DELTA: Dual Consistency Delving with Topological Uncertainty for Active Graph Domain Adaptation
Authors: Pengyun Wang
Yadi Cao
Chris Russell
Yanxin Shen
Junyu Luo
Ming Zhang
Siyu Heng
Xiao Luo
Venue: Accepted by TMLR ()

Abstract: Graph domain adaptation has recently enabled knowledge transfer across different graphs. However, without the semantic information on target graphs, the performance on target graphs is still far from satisfactory. To address the issue, we study the problem of active graph domain adaptation, which selects a small quantitative of informative nodes on the target graph for extra annotation. This problem is highly challenging due to the complicated topological relationships and the distribution discrepancy across graphs. In this paper, we propose a novel approach named Dual Consistency Delving with Topological Uncertainty (DELTA) for active graph domain adaptation. Our DELTA consists of an edge-oriented graph subnetwork and a path-oriented graph subnetwork, which can explore topological semantics from complementary perspectives. In particular, our edge-oriented graph subnetwork utilizes the message passing mechanism to learn neighborhood information, while our path-oriented graph subnetwork explores high-order relationships from substructures. To jointly learn from two subnetworks, we roughly select informative candidate nodes with the consideration of consistency across two subnetworks. Then, we aggregate local semantics from its K-hop subgraph based on node degrees for topological uncertainty estimation. To overcome potential distribution shifts, we compare target nodes and their corresponding source nodes for discrepancy scores as an additional component for fine selection. Extensive experiments on benchmark datasets demonstrate that DELTA outperforms various state-of-the-art approaches. The code implementation of DELTA is available at https://github.com/goose315/DELTA.

Published in Transactions on Machine Learning Research (02/2025)
Dual Consistency Delving with Topological Uncer- tainty for Active Graph Domain Adaptation
DELTA:
Pengyun Wang
Pywaagg3 15 Agmail com yadicao95 com chris, parisrussslly russell Gol. oz. ac. uk shenyanainn 5 163. com luo junyyu @outlook. com mzhang es Upku. edu. on siyuheng yn edu zinoluo Bes, ucla edu
Yadi Cao²
Chris Russell
Yanxin Shen
Junyu Luo
Ming Zhang
Siyu Heng
Xiao Luo 6*
Orford Internet Institute, University of Orford
Department of Computer Science and Engineering, University of California, San Diego
School of Economics, Nankai University
School of Computer Science, Peking University
Department of Biostatistics, School of Global Public Health, New York University
Department of Compuler Science, University of California, Los Angeles
Reviewed OpenReview: https: openreview. net/ formm id= dd=55y8aLKGb
Abstract
Graph domain adaptation has recently enabled knowledge transfer across different graphs. However, without the semantic information on target graphs, the performance on target graphs is still far from satisfactory. To address the issue, we study the problem of active graph domain adaptation, which selects small quantitative of informative nodes the larget graph for extra annolation. This problem is highly challenging due to the com- plicated topological relationships and the distribution discrepancy across graphs. In this paper, we propose a novel approach named Dual Consistency Delving with Topological Uncertainty (DELTA) for active graph domain adaptation. Our DELTA consists of an edge-oriented graph subnetwork and a path-oriented graph subnetwork, which can explore topological semantics from complementary perspectives. In particular, our edge-oriented graph subnetwork utilizes the message passing mechanism to learn neighborhood informa- tion, while path-oriented graph subnetwork explores high-order relationships from sub- structures. To jointly learn from two subnetworks, we roughly select informative candidate nodes with the consideration of consistency across two subnetworks. Then, we aggregate local semantics from its K-hop subgraph based on node degrees for topological uncertainty estimation. To overcome potential distribution shifts, we compare target nodes and their corresponding source nodes for discrepancy scores as an additional component for fine selec- lion. Extensive experiments benchmark datasets demonstrate that DELTA perporosms various state-of-the-art approaches. The code implementation of DELTA is available at https::/githhs trggg..h..... com//ooss335/DELTAA
1
Introduction
Graph data is widely applied in various real-world scenarios, for example in social networks (Guo & Wang, 2020 Zhang et al. 2022b academic networks (Tang et al., 2008 West al.) 2016), transportation net-
* Cooreespondigg authors.

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Active Learning Budget
Target Domain
Active Learning Query
Target Domain after Annotations
Figure 1: The problem sctting of active learning for graph domain adaption. We have fixed budget and aim to find the most informative nodes for data annotalion.
works (Li al., 2022: Jin et al., 2020), biological networks (Liu et al. 2024; Shen al.; 2021), compound networks (Sun al. 2022 Cai et al. 2022), , and drug discovery {Li al.) 2024 Wu al.) 2022b). In the collection of graphs, variations in the standards and timing often cause two graphs in the same domain to exhibit different node attributes and edge structures [Zhu et al. 2021 Pilancı & Vural 2020
Towards this end, unsupervised graph domain adaptation has received ever-increasing attention in the field of data mining and graph machine learning. Given a partially labeled source graph and a fully unlabeled target graph, graph domain adaptation narrows the distributional differences between the source and target graphs, enabling the model trained on the source domain to better adapt to graph data in the target domain, thereby
improving task performance in the larget domain (Hedegaard al., 2021 Li et al. 2022 Cai al. 2024
Current approaches to graph domain adaptation primarily usually involve adversarial learning (Qiao et al.
2023 for domain alignment, minimizing the distance between node representations (Wu et al. 2024),
filtering out irrelevant information between the source and target graphs through the information bottleneck
strategies (Qiao et al. 2024).
However, the performance on the target graph is still far from satisfactory for unsupervised domain adapta- tion methods due to the absence of labels in the target graph (Cai et al., 2024). Due to constraints such labeling costs, is not feasible to extensively label the nodes the target graph. Although pseudo-labeling strategics have boen developed to address label scarcity issues in target graphs, they still fail to provide accurate supervision signals for the target graph, resulting in polential error accumulation (Qiao et al. 2024 Guo et al. 2022 Qiao et al. 2023). To reduce the annotation cost, we study the problem of active graph domain adaptation (sce Figure D) which aims to acquire the most valuable true labels for the target graph under a limited labeling budget, thereby maximixing the performance improvement on the target graph in a cost-effective manner.
Despite significant advancements in graph domain adaptation rescarch, several challenges still need to be considered when applying active learning to graph domain adaptation (Li et al.
2022 Wang et al. 2023a Shen et al. 2023a). Pirstly, though extensive active learning methods (Hsu & Lin
2015 have been proposed for images and texts, they focus on independent and identically distributed (i.i.d.) data. In contrast, graph data exhibit complex and high-order topological relationships, such as the mumber and density of nodes and edges, the heterogeneity of node degree distribution, and topological structure. These complicated factors greatly cuhance the difficultics of identifying informative nodes on the target graph. Secondly, the source and (arget graphs have huge distribution discrepancies, which could deteriorate domain adaptation and result in biases in uncertainty estimation well (Li et al. 2022 Qiao et al. 2024 2023).
In this paper, we address the aforcmentioned challenges by introducing Dual Consistency Delving with Topological Uncertainly (DELTA) for active graph domain adaptalion. The core of our DELTA is to ex- plore graph topological data from complementary views for information-rich candidate nodes the target graph. In particular, our DELTA consists of an edge-oriented graph subnetwork and a path-oriented graph subnetwork. Our edge-oriented subnetwork utilizes the message passing mechanism to learn topological se- mantics implicitly while path-oriented subnetwork aggregates information from different paths explicitly.
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Then, we combine two subnetworks by measuring the inconsistency across these subnetworks of nodes the target graph for coarse selection. Furthermore, we measure the uncertainty by combining node degrees with K-hop subgraphs to learn from local topological semantics for each node. To mitigate the distribution shifts, we also calculate the discrepancy scores by comparing target nodes and their corresponding source nodes. In the end, we combine both uncertainty scores and discrepancy scores for fine selections.
We validate the effectiveness of DELTA through extensive experiments on benchmark datasets, compar- ing it with state-of-the-art approaches. We also demonstrate our advantages qualitatively through t-SNE visualization. The main contributions of this study are follows:
We study the problem of active graph domain adaptation and benchmark the performance of recent state-of-the-art approaches in transfer learning scenarios.
We propose DELTA, a novel and cost-effective active learning sampling strategy that explores topological semantics from complementary edge and path perspectives, incorporating subgraph-level uncertainty and weightd attribute discrepancy between the source and target graphs
We conduct extensive experiments on popular graph transfer learning benchmarks, demonstrating that the proposed DELTA perforins better than slate-of-the-art active learning approaches.
2
Related Work
Active Learning on Graphs. Active learning has been extensively studied in the field of computer
vision Hsu & Lin 2015). but limitod studics have applicd active learning to graph-oricnted deep learning CCai
ee al.
2017
Gao et al. 2018 Chen et al.] 2019 Hu al.] 2020 Cui el. al.] 2022 Zhang et al.
2022c
et al.
2024
Zhang et al. 2022a) Earlier research generally does not consider the topological structure
features of graphs. Still, it effectively combines node uncertainty and representativeness (Cai et al.
2017
Hu
ct al. 2020 where uncertainty is measured by information entropy, and representativeness is measured by
information density and graph centrality (Gao et al., 2018 Chen et al. 2019). Many of these methods employ
multi-armed bandit mechanisms to identify the weights of active learning strategies (Cai et al.) 2017 Gao
ct al. 2018 Chen et al., 2019 Hu et al.] 2020). More recent studies combine active learning strategies with
reinforcement learning, formalizing active learning as a Markov decision process (Hu et al. 2020 Cui et al,
2022 Zhang et al.] 2022c Yu et al., 2024). They measures such PageRank centrality and predictive
entropy to evaluate the informativeness and uncertainty of nodes (Zhang et al. 2022c) and combine metrics like KL divergence to assess the information value of nodes (Cui et al. 2022). However, although there are studies applying active learning to GNNs, most are based on a single graph. Few studies focus on applying this technique to graph transfer lcarning, which is more challenging compared to singlo-graph classification tasks (Shi et al., (024)). This study aims to fill this gap by conducting active learning across graphs and innovatively selecting nodes on the target graph that exhibit significant differences from the source graph. By leveraging active learning for labeling, we reduce information interference and distributional discropancies in cross- pross-graph learning, aligning with the specific characteristics of graph domain adaptation tasks.
