mathcal{L}_{cb}$), the single-branch settings still allow the model to benefit from at least one semantic view, thus preserving some consistency in the learned class features.** Therefore, w/o local and w/o global perform better than w/o $\\mathcal{L}_{cb}$. We promise we will include a detailed explanation of this setting in the revised version to help readers better understand our experimental setup.\n>Q4: Discussion of the Imbalanced Distribution in the  Target Domain.\n\n**A4:** Thanks for comments! **We conduct additional experiments** where the target domain is also processed to follow a long-tailed distribution using the same imbalance factor $\\rho$ as the source domain. To provide a fair comparison, we selected the two most competitive baselines (TAM, GraphSHA) from our main experiments and report the results in the following table:\n\n\nFor TAM：\n$\\rho$|A2C|A2D|C2D|\n-|-|-|-|\n10| $\\downarrow$ 7.16%| $\\downarrow$ 6.99%| $\\downarrow$ 14.01%\n20|$\\downarrow$ 9.65%| $\\downarrow$ 11.69%| $\\downarrow$ 18.54%\n50|$\\downarrow$ 11.69%| $\\downarrow$ 18.16%| $\\downarrow$ 21.36%\n\nFor GraphSHA:\n$\\rho$|A2C|A2D|C2D|\n-|-|-|-|\n10| $\\downarrow$ 6.65%| $\\downarrow$ 8.00%| $\\downarrow$ 5.43%\n20| $\\downarrow$9.77%| $\\downarrow$8.20%| $\\downarrow$8.14%\n50| $\\downarrow$13.08%| $\\downarrow$20.42%| $\\downarrow$9.82%\n\nFor ImGDA：\n$\\rho$|A2C|A2D|C2D|\n-|-|-|-|\n10|$\\downarrow$**1.64%**|$\\downarrow$**5.14%**|$\\downarrow$**4.35%**\n20|$\\downarrow$**6.52%**|$\\downarrow$**4.58%**|$\\downarrow$**6.68%**\n50|$\\downarrow$**0.30%**|$\\downarrow$**1.36%**|$\\downarrow$**4.37%**\n\nIn each cell of the table, the value indicates the **percentage decrease** in micro score compared to our experimental results (with balanced target domain in Table 1) under the imbalanced target domain setting.\n\nAs shown in the table above, class imbalance in the target domain indeed leads to a noticeable performance drop for the models, particularly as the imbalance factor increases. In contrast, our method **maintains relatively stable performance** under the same conditions. This demonstrates that our approach not only effectively addresses the imbalance in the source domain but also exhibits strong robustness when faced with imbalance in the target domain. We speculate that this robustness stems from the contrastive learning component in our framework, which encourages the model to learn more stable and semantically consistent node representations, thereby mitigating the adverse effects of distributional bias in the target domain.\n\nIn fact, in the experimental settings, we consider a scenario where the source domain exhibits a long-tailed label distribution while the target domain remains relatively balanced. Detailed statistics regarding the data distributions are provided in Appendix G. In the current body of research on GDA—including unsupervised GDA, semi-supervised GDA, and open-set GDA—most experimental setups assume that both the source and target graphs follow balanced distributions. In contrast, our work is **the first** to explicitly investigate the GDA task under the assumption that the source domain exhibits data imbalance, without imposing assumptions on the target domain distribution. This is **motivated by practical considerations:** source domain data is typically labeled and easier to obtain, making it feasible to observe and address long-tailed distributions; whereas for the target domain, due to the absence of labels, it is difficult to verify whether it is balanced or long-tailed. \n\nWe hope these additional experiments and analyses help to address your concerns.\n> **Thank you again for your suggestions. We hope the responses above could address your concerns and highlight the practical significance and robustness of our work.**"}, {"review_id": "iTJc8HN85k", "reviewer": "Reviewer_Gadc", "summary": "The paper addresses an important problem of class imbalance in unsupervised graph domain adaptation (GDA). The proposed ImGDA framework integrates dual-branch encoders, prototype construction, and contrastive learning to mitigate source-domain bias and domain shifts. While the approach is technically sound and well-structured, significant concerns regarding motivation, novelty, and experimental design limit its contribution.", "questions": "See Weaknesses.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 1, "strengths_and_weaknesses": "Strengths\n\n1. Clear Formulation: The problem setup (Section 3) and modular framework (Section 4) are well-presented.\n\n2. Theoretical Grounding: The theoretical analyses of the prototype contrastive loss (Theorems 4.1–4.2) provide a solid foundation.\n\nWeaknesses\n\n1. Insufficient Motivation and Empirical Analysis\n\nThe claim that class imbalance \"inevitably leads to knowledge extraction bias\" in GDA lacks robust empirical validation. The authors rely on a synthetic example (Figure 1) without demonstrating the prevalence of this issue in real-world graph datasets. Recommend to provide a thorough analysis of class imbalance in established graph benchmarks to quantify its impact on existing GDA methods. Statistical evidence would strengthen the motivation.\n\n2. Limited Methodological Novelty\n\nPrototype-based contrastive learning and anchor-based graph construction are well-studied in non-graph domains (e.g., CV/NLP) and recent graph learning. The paper does not clarify how ImGDA fundamentally advances these concepts for graphs. No graph-specific innovations (e.g., handling heterophily, noisy edges) are discussed. Recommend to explicitly differentiate ImGDA from prior work:\nHow do the \"prototype-enhanced\" losses uniquely address graph structural biases?\n\n3. Weak Experimental Design\n\nSynthetic Imbalance: Artificially inducing imbalance on balanced datasets (ACM/DBLP) does not reflect real-world scenarios. Performance on naturally imbalanced graphs (e.g., social networks with skewed communities) remains unverified.\n\nSmall-Scale Datasets: Experiments are limited to citation graphs. Larger heterogeneous graphs[1] can be also used in graph domain adaption task and should be included to test scalability and generalizability.\n\n[1] Jiang X, Jia T, Fang Y, et al. Pre-training on large-scale heterogeneous graph[C]//Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining. 2021: 756-766.", "was_revised": true, "final_justification": "Thank you for your detailed and thoughtful rebuttal. I will raise my score.", "rebuttal": "Thank you for your insightful comments, and we will try our best to address your concerns below.\n>Q1: Empirical Analysis about the Class-imbalanced Real-world Graph Datasets.\n\n**A1**: Thanks for your valuable comment! We appreciate the reviewer’s concerns regarding the motivation of our proposed scenario. In fact, multiple real-world scenarios exist where the source domain exhibits class imbalance with available labels, while the target domain remains entirely unlabeled. These scenarios have been under-explored, making our proposed approach both novel and significant.\n\nFor instance, in citation networks, early citation networks serve as the source domain with abundant labels, while later citation networks constitute the unlabeled target domain. Due to the limited research in certain emerging fields during earlier periods, severe label imbalance exists. For instance, in the **arXiv citation network(which can be found in the OGB websites)**, articles are categorized into 40 fields. In the early citation network (spanning **1990–2010**), some fields contain as few as **six articles**, while the most populated field has **3,122 articles**, resulting in an extreme imbalance factor of **520**. And we give the specific statistical data of arXiv citation networks in the table below:\n\nDatasets|0|1|2|3|4|5|6|7|8|9|\n|-|-|-|-|-|-|-|-|-|-|-|\narxiv[1970-2010]|63|36|887|122|403|485|147|71|619|650\n\nDatasets|10|11|12|13|14|15|16|17|18|19|\n|-|-|-|-|-|-|-|-|-|-|-|\narxiv[1970-2010]|1134|83|9|197|137|52|200|25|**6**|9\n\nDatasets|20|21|22|23|24|25|26|27|28|29|\n|-|-|-|-|-|-|-|-|-|-|-|\narxiv[1970-2010]|331|63|283|247|455|12|37|143|**3122**|33\n\nDatasets|30|31|32|33|34|35|36|37|38|39|\n|-|-|-|-|-|-|-|-|-|-|-|\narxiv[1970-2010]|399|182|33|116|935|24|384|289|202|349\n\n\nThe numbers 0 to 39 in the table denote the fields of articles, and the second row of each table denotes the number of the article. Similarly, in social network analysis, influential or highly active users (often a minority group) provide labeled data that is inherently imbalanced compared to the broader, unlabeled user base. In financial fraud detection, confirmed fraud cases (which are relatively few) serve as labeled source data, while the majority of transactions in emerging markets remain unlabeled, necessitating domain adaptation techniques for effective fraud detection.\nThese examples demonstrate that domain adaptation in settings where the source domain is imbalanced and the target domain is unlabeled is not only relevant but also practically significant, particularly when leveraging graph-structured relationships through Graph Neural Networks (GNNs).\n>Q2: Explanation of the Methodological Novelty.\n\n**A2**: Thanks for the comment! Our work introduces a **new problem setting**: **graph domain adaptation (GDA) with class imbalance in the source domain**. To address this, we integrate GNNs with contrastive learning in a **dual-branch contrastive framework, which consists of a local branch and a global branch.