Graph Domain Adaptation. Existing methods for graph domain adaptation can be categorized into three main streams (Shi et al. (0024]: First, methods that enhance node embeddings on the source graph to improve performance on the target graph. This is achieved through adversarial loss functions
Yang
et al.] 2022. Yuan et al., 2023 Wu et al.] 2022a Yin et al.] 2023)] Qiao et al.] 2023 Zhang et al., 2021
or by modilying the message passing mechanisms of GNNs (Wu et al.) |020 Dai et al. 2022, Shen et al.
2023b). Second, methods that focus better adapting the knowledge learned from the source graph domain
to the target graph domain. This is achieved through data augmentation (Jiang et al. 2020
Qiao et al,
2024), spectral methods (Pilancı & Vural 2020 You et al. 2023). , spatial methods (Guo ct al. 2022 Wu el al. 2023), or pseudo-label aligument (Yin et al. 2022 Song el al.) 2020). Third, met that directly utilize information from the target graph to build models WWagg et al. 2023a b Shhen et al. 2023a), using
the probability distribution of predicted labels on the target graph (Wu Rostami 2023 Wang et al.
2023a) and semantic information (Wagg et al.) (202bb] Shen et al., 2023b). However, there is still a lack of methods that explicitly utilize graph topological information, while existing approaches only explore semantic
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information from single view, whether edge, path, or node. Current methods also rarely explicitly utilize the attribute distribution differences between the nodes in the source and target graphs, with most existing
methods addressing this through distribution aligument loss functions (Sun et al. 2015 Cai et al.) 2024).
Furthermore, few methods directly address label sparsity in both the source and target graphs. Most existing
studies assume high proportion of labeled nodes the source graph (Pilancı & Vural 2020 Zhang et al.
2021 Guo ct al. 2022 Wu et al. 2023; Sun et al. 2015; Cai et al., 2024). As a related problem, graph out-of-distributtin detection aims identify nodes that do not belong a training distribution [Song & Wang (2022): ; Gong & Sun (2024) Bao et al. (2024). In comparison with these aforementioned approaches,
our DELTA enriches the labels of the target graph through active learning and innovatively utilizes an edge- oriented graph subnetwork and a path-oriented graph subnetwork to explore topological semantics from complementary perspectives.
Active Learning for Domain Adaptation. Existing rescarch has not fully explored the integration of active learning with domain adaptation (Zhan et al., 2021 2022 Han et al.) 2023). ALDA uses the best classifier learned from the source domain as an initial hypothesis in the target domain and adjusts weights to query labels (Rai et al. 2010). Furthermore, the JO-TAL utilizes Maximum Mean Discrepancy (MMD) to mcasure marginal probability distribution differences between source and target domain samples. selecting instances from the unlabeled target domain dataset to minimize this discrepancy (Chattopadhyay et al. 2013). Additionally, AADA combines Domain-Adversarte Neural Networks (DANN) with a sample selection strategy based on Importance Weighted Empirical Risk Minimization (IWERM) to achieve domain- invariant feature learning (Su et al.) 2020). CLUE builds upon AADA by further integrating predictive entropy to measure information content. and using weighted k-means clustering to group similar target instances (Prabhu et al. 2021). Recent studics include EADA and ADCD. EADA seleets and annotates the most informative unlabeled larget samples by utilizing free energy, achieving combination of inter-domain feature and instance uncertainty (Xie et al. 2022). ADCD improves active learning in domain adaptation by combining protocol scoring, domain discriminator scoring, and cosine difference scoring (Menke et al. 2024). In summary, there are currently no specialized studies based on active learning for graph domain adaptation Given its significant practical implications, research in this direction is necessary (Shi et al. 2024 Redko et al.] 2020). The proposed DELTA franework aims to fill this gap by comprehensively considering the complexity of graph topological structures and the distributional discropancies in pross-graph learning.
3 Preliminaries
3.1 Problem Definition
Consider two graphs one the source graph G* = (V*, EV,,,",X*,Y'' and one the target graph G (V', X Y") Here, V and V represent the sets of nodes in the source and target graphs, respectively, E and Et represent the sets of edges in the source and larget graphs, respectively, X* and X donate the feature matrix of nodes from the source and target graphs, and Y and Y represent the sets of node class labels in the source and target graphs, respectively. The source graph and target graph have a serious domain gap but share the same label space, with only a small portion of Y being labeled and y being completely unlabeled (Wilson & Cook. 2020). The objective of active graph domain adaptation is to find the most valuable nodes for labeling in the target graph G within a fixed budget of k assign them annotations Yt and perform graph domain adaptation using graph neural network model shared between the source
and target graphs (Hsu & Lin 2015 Xie et al. 2022 Rai et al. 2010
3.2 Graph Domain Adaptation
We briefly present the typical framework of graph domain adaptation, a semi-supervised learning framework that has been widely applied (Dai et al., 2022 Yin et al. 2023 Qiao et al., 2024). Graph domain adaptation aims to ensure that node emboddings output by the feature extractor have similar distributions across different domains and ultimately label the unlabeled target nodes. Therefore, classifier on node embeddings would generate predictions from the shared conditional distributions across the two domains. Tn formulation,
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Efge based Graph Subnetwork
Topological Uncertainty
Logts
Source Domain
Comsistency Delving
Candidate Target Node Set
Source Domain
Compostte Sczres
Active Labeling
Adapptation
Domaln Discrepancy Soores
GAN
Erieesling
Lngis
Target Domain
Target
Figure Overview of the proposed DELTA framework. DELTA first captures complementary topological seraantics from the larget graph via edge-oriented and path-oriented subnetworks. It then identifies candidate nodes with semantic inconsistencies between these subnetworks. DELTA computes topological uncertainty using degree weighting and K-hop subgraphs, and domain gap between the source and target graphs for informative node selection.
given the source and target embedding matrix Z and Z', respectively, we have;
L = Sup z Y*) + ALDA Zz),
(1)
where Lsup denotes the cross-ent ropy objective on the labeled source graph G*, and Lpa denotes the domain adaptation loss, such as the adversarial learning objective LDA (Qiao et al. 2024):
LDA
min max [Eiev- log D(z)) +Ejev log(1 D(z))))
0x
D(-) denotes a domain discriminator that predicts whether the imput embedding is from the source graph or the target graph. zf and 2 denotes the node embeddings of node E V and j E V", respectively. 0g and Φa denote the network parameters the feature extractor and the classifier, respectivcly.
4 Methodology
4.1
Overview
In this work, we propose a new approach named DELTA for active graph domain adaption. DELTA consists of three main components as follows. (1) Dual Graph Subnetwork with Consistency Delving, which consists of an odge-oriented graph subnetwork and a path-oriented graph subnetwork trained on both the source and (arget graphs. Then, explore complementary neighborhood information and high-order rela- tionships from the target graph, resulting in informative candidate nodes denoted T. (2) Topological Uncertainty Measurement, which explores both target graph node degrees and K-hop subgraphs to ag- gregate local entropy, thereby capturing the topological uncertainty of the target graph nodes. (3) Domain
Discrepancy Measurement, which calculates the distance between target nodes and their corresponding source labeled nodes, thus overcoming potential distribution shifts. By aggregating topological uncortainty and domain discrepancy scores on T, we select the target graph nodes be labeled in single round for better convenience following (Sener & Savarese 2017). The overview of the proposed method illustrated in Figure
4.2 Dual Graph Subnetwork for Consistency Delving
In our DELTA, we adopt a dual graph subnetwork framework that operates simultancously on both the source and target graphs to explore graph semantics from complementary edge-centric and path-centric perspectives. Since the target graph is entirely unlabeled, while only portion of the source graph is labeled,
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this allows to leverage supervision signals from the labeled nodes in the source graph, enabling the model to learn domain distribution discrepancies between the two graphs. thereby acquiring more accurate topological information for the nodes in the target graph (Zhao et al. 2024 Zhang et al., 2024 Qiao et al. 2023). By leveraging complementary topological information, DELTA is able to better identify candidate nodes with more complicated topological information on the larget graph, which can then be used for active learning.
4.2.1 Edge- orige-oieette Graph Subnetwork
message passing neural networks have been adopted in a large number of graph machine learning tasks Dai et al. 2022) based on neighborhood aggregation. Therefore, we first introduce an edge-oriented graph subnetwork, which aggregates information from the neighboring nodes of each node. The subnetwork can gradually expand the receptive field of the nodes at each layer of the network and thus capture more topological information (Kipf & Welling 2016) in implicit manner. The update rules of the subnetwork at layer I can be expressed as follows:
N = AGGREGATE (INTD:JENN)
:j JENi)). (1) UPDATE (h. (L (I-D.N(-1) h
(3)
(4)
where b1²=1) and No represents the node embedding and neighborhood embeddings at the (1 1)-th layer, respectively. The node roprosentations at each layer are updated through a two-step process. First, the AGGREGATE function collects information from neighboring nodes. This step is typically achieved through matrix operations, which generate new feature representations. Then, the UPDATE function applies a nonlinear transformation to the aggregated information, producing the node features h layer. After stacking Ledge layer, the final node embedding for each node is denoted as Zedge,
(9) for the current
4.2.2 Path-oriented Graph Subnetwork
However, graph data contains high-order structure semantics, and our edge-oriented graph subnetwork is difficult to capture them (Ma et al. 2020 Yo et al. 2024). To solve this, we introduce a path-oriented graph subnetwork, which can explicitly capture the topological semantics of graph from the perspective of path connections (Ma et al.] (020)). In particular, we aggregate information by computing the weighted sum of all possible paths between nodes. These paths consider not only the direct connections between nodes but also the indirect connections and the overall structure of the paths. The path-oriented subnetwork can capture deeper relationships between nodes and the global topological features of the graph. The updated rule of the path-oriented subnetwork at layer / can be expressed as follows:
e A"M 1/2 - W(-)).