** The local branch focuses on capturing local structural features from the graph using its original adjacency matrix, while the global branch incorporates high-level topological information via a PPMI matrix constructed from random walks, which captures more comprehensive global structural connectivity. Unlike prior works that directly apply prototype-based contrastive learning or anchor-based prototype construction, we embed these strategies into our dual-branch design, **enabling the consistent integration of both local and global structural information** throughout the entire model pipeline. This constitutes a graph-specific solution rather than a generic adaptation. Besides, our method inherently incorporates a mechanism that **alleviates graph structural biases through its dual-branch design.** Specifically, both the source domain imbalance handling and the cross-domain knowledge alignment are conducted within a dual-branch framework that leverages two different views—each constructed from a distinct adjacency matrix. One view retains the original graph structure, while the other captures a more global structural perspective. By applying cross-branch prototype contrastive learning based on these two views in the source domain, our method effectively **introduces structural perturbations** and learns semantically consistent node representations under such perturbations. This approach enhances the robustness of learned semantic information, **making it more resilient to structural shifts in the target domain graph.** Consequently, it helps to stabilize cross-domain semantic transfer and improves overall knowledge transfer performance.\n\nIn summary, our work is **the first** to propose the problem of domain adaptation under source graph imbalance and **introduces a graph-specific dual-branch contrastive learning framework.** This design **mitigates the impact of graph structural biases by introducing structural perturbations** in the source domain, which makes the GNNs more resilient to structural shifts in the target domain, thus providing a promising solution in this regard. We appreciate your insightful suggestion and will consider explicitly addressing graph structure bias as a future research direction. This will be included in the revised version under the \"Future Work\" section to further advance research in imbalanced graph domain adaptation. We hope this explanation addresses your concerns regarding the novelty of our method.\n> Q3: More Experimental Results.\n\n**A3:** Thanks for the comment! As mentioned above, we have identified the OGB Arxiv citation graph as a naturally imbalanced dataset, and now we conduct additional experiments on this dataset, with Arxiv papers from 1970–2010 as the source domain and papers from 2012–2014 as the target domain. Meanwhile, we also compare our method with two strong baselines identified in the main manuscript. The experimental results are shown in the table below:\n\nMethods|arxiv[1970-2010]->arxiv[2012-2014]\n|-|-|\nImGDA|42.34+-4.32/33.43+-2.26\nTAM|33.21+-6.89/25.31+-5.6\nGraphSHA|36.84+-3.24/23.45+-3.89\n\nIn the table above, each cell presents micro-F1 / macro-F1. As shown, our method consistently **outperforms baselines on both metrics.** However, all methods yield relatively low macro-F1 scores, which is expected due to the inherent imbalance in the target domain (Arxiv 2012–2014). Macro-F1 is more sensitive to performance on minority classes, and the long-tail nature of the data exacerbates this sensitivity.\n\nAdditionally, to evaluate our method on large-scale graphs, we conduct experiments on the CS dataset from the Open Academic Graph (OAG) [1]. Since OAG is a heterogeneous graph while our method is designed for homogeneous settings, we extract a homogeneous subgraph from the CS domain by using P-P (paper-paper) connections as edges, and treat \"field\" as the node label, with the remaining features used as attributes. We use the 2014 CS snapshot as the source domain and the 2017 snapshot as the target domain for node-level field classification. Due to the massive size of this dataset, we adopt a batching strategy for training and inference. We include two additional baselines for comparison. The micro-F1 results are presented below:\n\n$\\rho$|ImGDA|TAM|GraphSHA\n|-|-|-|-|\n10|32.25|18.47|16.62\n20|25.64|12.84|11.92\n50|20.68|10.97|9.83\n\n\nIn this table, we observe that the performance of all methods degrades significantly on ultra-large-scale graphs. As the graph size increases, so does its complexity in terms of the number and diversity of nodes, placing substantial demands on GNN scalability and learning stability. Despite this, our method still shows a clear advantage over baselines, highlighting its robustness in handling large graphs.\n\nIn summary, these additional experiments demonstrate the scalability and practical applicability of our method in both real-world imbalanced scenarios and extremely large graphs. We hope these results address your concerns and further validate the effectiveness of our proposed approach.\n\n[1] Jiang X, Jia T, Fang Y, et al. Pre-training on large-scale heterogeneous graph[C]//Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining. 2021: 756-766.\n\n> **Thank you again for your thoughtful comments. We hope our response can address your concerns and demonstrate the effectiveness and validity of our approach.**"}, {"review_id": "OsREmeHVro", "reviewer": "Reviewer_RspL", "summary": "This paper presents ImGDA, a dual-branch prototype-enhanced contrastive framework for unsupervised class-imbalanced graph domain adaptation that captures both local and global structure to generate class-specific prototypes from a distilled anchor set. It leverages cross-branch prototype contrast to rebalance and align class semantics within the source graph, and cross-domain prototype contrast—with non-parametric pseudo-labels and an adaptive temperature mechanism—to reduce distribution shifts and mitigate imbalance during training. Extensive experiments across multiple real-world graph datasets show that ImGDA consistently outperforms SOTA domain adaptation and imbalanced learning baselines.", "questions": "See Weaknesses.", "limitations": "See Weaknesses.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The proposed setting that integrates class imbalance with unsupervised graph domain adaptation is novel and addresses real-world distribution shifts overlooked by prior work.\n-\tThe dual-branch prototype-enhanced contrastive framework is effective at capturing both local and global semantics to rebalance source classes and align representations across domains.\n-\tExtensive experiments on multiple real-world datasets demonstrate ImGDA’s consistent superiority over SOTA baselines.\n\nWeaknesses:\n-\tThe authors only compare against standalone domain‐adaptation and standalone imbalance methods—intuitively, such methods perform poorly on tasks that combine domain shift with class imbalance—without evaluating combinations of domain‐adaptation GNNs with mature imbalance techniques, many of which can be integrated via simple plug-in loss functions or sampling strategies without any architectural changes.\n-\tSome recent baselines are missing, including the graph domain adaptation methods Pair-Align [1] and TDSS [2], as well as the graph imbalance learning method ConsisGAD [3].\n-\tAlthough the paper reports empirical efficiency metrics for ImGDA, it lacks a formal time and space complexity analysis to clarify how runtime and memory scale with graph size, class count, and anchor set.\n\n[1] Shikun Liu, Deyu Zou, Han Zhao, and Pan Li. \"Pairwise Alignment Improves Graph Domain Adaptation.\" ICML 2024.\n[2] Wei Chen, Guo Ye, Yakun Wang, Zhao Zhang, Libang Zhang, Daixin Wang, Zhiqiang Zhang, and Fuzhen Zhuang. \"Smoothness really matters: A simple yet effective approach for unsupervised graph domain adaptation.\" AAAI 2025.\n[3] Nan Chen, Zemin Liu, Bryan Hooi, Bingsheng He, Rizal Fathony, Jun Hu, and Jia Chen. \"Consistency training with learnable data augmentation for graph anomaly detection with limited supervision.\" In The Twelfth International Conference on Learning Representations. 2024.", "was_revised": true, "final_justification": "The rebuttal clarifies to some extent, and I have adjusted the score.", "rebuttal": "We appreciate your thoughtful comments and suggestions. We will make every effort to address your concerns as follows.\n> Q1: Additional Baselines.\n\n**A1:** Thanks for the comment! We appreciate your attention to our experimental design and insightful suggestion to combine domain adaptation GNNs with established long-tail learning methods. Additionally, we **conduct experiments incorporating several GDA methods combined with imbalance techniques and recently proposed domain adaptation methods** to assess their performance under our task setting. \n\nWe choose GDA-SpecReg[1] as the baseline GDA method and combine it with either upsampling or loss function modification to compare their performance against our proposed method. The results are shown in the table below.