H 11 = σ
1/2
(5)
0=
where Dh e fpr A represents the path aggregation and weighted summation, where n denotes the path length ranging from 0 to L (with L set to 3). A" is the n-th power of the adjacency matrix A, indicating the adjacency relationships of nodes at distance of n hops in the graph. e - represents the learnable path weight, determined by the path energy En and the temperature coefficient T. (( the input feature matrix at layer 1-1, 1, w is the weight matrix at layer 1-1, 1, and a(-) the ReLU activation function. After stacking Ledge layers, the final node embedding for each node is denoted as Zpath,s. The inverse square root of the normalization matrix M-1 Diag(M :... / can be defined as:
M; Σ En ("
(6)
where [i,j] returns the corresponding element of the matrix. When n > 1, our path-oriented subnetwork can explore the high-order path-based semantics embedded, which edgo-oriented graph subnetwork cannot explore. The following theorem shows that our path-oriented subnetwork takes all paths with the same length equally but treats paths with different lengths inequally.

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Theorem 4.1. According to Eqn. 5 in the main text, the message passing process of our path-oriented graph
subnetwork is influenced equally by the paths of the same length. Moreover, if Fo # Fn # ... # Er., the paths of different lengths contribute differently.
The proof can be found in Appendix D From Theorem 4.1 our path-oriented graph subnetwork is more
dependent on the path view instead of node attributes. Therefore, it can provide a different view from the edge-oriented subnetwork for topological modeling.
4.2.3 Consistency Delving for Informative Candidate Nodes
The dual graph subnetwork framework allows for the complementary integration of information for the target graph nodes, which are oriented on edges and paths, respectively. Therefore, appropriate aggregation of this complementary information is crucial, as need to select target graph nodes that are rich in complicated edge and path topological information. Typically, target nodes with high inconsistency across subnetworks should have high uncertainty and carry complicated semanties. In our DELTA, instead of simply using nodes with inconsistent predicted classes, we calculate the Euclidean distance between the logit scores Sedge.j = Bedge (Zedge.) and Spath., = Spath (Zpath.5) with two classifiers on the target graph and identify the set of coarse candidate nodes whose Euclidean distance exceeds customizable consistency threshold y as the coarse candidate set T, follows:
d(s d(Sedge.J Spoth.s) = /edge. - Spoth.
(7)
T= {j d(Sedge Spath.) > 7).
(8)
Here, Euclidean distance between two branches can indicate the inconsistency of logic between two branches. Morcover, if two predictions from different subnetworks are inconsistent, the predictions sensitive to the architectures, which indicates the uncertainty of the predictions with rich values to be labeled. Compared to using two identical subnetworks with different parameters to select nodes with inconsistent predictions, the dual graph subnetwork architecture allows us to obtain information about target graph nodes from two different views. This complementary approach enables the capture of more comprehensive node information and identifies target graph nodes with richer information and inconsistent predictions.
4.3 Topological Uncertainty Measurement for Node Selection
In active learning, uncertainty refers to the degree to which the model's predictions are less certain for different samples. By annotating nodes on the target graph where uncertainty is stronger, model performance
can improve (Ma et al. 2024 Sharma & Bilgie 2017 Fuchsgruber et. al.] 2024b. Previous work mainly uses
prediction entropy to measure uncertainty (Cai et al. 2017 Gao et al. 2018 Ren et al. 2022) for each node independently, while they neglect that the information of cach node is highly related its neighborhood. To tackle this, we propose topological uncertainly scores based local subgraphs and degrees to capture topological semantics.
In particular, for cach central node from T of the target graph, we first extract its K-hop subgraph and the logits of each node within it. Instead of directly averaging the logits of the K-hop subgraph, we compute the degree dm of each node in the K-hop subgraph and take the reciprocal as the weight w.. = d.. weighted K-hop logits for each node can be calculated as follows:
1. The
Sedge.j
Σ mcK-hop(/)
Wm Wmdeegen
(9)
Spath.j
Σ
Wm Spathhhhmm
(10)
mEK-hop(j)
where K set 2 empirically (Azabou et al. 2023). The reason behind using the reciprocal of a node's
degree as the weight is that if a node has stronger connectivity (higher degree), its topological information can be inferred from the neighborhood with weaker importance (Fuchsgruber et al. 2024
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Then, we compute the topological uncertainty scores for each node in T as follows:
C
Centropy Dontropy(Beddger (Bedge.)
Σ
ply = -1| bedge.)) log p(Y = 1 Bedge.)),
(11)
C
Pentropy (Spath.))
Σ
p(y =1 $path.,) log P(Y = Spath.))
(12)
where Ecn p(fce = 1 Spath.)) represents the probability that the weighted K-hop logits centered at node j belong to category c.
Finally, each node j from T of the target graph can obtain the topological uncertainty score U, from the dual graph subnetwork:
U₃- = (Bedgay
i) + Pentropy (Spath.)).
(13)
By quantifying the topological uncertainty at the subgraph level, more comprehensive subgraph topological information can be obtained compared to node-based uncertainty. We also integrate the uncertainty scores from both the edge and path levels of the dual graph subnetwork, thereby aiding in the identification of more valuable nodes from different views.
4.4 Domain Discrepancy Measurement for Node Selection
Another obstacle in graph domain adaptation is the distribution differences between the source graph and the target graph (Yin et al. 2023: Yan et al. 2017). Even though several domain alignment approaches have been proposed to reduce the discrepancy; target nodes with high discrepancy with the source nodes would be more difficult for graph domain adaptation approaches (Qiao et al. 2024 to align and thus classify accurately. To this end, we propose domain discrepancy scores, which mcasure the attribute distance between the labeled nodes in the source graph and the candidate node set. T in the larget graph.
Specifically, given the attribute vector x of a target graph node E T, and the attribute vectors x; of nodes in the set of labeled source graph nodes S, we compute the weighted average Euclidean distance between each j and all labeled nodes in the set S. The weights are determined by the degree dj of nodes in S. The domain discrepancy score D; for each target graph node j E T is defined as follows:
Dj = Eiesd; d, |x] xfl12
(14)
S
The reason behind using the degree of nodes in as weights that nodes with higher connectivity in the source graph are more influential in graph domain adaptation. Tn detail, they provide stronger supervision signals, thereby playing more significant role in domain discrepancy scores. This design not only accounts for the differences in node altributes between the source and larget graphs but also considers the topology of the source graph. Consequently, through the active learning process, our model focuses on target graph nodes less related to the source graph, ultimately enhancing the performance of graph domain adaptation.
4.5 Summarization
We combine the topological uncertainty scores U, and domain discrepancy scores D, of the target graph node j E T to compule the composite score: -U
(15)
We first warm up both branches of subnetworks on the labeled source graph. Given the labeling budget k we select the top l nodes on with the highest composite scores for active learning a onc-round manner, which selects the target graph nodes to be labeled in a single round as in (Sener & Savarese 2017). The supervised loss objective is also applied when learning on the target graph additional signal, following
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Algorithm Algorithm of DELTA
Input: Source graph =² = (V*, E X*), labeled source graph set S, target graph G" = (V', E", x'), anno- (ation budget k, consistency threshold 7, K for K-hop subgraph.
Output: Selected target graph nodes for active learning.
1: // DDual Graph Subnetwork Training
Train edge-oriented subnetwork on 9 and g', obtain logits Sedge.j Train path-oriented subnetwork g and g", obtain logits Spath.j-
// Consistency Exploration
5: Calculate Euclidean distance between Sndge, and Spath, for each target node j E V
6: Identify candidate node using Equ.
7: // Topological Uncertainty Measurement
for each node j E T do
Extract the K-hop subgraph centered at j. 10: Calculate topological uncertainty score U; using Eqn. 13
11: end for
12: // Domain Discrepancy Measurement
13: for each node T do
14: Compute domain discrepancy score Dj using Eqn.
14
15: end for
16: // Final Scores Computation
17: for each node 0; T do
18: Compute the composite score using Eqn.
15
19: end for
existing graph domain adaptation frameworks (Qiao et al. 2024p. The whole algorithm is summarized in Algorithm [ and the computational complexity is provided in Appendix D
In summary, the proposed DELTA framework provides novel approach to active learning across graphs. It integrates complementary information from edge-oriented and path-oriented graph subnetworks and delves the inconsistency across two subnetworks for coarse candidate nodes. Then, it combines topological uncer- tainty scores with domain discrepancy scores for fine selection. This combination quantifies the uncertainty at the subgraph level within the target graph and the cross-domain distribution discrepancy between the target and source graphs, which significantly enhances the performance on the target graph with minimal annotation budget.
5
Experiment
5.1
Experimental Settings
5.1.1 Datasets and Metrics
ArnetMiner is a system designed for exploring academic social networks (Tang et al. 2008 We select three citation networks from ArnetMiner: ACMv9 (A), Citationvl (C), and DBLPv7 (D). Each node stands for a paper, and each edge denotes a citation relationship between the two papers. The node attributc is generated from the title followed by bag-of-words model. The selected citation networks, ACMv9, Citationvl, and DBLPv7, each consist of five node categories. More details of the selected datasets can be found in Appendix A
We adopt Micro-F1 and Macro-F1 as evaluation metries Hast et al. 2004 Murphy 2012 Unless otherwise specified, we report the average and variance of the results for the aforementioned metrics over five runs. Higher Micro-F1 and Macro-F1 values indicate better results.

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Table 1:
Summary of the performance of DELTA and baseline algorithms on each benchmark dataset, 5%
nodes of souree datascts are labeled, and 125 nodes of target datasets are labeled by active learning. The mean and variance over five runs are reported. A denotes acmv9, C donates citationyl, and D donates dblpv7. Macro donates Macro-F1, Micro donates Micro-F1. The best and second best are displayed in bold and underlined, respectively.
Methods
A
A-D
D-C
D-A
C-+A
C-D
Average
Maero
Miero
Macro
Micro
Macro
Miero
Macro
Miero
Marro
Miero
Macro
Miero
Marro Miero
GIFI
73.9=1.2
75.910.9
67.940.7
70.920.9
67.0=1.7
69.841.4
63.921.6
63.7+1.2
07.840.9
69/4111
68 241.
70.740.9
68.1
70.1
SGDA
74.2209
76.510.8
68.911.
70.9111
70.120.6
71.2403
65,242.3
6655113
68910.5
70.1=0.7
68.4114
70.811.5
69.3
71.1
Random
75.9=0.9
77.5+0.7
69.7+144
72.6+13
72.3=0.6
71.1004
67.5+100
67,0+100
70,3+0.8
09.3=0.8
70.0=199
72.++111
70.9
72.2
GraphPart
76.0+0.7
77.6+0.6
11.7-0.574.0000
71.5+0.9
73.5+0.44
68.0+0.6
67.3+0..4
71.0+0.7
70.0-0.5
72.1+0.8
74.0+00.7
71.7
72.7
AGE
76.211.4
77.911.3
70.5.11.7
72.111
72.3125
74.112.
68.711.2
68.011.2
70.4110
6..3-0.8
72.811.
74.010.9
11.8
72.7
ANRMAB
7119=10
76.8#088
69.6+1.0
71.900.7
70.7=13
73.0+088
06.6+0.7
66.0+0.6
70,0#0.6
09.0=0.6
69.5#155
71811.1
70.2
71.1
Dissimilarity
76.3+1.4
77.9+1.3
70.0+2.3
72.6+1.9
73.3+19
75.1+16
68.1+0.7
67.5+0.6
69.7+0.8
08.8-05
71.0+23
1..8+
71.4
72.4
Degroe
74.510.9
76.310.8
68.7.11.2
71.1111
71.11.0
78.510.7
66.311.0
65.910.8
68.41044
67.7
70.7.0.6
72.210.3
70.0
71.
Density
74.7+008
76.4400.8
68.840.8
71.7+08
70.6+1.0
72.940.6
66.4+1.2
06.0+
08.9+1.2
68.0-10
69.441.4
71.740.9
09.8
71.1
Uncertaiaty
76.021.2
77.711.2
71.11.
7822122
71811T
73.9115
68.511.7
67.9114
71.210.1
70.3-022
70.113
72.5.1666
71.6
72.6
Proposed
77.3+1.388.911.1 70.442.6
728842.1
74.5+1.1
76.2+0.9
70.9+
70.0
0.7 72.5 0.871.540.77
75.542.075.0-1.44
73.2
74.1
5.1.2 Baseline Algorithms
To validate the effectiveness of our DELTA, we compare it with a range of state-of-the-art baselines including GIFI (Qiao et al.) 2024), SGDA (Qiao et al. )023). GraphPart (Ma et al.) 2023). AGE (Cai et al.) 2017). ANRMAB (Gao et al. 2018), Dissimilarity (Ren et al. 2022). Degree (Cai et al. 2017), Density (Ren et al. 2022 Uncertainty (Settles & Craven 2008) and Random. Random refers to labeling randomly selected
samples with the budget. More details can be found in Appendix B
5.1.3 Implementation Details
We use the GTFT model (Qiao et al. 2024) as the backbone model for graph domain adaption. The hidden channels are set to 512, out channels are set to 256, training epochs are 200, the dropout ratio is 0.1, and the Adam optimizer (Kingma & Bal 2014) is utilized with a learning rate of 0.001, with a weight decay of 1e-4. We adopt GCN (Kipf & Welling 2016 and PAN (Ma et al. 2020) to implement our two subnetworks, respectively. Following previous works (Sener & Savareso] 2017], we adopt a onc-round setting our experiments, which is more convenient in the real world with iteration number 1. For the GCN and PAN, both of them have two layers with di-dimmnnionn node embeddings. The experimental configuration features Linux server powered by NVIDIA A100 GPUs (80GB) and an Intel Xeon Gold 6354 CPU. The software environment includes PyTorch 1.11.0 and Python 3.9.16.
(Paszke et al. 2019
2.5.3 Fey & Lenssen 2019
5.2 Main Experimental Results
To quantitatively demonstrate the performance of our proposed DELTA, we report the results of DELTA and other baseline algorithms across six data combinations in Table [ where 125 target graph nodes are labeled for active learning. From the results, we can observe that: (1) The proposed DELTA consistently outperforms the random selection method for active learning node selection, with an average lead of over 2% across the six data combinations. Note that random selection quite strong with decent performance with a relatively large number of selected nodes. (2) Except for A-D, DELTA consistently outperforms other baseline algorithms, with the performance increasement range from 1.2% to 5% across the six data combinations. In D-+C, D-A, and C-AA, DELTA shows the largest margin, with average lead of over 2%. (3) Bascline algorithms based on uncertainty, or combining uncertainty with other structural metrics, such as Uncertainty, GraphPart, AGE, and Dissimilarity, significantly outperform baselines using only urrultural metrics such as Degree and Density. (4) On average, Micro-Fl is greater than Macro-F1, indicating better classification performance for the larger classes, which reflects the issue of data imbalance. These results demonstrate the superior performance of the proposed DELTA, highlighting its advantage in reducing the annotation cost on the target graph. Notably, DELTA operates in one-round manner for point selection on
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Published in Transactions on Machine Learning Research (02/2025)
DBLPv7 - Citationvl
Citationv1 - ACMV9
73
76
72
Macro-PI
Macro-PI
71
72
68
68
67
25
50
75
100
125
150
25
50
75
100
125
150
Number of nodes for active learning
Number of nodes for active learning
Proposed
AGE
Dissimilarity Degree
Density
Random
GraphPart
ANRMAB
Uncertainty
Figure 3: Performance of proposed method and baseline methods by active learning budget, averaged from different runs. The Macro-F1 scores are plotted.
Table 2: The results of our ablation studies, in which 5% nodes of source datasets are labeled, and 50 nodes of target datasets are labeled by DELTA. The mean and variance over five runs are reported.
Methods
A-C
A-D
D-C
D-A
C-A
C-D
Average
Maero
Miero
Macro
Micro
Maero
Micro
Macro
Micro
Macro
Micro
Macro
Micro
Macro Miero
75.0+1.1
76.9+110
69.1+114
71.8+0.9
72.3+1.1 74.0+1.2
67.54-0.9
67.040.8
70.540.4
69.740..
69.5+-14
71.840.8
70.7
71.8
68.31888
7222389
66.8009 725113 70221111 74.8116
63.615.9
65.11332
68.116
67.611.
63.05..2
68.6130
70.1
75.2+0.4
77.1=033
69.220.6
7188003
717=111
73.5=0.6
66.1+0.9
66.040.9
69.5+0.4
68.820.5
69.7411
71.+1.1
70.3
71.5
14
75.5+1.2
773==11
09320.8
7233003
70.211
73.2=1.4
66.62133
663111
70.12113
69331.1
70.2116
723410
70.4
71.8
Proposed
75.711.277.510.
70.7 73.1 72.11188
74.0.1..3
67.9
1.1
67.2
0.8
70.6.106668
69.7 10.5 71.2. 1.5
71.4
72.4
the target graph in active learning, while AGE, ANRMAB, and Dissimilarity involve iterative point selection, which indicates our DELTA achieves superior performance with lower computational costs.
To investigate the performance of DELTA and baseline algorithms under varying numbers of nodes selected for active learning, visualized the results in Figure D where the number of selected nodes ranges from 25 to 150. From the results, it can be observed that: (1) Regardless of the number of nodes selected for active learning, DELTA consistently oulperforms all baseline algorithnıs.
(2) As the node number increases, DELTA's performance shows a continuous upward trend, and the performance gap between DELTA and other bascline algorithms tends to widen, which further proves the effectiveness performance across the six data combinations with active learning node counts of 100, 125, 150, 175, and 200, please refer to Table A2 in the Appendix, where the conclusions remain consistent.
DELTA. For DELTA's
5.3 Ablation Study
In this section, we introduce several variants to evaluate the effectiveness of different components in DELTA:
(1) VI adopts two edge-oriented subnetworks with different parameters for inconsistency delving; (2) V2 adopts two path-oriented subnetworks with different parameters for inconsistency delving; (3) V removes domain discrepancy scores; (4) V4 removes topological uncertainty scores. Table 2 presents the results of the ablation study, from which we can observe the following: (1) In most cases, the performance of DELTA consistently surpasses that of any of its ablated variants, with DELTA outperforming its variants by approximately 1% average. (2) VI and V/ indicate the use of two edge-oriented subnetworks the use of two path-oriented subnetworks in our dual architecture. These variants do not realize complementary graph information acquisition, leading to less informative nodes in the candidate node set T compared to DELTA, thereby resulting in inferior performance in most cases. (3) V3 refers to the use of only topological uncertainty scores without domain discrepancy scores. This variant underperforms DELTA across all datasets due the failure account for attribute differences between the source and target graphs cross- graph learning, thus neglecting nodes with higher confusion during active learning. (4) V4 represents the use of only domain
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Published in Transactions on Machine Learning Research (02/2025)
DBLPv7 Citationvl
Citationv1 ACMv9
72
Macro-F1
Macro-P
68-
68
25
75
25
300
150
Number of labels for active learning
Number of labels for active learning
Proposed
v1
V2
V3
V4
Figure 4: Performance comparison of ablation study.