\n\nFor GDA-SpecReg + modify loss functions:\n$\\rho$|A2C|A2D|C2D\n|-|-|-|-|\n10|70.69+-2.44/67.56+-2.86|69.43+-1.98/63.43+-2.08|72.53+-2.18/67.32+-1.54\n20|67.44+-2.34/63.59+-2.32|65.78+-2.41/59.32+-2.89|67.42+-2.68/63.02+-1.96\n50|65.47+-2.68/58.46+-2.48|63.42+-2.38/56.35+-2.14|65.54+-2.24/60.78+-2.33\n\nFor GDA-SpecReg + upsampling:\n$\\rho$|A2C|A2D|C2D\n|-|-|-|-|\n10|68.31+-1.04/66.31+-1.26|67.36+-1.28/61.42+-1.04|70.44+-1.46/65.41+-0.98\n20|65.23+-1.48/62.61+-1.12|63.44+-1.89/60.28+-1.96|66.54+-1.38/62.68+-1.36\n50|60.27+-1.46/55.74+-1.35|59.86+-2.03/54.33+-2.04|63.16+-1.64/58.69+-2.06\n\nFor ImGDA:\n$\\rho$|A2C|A2D|C2D\n|-|-|-|-|\n10|77.93+-1.03/73.98+-2.74|71.34+-2.61/66.82+-1.82|73.06+-2.16/69.62+-2.98\n20|77.30+-1.05/73.92+-0.83|71.23+-1.59/65.66+-1.25|68.48+-1.55/63.42+-2.03\n50|73.53+-1.40/67.42+-1.23|69.14+-1.63/61.27+-1.50|70.57+-1.19/66.32+-1.86\n\nEach cell in the table presents both micro and macro scores. From the results, we can observe that simply integrating GDA with imbalance-handling techniques does improve performance on this task. However, as the imbalance factor increases, the performance of these models drops significantly. Among them, models based on upsampling perform worse than those using loss modification. We speculate that this is because upsampling methods heavily rely on the quality of the sampled data. Under severe data imbalance, the number of reference samples for tail classes is limited or overly homogeneous, which may lead to overfitting on those classes and thus result in poor generalization to the target domain. In contrast, our method **significantly outperforms both strategies,** clearly demonstrating that the proposed dual-branch contrastive learning framework achieves robust and consistent performance across various degrees of data imbalance.\n\nMeanwhile, we choose Pair-Align[2], TDSS[3], ConsisGAD[4] as additional state-of-the-art GDA methods and class-imbalanced methods to evaluate their performance under our task setting, and the results are shown below.\n\nFor Pair-Align:\n$\\rho$|A2C|A2D|C2D\n|-|-|-|-|\n10|62.34+-0.18/56.87+-1.12|58.36+-3.46/53.74+-1.28|60.49+-1.63/58.44+-0.98\n20|54.37+-1.24/49.54+-2.36|54.32+-1.08/48.24+-0.86|56.48+-2.14/52.34+-0.32\n50|48.56+-2.10/35.32+-1.84|49.53+-3.46/43.43+-3.21|50.12+-1.65/42.42+-0.38\n\n\nFor TDSS:\n$\\rho$|A2C|A2D|C2D\n|-|-|-|-|\n10|66.46+-0.48/62.42+-0.32|64.64+-1.26/59.89+-2.26|65.74+-0.43/61.48+-0.80\n20|60.48+-0.87/56.43+-1.45|58.43+-2.28/50.36+-0.94|58.32+-1.12/54.36+-2.52\n50|52.56+-1.26/43.46+-1.48|50.52+-2.36/42.03+-1.32|52.32+-3.84/43.74+-2.37\n\nFor ConsisGAD:\n$\\rho$|A2C|A2D|C2D\n|-|-|-|-|\n10|72.48+-1.44/66.39+-0.32|68.43+-2.02/64.44+-1.28|69.98+-1.42/64.32+-1.45\n20|66.34+-2.36/60.39+-1.98|64.56+-2.39/55.37+-2.44|64.43+-2.52/60.45+-1.30\n50|62.32+-2.45/53.64+-2.04|60.86+-2.33/52.68+-2.59|58.33+-2.48/52.37+-1.28\n\nFor ImGDA:\n$\\rho$|A2C|A2D|C2D\n|-|-|-|-|\n10|77.93+-1.03/73.98+-2.74|71.34+-2.61/66.82+-1.82|73.06+-2.16/69.62+-2.98\n20|77.30+-1.05/73.92+-0.83|71.23+-1.59/65.66+-1.25|68.48+-1.55/63.42+-2.03\n50|73.53+-1.40/67.42+-1.23|69.14+-1.63/61.27+-1.50|70.57+-1.19/66.32+-1.86\n\nReviewing the three newly added baselines, we observe trends consistent with the conclusions in Section 5.2 of our main paper. Specifically, domain adaptation methods such as Pair-Align and TDSS perform poorly in our task setting, and their performance degrades significantly as the imbalance factor increases. Compared to other approaches, methods specifically designed to address class imbalance in graphs, such as ConsisGAD exhibits notably stronger performance. This highlights that source domain imbalance significantly hinders cross-domain knowledge transfer—potentially even more so than the domain discrepancy itself. Our method **outperforms** ConsisGAD by a substantial margin. As the imbalance factor increases, the performance of these baselines degrades considerably, whereas our method maintains relatively stable results. This clearly demonstrates the **effectiveness and robustness** of our approach in tackling the domain adaptation problem under source domain imbalance. \n\nTo provide a more comprehensive evaluation of our method, we commit to including these baselines in the revised version. Thank you again for your valuable suggestion, and we hope these additional experiments adequately address the reviewer’s concerns.\n\n[1]You Y, Chen T, Wang Z, et al. Graph domain adaptation via theory-grounded spectral regularization[C]//The eleventh international conference on learning representations. 2023.\n\n[2] Shikun Liu, Deyu Zou, Han Zhao, and Pan Li. \"Pairwise Alignment Improves Graph Domain Adaptation.\" ICML 2024. \n\n[3] Wei Chen, Guo Ye, Yakun Wang, Zhao Zhang, Libang Zhang, Daixin Wang, Zhiqiang Zhang, and Fuzhen Zhuang. \"Smoothness really matters: A simple yet effective approach for unsupervised graph domain adaptation.\" AAAI 2025. \n\n[4] Nan Chen, Zemin Liu, Bryan Hooi, Bingsheng He, Rizal Fathony, Jun Hu, and Jia Chen. \"Consistency training with learnable data augmentation for graph anomaly detection with limited supervision.\" In The Twelfth International Conference on Learning Representations. 2024.\n\n>Q2: Time Complexity and Space Complexity.\n\n**A2**: Thanks for the comment! We will provide the time complexity and space complexity below. \nFor the time complexity, let $N^s$ and $|\\mathcal{E}^s|$ denote the number of nodes and edges in the source domain graph, and $|N^t|$ and $|\\mathcal{E}^t|$ denote the number of nodes and edges in the target domain graph. Assuming an $L$-layer GCN encoder with a feature dimension of $d$, the computational complexity of feature encoding is $\\mathcal{O}(L|\\mathcal{E}|^sd + LN^sd^2)$ for the source domain, and $\\mathcal{O}(L|\\mathcal{E}|^td + LN^td^2)$ for the target domain. When $|\\mathcal{E}|^s \\gg n$, this simplifies to $\\mathcal{O}(|\\mathcal{E}|^sd)$ and $\\mathcal{O}(|\\mathcal{E}|^td)$, respectively. For anchor node sampling, we sort nodes based on their degree and select $m$ nodes per class. Since $m \\ll N^s$, the complexity is $\\mathcal{O}(N^s \\log N^s)$. For prototype computation, the Mean prototype computation per class takes $\\mathcal{O}(md)$, the Cross-branch prototype contrastive loss takes $\\mathcal{O}(md)$, the Cross-domain prototype contrastive loss takes $\\mathcal{O}(N^td)$, and the Supervised loss computation in the source domain takes $\\mathcal{O}(N^sd)$. Thus, the total time complexity is $\\mathcal{O}(|\\mathcal{E}^s|d + |\\mathcal{E}^t|d + N^s \\log N^s + md + N^td + N^sd)$\nWhen $|\\mathcal{E}^s| \\gg N^s \\log N^s$, computation is dominated by the number of edges. When $|\\mathcal{E}^s| \\approx N^s\\log N^s)$, sorting complexity becomes a key factor. If $N^t$ is very large, computation is significantly affected by the target domain nodes. As a result, the overall complexity can be approximated as:$\\mathcal{O}(\\max(|\\mathcal{E}^s| + |\\mathcal{E}^t|, N^s\\log N^s, N^td))$. Besides, we have a detailed discussion of the time complexity of our method and several baselines in the appendix, please refer to it for more details.\n\nAs for the space complexity: storing node features incurs a complexity of $\\mathcal{O}(Nd)$; storing the sparse adjacency matrix requires $\\mathcal{O}(\\mathcal{|E|})$; the PPMI matrix has a space complexity of $\\mathcal{O}(N^2)$; the model parameters require $\\mathcal{O}( D^2)$; and storing the prototypes and pseudo-labels requires $\\mathcal{O}(Cd)$ and $\\mathcal{O}(NC)$ respectively, and C denotes the number of classes. In summary, the main space cost of our method arises from the PPMI matrix, which is $\\mathcal{O}(N^2)$.\n\n> **We hope our responses above can address your concerns and show the stability and effectiveness of our proposed method**"}, {"review_id": "ZU4ld8Q31F", "reviewer": "Reviewer_XCp7", "summary": "This paper proposes a dual prototype-enhanced contrastive framework, ImGDA, which focuses on the challenge of class imbalance in graph domain adaptation. The goal is to transfer imbalanced label knowledge from a labeled source graph to an unlabeled target graph.", "questions": "1. In Section 3, the imbalance factor (IF) ρ is defined as N1/NC. What is the rationale behind this definition? When there are multiple tail classes, this formulation may not adequately reflect the degree of imbalance in the sample distribution. In the experimental setup, what is the ratio between head and tail classes?\n\n2. The Cross-Domain Prototype Contrast relies on pseudo-labels in the target graph. How is the reliability of these pseudo-labels evaluated or ensured?\n\n3. While Anchor-Based Prototype Construction may help alleviate class imbalance in the source graph, the Prototype-Enhanced Contrastive Learning still depends on pseudo-labels in the target graph. When the target domain also suffers from class imbalance, the pseudo-labels are likely to be biased toward head classes. Under such conditions, is the proposed method still robust and reliable?", "limitations": "The authors have discussed the limitations and potential negative societal impact of their work", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\nThis work is relatively innovative, with a well-organized and coherent structure.\n\nWeaknesses:\nSome technical details are insufficiently addressed, which impact the overall reliability of the proposed method.", "was_revised": true, "final_justification": "The author clarified my concerns about the imbalance factor with a more complete computation method and relevant results. In addition, they offered a detailed explanation of the reliability of pseudo-labels and the experimental outcomes under a long-tailed distribution in the target domain. Their responses have addressed the main issues to a reasonable extent, and I find it appropriate to raise the score slightly.", "rebuttal": "Thanks for your thoughtful suggestions. We will do our best to address your concerns below. \n>Q1: Explanation of Imbalance Factor.