DBLPv7 - Citationvl
DBLPv7 - Citationvi
76
75
74
ScoTeS
Scores
73
72
S
72
S
71
71
70
70
0.1
0.2
0.5
0.6
1.5
2.0
2.5
4.5
5.0
Consistency threshold
Number of hops for K-hop subgraph
Macro-F1
Micro-F1
Figure 5: Performance of the proposed method by the consistency thresholds (left) and the number of hops for the K-hop subgraph (right), averaged from 5 different runs. In each higufigure, the Macro-FF Fl and Micro- scores are plotted. 50 nodes are selected for active learning.
discrepancy scores without topological uncertainty scores. This variant also shows inferior results compared to DELTA across all datasets because it fails to consider the uncertainty of the target graph nodes, which severoly degrades the performance. Figure further illustrates the ablation study results when varying the number of nodes used for active learning, and the conclusions are consistent with those in Table 2
5.4 Parameter Sensitivity
In this part, we study the performance with respect to different consistency thresholds y and the values of K. controls the consistency between the dual graph subnetworks, and K is used to calculate topological uncertainty scores in K-hop subgraphs. We first conduct experiments by varying within the parameter space (0.1, 0.3, 0.5, 0.7] while keeping other parameters fixed. Then, we conduct experiments by varying K within the parameter space {1, 2, 3, 4, 5) while keeping other parameters fixed, as shown Figure B. We observe the following: (1) 7 exhibits an upward trend from 0.1 0.5, reaching its peak at 0.5, and then decreases to its lowest value at 0.7. The possible reason for this is that when is too small, the consistency constraint the dual graph subnetworks is too weak, leading to the inclusion of less informative nodes in
T. On the other hand, when 7 is too large, the consistency constraint becomes too strong, reducing the diversity of T. (2) When K is above 2, there is a slight downward trend in performance as K increases, which might be due to the increase in noise within the topological uncertainty scores. This results in the subgraph size becoming too large, thereby diminishing the importance of the central node's logits, leading decreased performance. Thus, we recommend setting y to 0.3 and K 2. Figures AT and A2 in the A Appendix provide further information with similar conclusions.
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Published in Transactions on Machine Learning Research (02/2025)
DBLPv7 - Citationvi
Citationvl ACMv9
80
Scores
70
70
65
60
60
Macro-F1
Micro-F1
Macro-F1
Micro-F1
Metrics
Metrics
GAT
SGConv
TAGConv
Figure 6: Performance of the proposed method by changing the odge-oriented backbones, averaged from 5 different runs. In each sub-figure, the Macro-F1 and Micro-F1 scores are plotted. 50 nodes are selected for active learning.
5.5 Further Analysis
In this subsection, we primarily investigate the generalizability of DELTA from two perspectives. First, we analyze the performance of DELTA when different backbones are employed in the edge-oriented subnetworks. Second, compare the runtime of DELTA with baseline algorithms to assess its efficiency. Third, utilize t-SNE to visualize the differences in the diversity of selected node distributions between the proposed DELTA and two classic baseline methods, Uncertainty (Settles & Craven 2008 and Degree
(Cai et al. 2017
5.5.1 Performance on Different Edge-oriented Subnetworks
It necessary to explore the generalizability of the edge-oriented graph subnetworks under different back- bones. We replace the edge-oriented graph subnetworks with Graph Attention Networks (GAT) (Veličkovid ct al. 2017). Simplifying Graph Convolutional Networks (SGConv) (Wu et al. 2019), and Topology adaptive graph convolutional networks respectively (TAGConv) Du et al. 2017), as shown in Figure These three types of encoders explore graph convolution operations from three representative perspectives, including adaptive weight allocation, efficiency optimization, and topological structures, respectively. We observe the following: (1) The best results are obtained when TAGConv is used as the first odge-oriented subnetwork, while the results are relatively poorer when GAT or SGConv is used as the edge-oriented subnetwork. (2) Overall, even with different backbones for the edge-oriented graph subnetwork, the proposed DELTA still remonst.ratss superior performance, which validates DELTA's 's strong generalizability and the effectiveness of achieving complementary information through different graph subnetworks. For more insights into the generalizability across additional datasets, please refer to Figure A3 in the Appondix, where the conclusions remain robust.
5.5.2 Performance vs Runtime
Figure 7 illustrates the trade-off between runtime and performance for the proposed DELTA compared baseline algorithms. From the results, it be observed that the runtime of DELTA is significantly shorter than that of AGE, ANRMAB, Dissimilarity scores, and GraphPart, but slightly longer than that of Degree, Density, and other remaining baselines. However, DELTA achieves the best performance. The potential reason is that AGE, ANRMAB, and Dissimilarity scores are iterative active Icarning algorithms with high time costs for each iteration (Cai et al. 2017 Gao et al. 2018 Ren et al.) 2022), while GraphPart involves community clustering (Ma et al.] 20233, which also requires a considerable amount of time. In contrast, the proposed DELTA takes only one-fifth of the time of AGE, ANRMAB, and Dissimilarity scores yet outperforms these methods. Figure A4 in the Appendix reports the runtime analysis across more datasets, where the conclusions remain robust.
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Published in Transactions on Machine Learning Research (02/2025)
NCMv3 Clbatoni
Ctatbev] AC369
703
760
Mocco
N45
Time (4)
Time 60)
Proposed
GraphPort
AGIZ
ANRMAI
Dteateslletty
Degrne
Denntly
Uncertainty
Random
Figure 7: Performance runtime of DELTA and baseline algorit 125 nodes selected for active learning.
Uncertainty
Degree
Our method
Class
Selected Indices
Figure ACMv9-DDBLPVT visualization of logits scores output by the domain adaptation model on the target domain using t-SNE, with astcrisks indicating the 50 nodes for active learning.
5.5.3 Visualization
Figure B shows the t-SNE visualization of the differences between the proposed DELTA and two classic basc- line algorithms, Uncertainty (Settles & Craven 2008) and Degree (Cai el. al. 2017) in the ACMv9-DBLPv* setting. From this, we can observe the following: (1) The nodes selected by the proposed DELTA cover each species category and are relatively evenly distributed across the target graph's 's node categories, highlighting the strong diversity of the nodes selected by DELTA. (2) In contrast, the nodes selected by Uncertainty and Degree are concentrated in 1 to 3 categories, with a highly uneven distribution. This contrast visually emphasizes the effectiveness and diversity of DELTA, as the richer the true labels of the nodes selected for active learning in the target graph, the casier it to optimize the semi-supervised loss function in the target graph during graph domain adaptation. The more informative the labeled nodes in the target graph, the greater the improvement in the performance of graph domain adaptation. Figures A5 and A6 in the Appendix show t-SNE visualizations additional datasets, where the conclusions remain consistent with those in Figure
6 Discussion and Conclusion
Active learning for graph domain adaptation is both practical and important due to several key challenges and opportunities. First, annotating graph data is inherently expensive, since graph data is not independent and identically distributed (i.i.d.,, and labeling nodes often requires domain expertise to account for graph structure, significantly increasing the cost (Yin et al.] 2023 Hu et al. 2020). Second, the growing focus on data-efficient learning, driven by sustainability goals and the need to reduce carbon emissions, highlights the importance of maximizing the labeling budget's effectiveness model training through active learning (Cail et al. 2017 Gao al. 2018): Ren al. 22022.. Third, recent unsupervised domain adaptation methods demonstrate limited performance without labeled data in the target graph, where minimal but strategic
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2023 Prabhu et al. 2021 These factors labeling can substantially improve results QQao et al. 2024 underscore the practicality and necessity of active learning in this context.
Therefore, in this paper, we investigate the problem of active graph domain adaptation and propose new approach named DELTA for this problem. Our DELTA consists of an edge-oriented graph subnetwork and a path-oriented graph subnetwork to explore topological semantics from complementary perspectives, and then selects target nodes with high inconsistency as candidate nodes. Then, DELTA combines both node degree and K-hop subgraphs to explore topological uncertainty for each node. It also calculates degree-weighted discrepancy scores to focus target nodes differently from source nodes for fine selection. Extensive experiments on various benchmark datasets demonstrate the effectiveness of our DELTA. In future work, we will extend our DELTA to more generalized problems, such as open-set graph domain adaptation, and utilize large language models to mitigate the annotation burden.
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Published in Transactions on Machine Learning Research (02/2025)
A Detailed Description of Datasets
Table A1 presents the descriptive statistics of acmv9, citationvl, and dblpv7. There are significant differences among the three graphs: acmv9 has the largest size (9,360 nodes and 15,602 edges), citationv has the highest average degree (1.691), and dblpv7 has the smallest graph size and the lowest average degree (5,484 nodes, 8,130 edges, average degree of 1.482). Regarding the node calegory ratios for the three graphs, the second category (Networking) is the most prevalent, while the fourth category (Information Security) is the least reprosented.
Table A1: The summary statistics of six graphs.
Datasets Node Number Edge Number Class Number Average Degree
ACMv9
9,360
15,602
5
1.667
Citationvl
8,935
15,113
5
1.691
DBLPv7
5,484
8,130
5
1.482
B
Baseline Algorithms
GIFI. GIFT is state-of-the--rt semi-supervised graph domain adaptation method, which employs varia- tional information bottleneck to keep the crucial semantics in the graph data (Qiao et al. 2024).
SGDA. SGDA utilizes an adversarial manner with shift parameters to align the distribution across different
domains (Qia et al. 2023
GraphPart GraphPart first parities the target graph into communitics. Then, it runs the K- K-means algorithm on each community and selects the node closest to the cluster center for labeling (Ma et al. 2023
AGE AGE calculates the information entropy, information density, and graph centrality for each node in the target graph, lincarly combines these metrics, and selects the node with the highest combined score for labeling (Cai et al. 2017
multi-armed bandit algorithm to weigh and combine the three metrics of AGE and selects the node with the highest combined score for labeling (Gao et al. 2018
ANRMAB ANRMAB
Dissimilarity. Dissimilarity scores build upon AGE by introducing the feature dissimilarity score (FDS) and structure dissimilarity score (SDS). These scores are lincarly combined, and it labels nodes with the highest combined scores (Ren et al. 2022
Degree. Selects the node with the highest degree centrality in the target graph for labeling (Cai et al. 2017 Ren et al. 2022
Density. Runs K-means on the hidden representations of the target graph nodes and selects the node with the highest density score for labeling (Cai et al.) 2017 Ren al. 2022).
Calculates the entropy of cach node and selects the node with the highest entropy for labeling (Settles & Craven 2008)
Uncertainty.
Random. Randomly selects nodes uniformly across the target graph for labeling.
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Published in Transactions on Machine Learning Research (02/2025)
C More experiments
In this section, we extend the experiments presented in the main text. First, we expand the comparison with baseline algorithms by using 100, 125, 150, 175, and 200 nodes for aclive learning to explore the elfectiveness of the proposed DELTA. Then, we report the parameter sensitivity experiments, generalizability experiments, runtime vs performance analysis, and visualization analysis on the complete dataset combination.
C.1 Performance Comparison
we report the comparison between the proposed DELTA and baseline algorithms when the number of nodes selected for active learning is set to 100, 125, 150, 175, and 200. From the results, we can observe the following: (1) On average, DELTA consistently outperforms all bascline algorithms. This further highlights the effectiveness of the proposed DELTA. (2) As the mumber of nodes selected for active learning increases, the performance gap of DELTA widens, from an average of 1-4% with 100 nodes to an average of 2-6% with 200 nodes. This indicates that DELTA performs better in medium to large-scale active learning tasks. (3) As the number of selected nodes increases, baseline methods based on community partitioning, such as GraphPart, and combined metrics, such as AGE, ANRMAB, and Dissimilarity, gradually fall behind simpler bascline methods based on single metrics, such as Uncertainty. The underlying reason that as the number of selected nodes increases, the internal clusters within these methods become smaller, leading to a loss of node representativeness.
In Table A2
C.2 Ablation Study
Table A3 presents additional ablation studies, where V5 denotes the removal of the dual subnetwork and its consistency-based strategy for identifying informative candidate nodes, leaving only a single edge-oriented graph network. Similarly, V6 represents the removal of the dual subnetwork and its consistency- based strategy, retaining only single path-oriented graph network. From Table A3 we can observe that the proposed DELTA method still significantly outperforms V6 and, on average, exceeds both V5 and V6. On the A-C and D-C tasks, DELTA slightly lags behind V5. A possible explanation for this is that DELTA focuses on identifying nodes with strong prediction inconsistency between the two subnetworks, potentially overlooking some valuable nodes for active learning whose predictions are consistent across the subnetworks, thus causing DELTA to neglect. them.
C.3 Parameter Sensitivity
Figure AT and Figure A2 report the results on the complete set of six dataset combinations for different values of 7 in the parameter space {0.1, 0.3, 0.5, 0.7] and K in the parameter space {1, 2, 3, 4, 5), respectively. From Figure A1 we can observe that the overall performance significantly declines when y exceeds 0.5, while the results are relatively better when y is between 0.3 and 0.5. This further validates our recommendation in the main text, suggesting that be set between 0.3 and 0.5 to achieve a balance between the richness of topological complementary information and node diversity. From Figure A2 we can observe that DELTA achieves optimal performance when is set to 2, which is consistent with our suggestion in the main text. We recommend sctting K between 1 and 2 to balance the richness of subgraph information while prescrving the contribution of the central node in the K-hop subgraph to topological uncertainty.
C.4 Further Analysis
Figure A3 and Figure A4 respectively report the results of DELTA when varying GNN encoders the complete set of six dataset combinations and the performance vs. runtime results on ACMv9 DBLPv7-ACM*v, and Citationv1+DBLPPZ. The results in Figure A3 are consistent. with the observations in the main text, where TAGConV performs the best when replacing the edge-oriented graph subnetwork. Overall, when changing edge-oriented encoders, the performance remains strong comparison to most bascline algorithms. This further demonstrates the effectiveness of the proposed DELTA framework. From Figure A4 we can also observe the same conclusions in the main text: the proposed DELTA's 's time cost
21

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ACMv9 Citationvl
ACMv9 DBLPV7
DBLPv7 Citationvi
76
74
78
Scores
Scores
Scores
74
76
68
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Consistency threshold
Consistency threshold
Consistency threshold
DBLPv7 - ACMv9
Citationvl - ACMv9
Citationvl -DBLPv7
74
71
Scores
Scores
68
70
68
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Consistency threshold
Consistency threshold
Consistency threshold
Macro-F1
Micro-F1
Figure Al: Performance of proposed method by the consistency thresholds, averaged from different runs. In each sub-figure, the Macro-F1 and Micro-F1 scores plotted, the number of hops is set to 2, and 50 nodes are selected for DELTA.
ACMv9 Citationv1
ACMv9 DBLPv7
DBLPv7 Citationvl
Scores
78
Scores
Scores
74
77
72
72
76
Number of hops for K-hop subgraph
Number of hops for K-hop subgraph
Number of hops for K-hop subgraph
DBLPv7 - ACMv9
Citationv1 - ACMv9
Citationv1 - DBLPv7
74
71
Scores
68
scores
Scores
72
67
69
66
1.0
2.5
1.0
2.5
4.0
1.0
2.5
Number of hops for K-hop subgraph
Number of hops for K-hop subgraph
Number of hops for K-hop subgraph
Macro-F1
Micro-F1
Figure A2: Performance of proposed method by the number of hops for K-hop subgraph, averaged from 5 different runs. In each sub-figure, the Macro-F1 and Micro-F1 scores plotted, consistency thresholds set to 0.3, and 50 nodes are selected for DELTA.
22

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Published in Transactions on Machine Learning Research (02/2025)
Table A2: Summary of the performance of active learning methods on each benchmark dataset, in which 5% nodes of source datasets are labeled, and 100, 125, 150, 175, and 200 nodes of target datascts are labeled by DELTA, respectively. The mean and variance over five runs are reported. A denotes acmv9, C donates citationvl, and D donates dblpv7. Macro donates Macro-F1, Micro donates Micro-F1.
A-C
A
D-C
D-A
C-A
C-D
Average
Methods
Macro
Micra
Macro
Micro
Macro
Micro
Marro
Micro
Macro
Micro
Macro
Micro
Marro Micro
100 nodes ure selected for active foorning
GraphPart
76.020.3
778820.2
72.1=0.8
74.
71.420.9
73.3209
67.820.3
67.240.1
70.320.5
69.4-0.5
71422088
73.7=0.5
11.5
72.6
AGE
76.4+1.3
78.0+1.2
09.7+119
72.1+14
71.2=0.6
73.3+0.6
08.2+1.0
67.7+0.9
70.4+0.7
09.5=0.5
71.+1.11
73.1+0.6
71.2
72.3
ANRMAB
74.6:10.7
76.440.6
68.7400.7
71.2408
69.3:14
71.541.3
65.841.0
65.411.7
70.410.6
69.5-0.5
68.6:19
71641.3
69.5
70.9
Dissimilarity
75.8+114
17.5+1.3
70.042.6
72.5+2.1
71.1-24
73.142.
65.7+1.6
65.5+1.3
70,240.8
09.1-08
71.742.7
73.5+2.
70.8
71.8
Degroe
74.210.8
75.9.10.7
68.311.
71.11.2
69.912.
723111.1
64.9.0.5
64.810.4
67.810.7
67.2-0.7
70.211.
723100.4
69.2
70.6
Density
71.2=0.7
76.240.8
69.8209
724410
69.3214
7188
65.620.7
65.240.8
68.520
67.8-077
69.3#13
81.20077
69.5
70.9
Uncertainty
26.0++10
27.8+0.9
70.3+1.5
12.7413
71.9-08
73.8+1.1
07.5+188
67.1
703+0.8
09.4-08
09:2:115
71.740.9
70.9
72.1
Random
75.3100.
77.010.7
69.6.1.6
7..51.4
71.310.5
73.2.0.7
67.1106
06.6.0..
70.4.111
6..4
68.9.122
716.0..5
70.4
71.T
Proposed
77.2:1.278.9111.2
77.2:1.2
78.911.2
69.91222
12511
74.122.3
76.0
08.4:1.96..711.
71.9-0.9
71.9-0.900.810..
70.810.7
711128
733118
72.1
73.2
185 nodes are solexted for action foorning
GraphPart
76.0=0.7
77.640.6
71.7=0.574.0-00
71.5=0.9
73.5+04
08.0
67.3+0.4
71.0+0.7
70.0=0.5
72.1=0.8
74.0+0.7
71.7
72.7
AGE
76.2+1.4
17.9+11.3
70.5++1.7
72.7+-.3
72.3+25
74.142.1
6.
08.0+1.2
70.4+1.0
69.3 0.8
72841.1
74.0+0.9
71.8
72.7
ANRMAB
74.911.0
76.8.00.8
69.611.0
719110.
70.7113
73.010.8
66.610.7
66.010066
70.0106
0.60
69.5.115
71811.1
70.2
71.4
Dissimilarity
76.3=114
77.9+1.3
70.042.3
72.6+19
73.3=19
75.1+16
08.1
67.5+06
69.7
08.8=05
71.0223
72 1.5
71A
72.1
Degree
74.520.9
76.320.8
68.71112
713111
71.411
78.520.7
66:3110
65.9408
68.4
67.7-05
70.720.6
72.210.3
7000
71.
Density
74.7=0.8
76.4+0.8
68.8+0.8
71.7+08
70,6=10
72.9+0.6
06.4+12
66.0+11
68.9+1
68.0-10
09.414
71.+0.9
69.8
71.1
Uncertainty
76.0+112
77.7+1.2
71.041.5
73.241.2
7188+17
73.9+1.5
6.7
67.9+14
71,240.1
70.3-02
70.8+1.