\n\n**A1:** Thank you for your comment. In our method, the imbalance factor is defined as $\\rho = N_1 / N_c$, where $N_1$ and $N_c$ represent the number of samples in the head class and tail class, respectively. During preprocessing, we first compute a constant $\\mu = \\left(\\frac{1}{\\rho}\\right)^{\\frac{1}{C-1}}$, where $C$ denotes the total number of classes. Then, we calculate the number of nodes in each class using the formula: $N_i = N_{\\text{max}} \\times \\mu^i$, where $N_{\\text{max}}$ refers to the number of nodes in the most frequent class. This design ensures that the ratio between the head and tail classes is $\\rho$, and the number of nodes in intermediate classes increases gradually from the tail class to the head class.\n\nThis imbalance factor effectively captures the extremity of distributional skew in the dataset, which is crucial for long-tailed scenarios where head and tail classes exhibit typical behaviors: head classes often dominate and influence other categories, while tail classes are more susceptible to such influence. **By defining the imbalance in this way, we can better characterize and address the long-tailed nature of the data, which is widely used in imbalanced graph research[1][2][3][4] in recent years.**\n\nIn our experiments, we set $\\rho \\in \\\\{5, 10, 20, 50, 100\\\\}$ to simulate various imbalance levels, ranging from mild to extreme, in the source domain. This design enables a thorough evaluation of the stability and effectiveness of our proposed method. We hope this explanation clarifies your concerns.\n\n[1] Park J, Song J, Yang E. Graphens: Neighbor-aware ego network synthesis for class-imbalanced node classification[C]//International conference on learning representations. 2021.\n\n[2]Li W Z, Wang C D, Xiong H, et al. Graphsha: Synthesizing harder samples for class-imbalanced node classification[C]//Proceedings of the 29th ACM SIGKDD conference on knowledge discovery and data mining. 2023: 1328-1340.\n\n[3]Song J, Park J, Yang E. TAM: topology-aware margin loss for class-imbalanced node classification[C]//International conference on machine learning. PMLR, 2022: 20369-20383.\n\n[4]Zhao T, Zhang X, Wang S. Graphsmote: Imbalanced node classification on graphs with graph neural networks[C]//Proceedings of the 14th ACM international conference on web search and data mining. 2021: 833-841.\n>Q2: Discussion about the Reliability of Pseudo-labels.\n\n**A2:** Thank you for your comment and for your attention to the technical details of our method. **Pseudo-label is widely used in several research[1][2][3][4],** and in our framework, we adopt a non-parametric approach to generate pseudo-labels for target domain nodes by measuring the embedding similarity between the source and target domains. Several design choices help ensure the quality of these pseudo-labels:\n\n- First, **the powerful representation learning capability of GNNs** enables effective feature extraction on graph-structured data. Nodes with the same label in the source and target domains often share similar neighborhood structures and features, resulting in embeddings that are highly comparable across domains.\n\n- Second, as shown in Equation (10), we compute the similarity between each target node and the anchor source nodes, and then use this similarity as a weight to aggregate the one-hot label encodings of the source nodes. The class with the highest aggregated score is selected as the pseudo-label. Unlike classifier-based labeling, this non-parametric method **leverages the rich label information from the source domain and considers multiple source nodes for each decision,** thereby enhancing pseudo-label reliability.\n\n- Third, we construct a **high-quality anchor set** by sampling nodes based on node degree. These anchors are then used for prototype construction and pseudo-label generation. Since high-degree nodes typically exhibit more representative category features and are less noisy, they help reduce the impact of label noise and further improve pseudo-label quality.\n\nIn summary, our method incorporates several strategies to **enhance the reliability of pseudo-labels** in the target domain, which in turn supports high-quality contrastive learning and effective knowledge transfer. We hope this response addresses your concern.\n\n[1]Qiu Z, Zhang Y, Lin H, et al. Source-free domain adaptation via avatar prototype generation and adaptation[J]. arXiv preprint arXiv:2106.15326, 2021.\n\n[2]Qiao Z, Luo X, Xiao M, et al. Semi-supervised domain adaptation in graph transfer learning[J]. arXiv preprint arXiv:2309.10773, 2023.\n\n\n[3]Zhang Z, Liu M, Wang A, et al. Collaborate to adapt: Source-free graph domain adaptation via bi-directional adaptation[C]//Proceedings of the ACM Web Conference 2024. 2024: 664-675.\n\n[4]Chen N, Liu Z, Hooi B, et al. Consistency training with learnable data augmentation for graph anomaly detection with limited supervision[C]//The twelfth international conference on learning representations. 2024.