72.540.6
71.6
72.6
Randon
75.920.9
77.520.7
72611.3
72.3206
74.1104
67.510
67.0110
70.0199
72.11.1
70,9
72.2
Proposed
78.99117
70.1422.6
72.842.11
71.5#1.1
76.2=0.9
00.9+0.900.0:00
72.6=0.8
71.5+0.7
15.3+22.77500111
73.2
74.1
150 nodes are selected for actire lourning
GraphPart
76.5+0.6
77.9+0.55
71.9-1.374.3-11
1.2
72.0+0.5
73.7+0.6
68.3+0.5
67.8+0.44
70.
10.14005
0..
71.7+0.9
74.3+0.3
71.7
72.8
AGE
75.411.1
77.11.0
72.711.7
74.7.18
68.8
68.110.
69.7
710128
79.111.5
71.5
72.6
ANRMAB
75.7=0.7
77.10077
69.3::.1
71.81:1
7100=10
73.1
68.1+16
65.7+144
70.5+12
69.3=10
68.6119
71.11.11
70.2
71.5
Dissimilarity
76.5+114
78.1+1.2
70.2+1.9
72.7+1.7
73.5+13
75.4+088
67.1+188
66.7+1.7
70.7+0.7
09.-007
09.1+23
71.
71.2
72.4
Degroe
74.810.7
76.5.10.6
68.7.11.3
7131112
72.7112
66.31044
66.010.2
68.40..4
67.8
71.01.88
725..0.7
69.9
71.1
Density
75.2++0.7
76.9++0.6
70.0+1.1
728+008
70.3+1.2
72.6+0.5
66.0+144
65.6+1.2
08.64088
678-08
70.3+1.6
72.6+1.0
70.1
71.4
Uncertuiaty
75.5.11.6
77.5.1.0
71.21111
73311.0
73.1112
75.111.1
68.9113
68.11111
71.1110
7.220.9
719126
78.5.1.7
71.9
73.0
Random
76.220.8
77.82066
70.5+11.
73.4+1.
72.1=11
71.020.7
67.8008
67.240.7
70.1+12
192-12
70.4119
82.
71.2
72.1
Proposed
77.5+1.5
79.1+1.2
715+2.7
73.8+2.3
76.6+16677.3112
70.242.1
69.3+1.8
12.2-0.871.11
72.042.5
7.
73.2
74.1
175 nodes
selected for actice learning
GraphPart
76.7.00.8
78.2.10.7
0.4 75.2.0..75...000
73.0
71.7.0.8
73.5.0.66
68.0.1..7
67.210.77
70.9.00.7
70.1
71.9.1.1
73.9.10.7
72.0
73.0
AGE
76.2#1.6
77.91144
70.5122
72.9220
73.1-2.5
748422
66.412.1
66.11188
70.5110
69.
73.610.8
7..7
71.7
72.6
ANRMAB
75.6=1.2
1.1
6..5+1.5
71.9114
72.40077
74.1
1.00
67.2+0.9
7088+0
098-099
70.2+2.2
7.
71.1
72.1
Dissimilarity
75.9-12.0
7.77+
69.812.4
7..41..8
74.8
76.240.7
67.8
67.31277
70.610.9
69.6-0.6
70.243.5
72.712.3
71.5
72.6
Degroe
74.6220.8
76.410.7
69.5115
720011
7122209
73.410.5
65.920.5
65.610.4
686610
0..9
69.320.88
72.000.
69.9
71.2
Density
75.0=0.9
76.7#0.8
69.7420
72.4+17
69.6=13
72.240.8
8500
66.540.9
688403
08
70.1=2.0
724+14
69.8
71.2
Uncestainty
77.4+1.5
78.9++1.
70.44288
72.742.0
73.9+15
75.6+1.4
68.3+244
07.7+2.1
72.0+0.8
71.0 0.8
73.2+17
7..3+1.3
72.5
73.4
Random
76.3=1.2
78.0+1.1
69.84233
72.8+19
72.2-16
74.1114
07.0+1.0
66.640.9
11.
10.1-04
70.7+112
73.240.7
71.2
72.4
Proposed
77.411.879.111
72.2129
74.1125
74.2.19
76.2
70.4
73.5
0..40..
728812.1
74.4117
73.4
200 nodes are selected for octive feorning
GraphPart
76.7+005
78.3+0.4
1..5+1.4
74.7+110
71.8+14
73.8+1.11
08-2+0.9
67.4+0.8
71.3+0.8
70.2-0.7
72.4+1.1
74.2+00.9
72.2
73.1
AGE
75.9=1.7 77.6+1.6
71.042.0
73.2+1.6
72.8-17
744+1.
08.3
67 67.6
70.2+12
69.2-111
71.4226
73.241.7
71.6
72.5
ANRMAR
75.7++0.8
77.5+0.7
69.94-1.6
72.5+133
71.5+22
73.5+1.5
67.24133
66641.2
71.3+05
70.2 0.6
70.2+1.9
7.33+1.4
71.0
72.1
Disimilluiity
76.51112
78.211.1
70.312.4
72.9188
73.2115
74.81144
68.5
67.910.7
71.2111
70.2-08
73.111.1
7431077
72.1
73.1
Degree
711620.7
76.120.7
69.24188
71.6+1.5
71.520.
73.520.6
66.02044
65.740.1
08.540.
67.9-077
70.2-0.9
72.240.7
70.0
71.2
Donsity
74.7+007
76.6++0.6
69.6++.6
72.4+13
60.1+2.1
71.440.9
05.5+1.2
65.3+1.0
00.140.4
08.3-05
71.140.8
73.140.6
00.9
71.3
Uncortainty
75.911.11
77.8.11.6
70.713.1
72.9120
74.811.0
76.3.0..8
69.4
08.8106
72.41..1
0.4
71412.
73.21188
72.4
73.4
Random
76.520.9
78.120.9
7166112
74.0088
72.5110
71321.1
68.2209
67.5208
7088114
69.91.0
70.0220
72.641.
71.6
72.T
Proposed
2..7200.600211..
744:1175.9911
73.611.3
75.411.3
70.511.669.7115
73.5
7.2.5.0.
73.813.0
75.422.4
74.1
74.9
is only one-fifth to one-sixth that of AGE, ANRMAB, and Dissimilarity, while it only takes about 10 to 20 seconds more than other bascline algorithms. Nevertheless, DELTA achieves the best performance.
Figure A5 and Figure A6 respectively report the I-SNE visualization results of the proposed DELTA com- pared with Uncertainty and Degree centrality on ACMre-+Citation and DBLPY7-ACMM* From Fig- ure A5 and Figure A6 we can observe the same conclusions as in the main text: DELTA achieves a more balanced and diverse selection of target graph nodes. In contrast, the nodes selected by Uncertainty and De- gree centrality are concentrated in 1-2 categories, and this imbalanced node distribution significantly reduces
23

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Published in Transactions on Machine Learning Research (02/2025)
ACMv9 Citationv1
ACMVS DBLPV7
DBLPY7 Citationvl
85
85
85
80
Scoress
Scores
65
60
60
60
Mecro-F1
Micro-F1
Macro-F1
Micro-F1
Mecro-F1
Micro-F1
Metrics
Metrirs
Metrics
ACMv9
Citationvl
Citationvi DBLPv7
85
85
85
80
80
80
Seorgs
75
Scores
75
75
60
Metrics
Metrirs
Metrics
GAT
SGConv
TAGConv
Figure A3: Performance of proposed method by changing the GNN backbones, averaged from 5 different muns. In each sub-figure, the Macro-FI and Micro-F1 scores are plotted. 50 nodes are selected for DELTA.
77.0
70
Mocro-F
Macro-F1 F3
89
Macro-FI
75.5
88
75.0
102
102
16:
10a
Time Disstmllarity
Proposed
GraphPart
AGE
ANRMAR
*
Degres
Density
Uncertainty
Random
Figure A4: Performance vs. runtime of DELTA and baseline algorithms, in which 125 nodes are selected for DELTA.
24

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Published in Transactions on Machine Learning Research (02/2025)
Table A3: The results of our ablation studies, in which 5% nodes of source datasets are labeled, and nodes of target datascts are labeled by DELTA. The mean and variance over five runs are reported.
A-C
A-D
D-C
D-A
C-A
C-D
Average
Methods
Macro
Micro
Macro
Micro
Macro
Miero
Macro
Micro
Macro
Micro
Macro
Micro
Macro Micro
V5
76.420.5 78.0+004 69 01114118811 72.320.5 74.020.5 d6 06.94115 66 4:1.2 09.540.9 780.5 10.3
70.7
71.9
V6
74.6445 62.545.3 70.142.4 68.345.0 74.422.
67 240.7 67 040.7 07.243.6 07.0=3.0 10.3:3.771.222
66.8 70.7
Proposed
75.7 70.741.5 73.1=11.0 72.1#1874.011
67.941.1 67 210.8 70.620.6
69.720.5
71.2415 73.1
71.4 72.4
Uncertainty
Degree
Our method
Class 1
Class 2
Class
Class
Class
Selected Indices
Figure A5: ACMvS->Citations visualization logits scores output by the domain adaptation model on the target domain using t-SNE, with astorisks indicating the 50 nodes for active learning.
the effectiveness of active lcarning. In comparison, DELTA's more uniform selection qualitatively provides evidence for the superior performance achieved by the proposed DELTA.
D Computational Complexity Analysis
Assume V represents the average node number in the input graph, E represents the average edge number in the input graph, and d is the hidden dimension. Calculating the K-hop subgraph has time complexity of O(E+V). Computing the K-hop subgraph for each node results in a total time complexity of ((V(E+V)). Averaging the logits for each subgraph node has a time complexity of O(Vd). Calculating the softmax for logits and subgraph logits has a time complexity of O(vd).