\n>Q3: Discussion about the Class-imbalanced Target GDA.\n\n**A3:** Thank you for your insightful comment. **We conduct additional experiments** where the target domain is also processed to follow a long-tailed distribution using the same imbalance factor $\\rho$ as the source domain. To provide a fair comparison, we selected the two most competitive baselines(TAM, GraphSHA) from our main experiments and report the results in the following table:\n\n\nFor TAM：\n$\\rho$|A2C|A2D|C2D|\n-|-|-|-|\n10| $\\downarrow$ 7.16%| $\\downarrow$ 6.99%| $\\downarrow$ 14.01%\n20|$\\downarrow$ 9.65%| $\\downarrow$ 11.69%| $\\downarrow$ 18.54%\n50|$\\downarrow$ 11.69%| $\\downarrow$ 18.16%| $\\downarrow$ 21.36%\n\nFor GraphSHA:\n$\\rho$|A2C|A2D|C2D|\n-|-|-|-|\n10| $\\downarrow$ 6.65%| $\\downarrow$ 8.00%| $\\downarrow$ 5.43%\n20| $\\downarrow$9.77%| $\\downarrow$8.20%| $\\downarrow$8.14%\n50| $\\downarrow$13.08%| $\\downarrow$20.42%| $\\downarrow$9.82%\n\nFor ImGDA：\n$\\rho$|A2C|A2D|C2D|\n-|-|-|-|\n10|$\\downarrow$**1.64%**|$\\downarrow$**5.14%**|$\\downarrow$**4.35%**\n20|$\\downarrow$**6.52%**|$\\downarrow$**4.58%**|$\\downarrow$**6.68%**\n50|$\\downarrow$**0.30%**|$\\downarrow$**1.36%**|$\\downarrow$**4.37%**\n\nIn each cell of the table, the value indicates the **percentage decrease** in micro score compared to our experimental results (with balanced target domain in Table 1) under the imbalanced target domain setting.\n\nAs shown in the table above, class imbalance in the target domain indeed leads to a noticeable performance drop for the models, particularly as the imbalance factor increases. In contrast, our method **maintains relatively stable performance** under the same conditions. This demonstrates that our approach not only effectively addresses the imbalance in the source domain but also exhibits strong robustness when faced with imbalance in the target domain. We speculate that this robustness stems from the contrastive learning component in our framework, which encourages the model to learn more stable and semantically consistent node representations, thereby mitigating the adverse effects of distributional bias in the target domain.\n\nIn fact, in the experimental settings, we consider a scenario where the source domain exhibits a long-tailed label distribution while the target domain remains relatively balanced. Detailed statistics regarding the data distributions are provided in Appendix G. In the current body of research on GDA—including unsupervised GDA, semi-supervised GDA, and open-set GDA—most experimental setups assume that both the source and target graphs follow balanced distributions. In contrast, our work is **the first** to explicitly investigate the GDA task under the assumption that the source domain exhibits data imbalance, without imposing assumptions on the target domain distribution. This is **motivated by practical considerations:** source domain data is typically labeled and easier to obtain, making it feasible to observe and address long-tailed distributions; whereas for the target domain, due to the absence of labels, it is difficult to verify whether it is balanced or long-tailed. \n\nWe hope that the additional experiments and analysis provide satisfactory answers to your concerns and demonstrate the robustness and stability of our method under long-tailed target domain settings.\n> **We hope our responses above can address your concerns and demonstrate the reliability and effectiveness of our proposed method**"}]

Author rebuttal:

Meta-review: This paper aims to address the class imbalance problem in graph unsupervised domain adaptation. The authors proposed a dual-branch prototype-enhanced contrastive framework named ImGDA. It leverages cross-branch prototype contrast to rebalance and align class semantics within the source graph, and uses cross-domain prototype contrast to reduce distribution shifts and mitigate imbalance during training. Experiments on multiple real-world graph datasets demonstrate the effectiveness of the proposed approach.  

All of the reviewers recognized the novelty and technical contributions of this work. The problem setting is well motivated and clearly presented. The theoretical analyses of the prototype contrastive loss provide a solid foundation. Also, it is impressive that the performance of the proposed approach remains stable for a large imbalance factor. Overall, the paper is well written and easy to follow.

Meanwhile, reviewers raised some questions regarding novelty, technical details, baselines, time complexity, etc. The authors have provided detailed responses with additional results, which have addressed the previous concerns from reviewers. The authors are strongly encouraged to incorporate the new results and discussions into the final version of the paper.
Decision: Accept (poster)