Considering the above steps, the overall time complexity for the uncertainty computation process can be expressed as:
(1 VV Vd) OVV(E 2V = O(V(E +V d)).
E
Proof of Theorem 4.1
Proof. We have
A" Σ Ai, Ak
(16)
kin An-1
Note that (i, ki, ... kn-2, kn kn-1 a random walk with ni Afi of Alk,,k)==... A |n 1. Therefore,
=
A [i
Σ
Aa Jexesssssss pexistss
(17)
k 16-1
25

---

Published in Transactions on Machine Learning Research (02/2025)
Uncertainty
Degree
Our method
Class 1
Class 2
Class 3
Class 4
Class
Selected Indices
Figure A6: DBLPV7-ACCM9: visualization of logits scores output by the domain adaptation model on the target domain using I-SNE, with asterisks indicating the 50 nodes for active learning.
We set the message passing matrix in Eqn. to be S En 3 A", which directly influences the path-oriented subnetwork. Then, we have
S
[i
Σ (iiks 1.
(18)
n=0
k An-1
From this, we can tell that every path with the same length contributes equally to the message passing Es
matrix Sh, and the weight for paths of length n is which finishes our proof.
7
26


Reviews:
[{"review_id": "LDAv1oTMmO", "reviewer": "Reviewer_6FHH", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "## Strengths\n- The paper is very well structured and procedurally developed to explain the methodology. The modularity of the methodology is very well maintained. The formulation of the idea is properly expressed in a simple manner that helps the reader to easily follow the paper.\n\n- The literature review is instructive and insightful. \n\n- The results on the ablation studies and parameter sensitivity sections are supportive.\n\n## Weakness\n- The major weakness is a lack of empirical evidence to support the hypothesis. It is approaching the lower bound to verify if the hypothesis is indeed supported according to the argued claims. Stronger and more convincing empirical studies and analysis would indeed provide more confidence to validate the hypothesis.\n\n- There are some unclear aspects of the methodology that needs elaboration and justification. They are mentioned in the \"Requested Changes\" section.\n\n- In section 4.2.3, the motivation behind why a Euclidean measure of distance between the two pathways is informative for the selection of the candidate nodes on the target graph is missing. It is not clear why the measure leads into \"richer information and inconsistent prediction\". It seems subjective and lacks proper qualitative definition and abstraction. Additionally, it is not clear if this process is applied to the source or target graphs or both and then how they are used later for the downstream modules in the framework.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The summary of the contributions of the paper is as follows:\n\n- The paper addresses active graph domain adaptation, focusing on improving performance on target graphs with limited semantic information.\n  \n- The problem is complicated by topological complexity and distribution discrepancies across source and target graphs.\n\n- The paper introduces *DELTA* (Dual Consistency Delving with Topological Uncertainty), a novel approach combining two encoding pathways to select informative target nodes by ensuring consistency across both subnetworks:\n  - **Edge-Oriented Subnetwork**: Uses message-passing to capture neighborhood information.\n  - **Path-Oriented Subnetwork**: Explores high-order relationships by analyzing substructures.\n  \n- It then aggregates local semantics from the K-hop subgraph of each node, weighted by node degrees, to estimate topological uncertainty. Additionally it compares target and corresponding source nodes to compute discrepancy scores for finer selection. The two scores are added for the final selection of target node selection for updating the model parameters and iterate.\n\n- experiments show DELTA outperforms existing state-of-the-art methods on citation 3 networks.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Based on the aforementioned strengths and weaknesses, the requested changes are provided below:\n\n- Overall, it is elusive from time to time to follow which of the two source or target graphs the authors refer to when they talk about nodes. Lack of proper notation and elaboration. For instance 4.2.3 it is unknown until the end of the section when it becomes clear the two sub-networks are applied to the target graph. Clarification and disentanglement is needed.\n\n- in Algorithm 1, it is unclear why step 2 and 3 are applied to the source graph. It is not clear how s_each and s_path on the source graph is utilized in the algorithm down the road. Elaboration is needed.\n\n- In section 5.5.1, the motivation behind the choice of the graph encoder backbones is not clear. \n\n- In the experimental setup, the information on the number of iteration and the procedure to predict the labels on the target graph is missing. Please fill out the missing information.\n\n- What does the following mean \"active learning in a one-shot manner\". Elaboration is helpful to help the reader follow the methodology.\n\n- In section 5.1.3, what is GIFI model? Additionally, for reproducibility purposes details on the hyper-parameters of the GCN and PAN encoders are missing (e.g. number of layers, number channels etc). Additionally, open sourcing the code will help the community to expand the methodology.\n\n- \"we one-shot select the top\" needs correction in 4.1.\n\n- What is consistency fusion in Figure 2? where is it explained? Additionally, the figure may need to be revisited to clarify if the source graph is the input to the two pathways?", "broader_impact_concerns": "There are no \"Broader Impact Concerns\" for this paper.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "QcglnGFSPp", "reviewer": "Reviewer_jbPu", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths \n\n- Studying graph domain adaptation in active learning settings is an important attempt as it could have high relevance to many applications at industrial level.\n- The proposed model, DELTA, is intuitively strong and innovative.\n- The ablation studies and sensitivity analysis are rich, and the interpretation of results is insightful.\n- The paper is exceptionally well-written.\n\nWeaknesses\n\n- The importance and innovation in studying graph domain adaptation in active learning settings is not emphasized enough.\n- The distinction between the theoretical roles of edge-oriented and path-oriented subnetworks is slightly unclear to me. Specifically, for any given node a two-layer MPNN as edge-oriented subnetwork involves information from neighbours at a distance of two at the final layer, like a path oriented subnetwork with $L=2$ in Equation (5). Existing GNNs can be viewed as a special case of path oriented convolution [1]. Although empirically shown to perform well, this raises questions about specific usage of edge and path oriented networks for discrepancy measurement at a theoretical level.\n- Many state-of-the-art graph domain adaptation models do not operate on active learning setting, thus may not be directly comparable to the proposed model. Having said that integration of various backbones used for domain adaptation for comparison purposes could be relevant.\n- Given the fact that the proposed method is only empirically proven to perform better than existing methods, it is very important to provide source code. Though I could not locate a public repository or supplementary material that could ensure reproducibility.\n\n[1] Zheng Ma, Junyu Xuan, Yu Guang Wang, Ming Li, and Pietro Lio. Path Integral Based Convolution and Pooling for Graph Neural Networks. arXiv preprint arXiv:2006.16811, 2020.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper studies active graph domain adaptation problem where there is 1) a partially labelled source graph and 2) an unlabelled target graph. The aim is identifying a set of nodes on target graph to acquire the true labels for under a limited budget and thus enhancing the overall classification performance on target graph. The proposed model, DELTA, consists of two sub-networks, 1) an edge-based and 2) a path-based GNN, learned by existing supervision of  labelled source nodes and evaluated both on source and target domains. The estimated logits are utilized to identify a set of candidate nodes on target domain that have high inconsistency between two sub-networks. The evaluated inconsistencies are further adjusted by neighbourhood sizes of nodes at different hobs.  The domain discrepancy is evaluated by comparing the source and target domain on node feature space, but the structural properties are again incorporated by first-hob neighbourhood sizes of source nodes. DELTA is evaluated on a set of benchmark datasets and shown to perform better than active graph domain adaptation baselines.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "- I think for this type of work it is very important to share implementation, so would be great if authors can provide source code as supplementary material or share a public repository at camera-ready version if accepted.\n- The baseline methods can to be broadened to include ideas from state-of-the-art graph domain adaptation methods. The active learning counterpart of following method could be important to compare to if possible:\n    - Ziyue Qiao, Xiao Luo, Meng Xiao, Hao Dong, Yuanchun Zhou, and Hui Xiong. Semi-supervised domain adaptation in graph transfer learning. arXiv preprint arXiv:2309.10773, 2023.\n- A theoretical explanation is needed to distinguish the contributions of edge-oriented and path-oriented subnetworks to topological modelling  would be insightful.\n- Minor:\n    - It would be useful to formalize the inverse square root of the normalization matrix in Equation (5) to improve the precision and reproducibility of the method.\n    - I believe this paper is listed twice:\n        \n        Ziyue Qiao, Xiao Luo, Meng Xiao, Hao Dong, Yuanchun Zhou, and Hui Xiong. Semi-supervised domain adaptation in graph transfer learning. arXiv preprint arXiv:2309.10773, 2023a.\n        \n        so the list of references may need a double check.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "r3UmgD4vOr", "reviewer": "Reviewer_czq2", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\nAchieves competitive scores compared to state-of-the-art methods.\n\nIntuitive and well-designed experiments.\n\nQuestions and Weakness:\n\nQ1: Chapter 4.2.1 describes the edge-oriented graph subnetwork, and Chapter 4.2.2 explains the path-oriented graph subnetwork. What is the difference between these two structures when n=1 for path-oriented graph subnetwork? Is the update formula combining Eq. (3) and Eq. (4) a special case of Eq. (5)? Is this a redundancy between these two structures? \n\n\nQ2: The paper introduces a dual-structure approach without explicitly illustrating the advantages of this structure over using only one graph.  Table 2 includes an ablation study with two edge-oriented graphs or two path-oriented graphs. However, it is unclear whether using a single graph (edge-oriented or path-oriented) would produce similar results.\nYou can provide comparisons on one dataset to demonstrate the advantages of dual-structure graphs here, and you should discuss more in the camera-ready version.\n\n\nQ3: In Table 1, \"random\" appears to refer to randomly selecting labels. Can you explain why \"random\" achieves surprisingly high F1 scores? I see GIFI[1] has lower scores in several datasets (e.g., A→C macro/micro, A→D micro)?\n\nQ4: Missing GIFI[1] Scores in Table 1 since the paper mentions GIFI is currently the latest and most advanced graph domain adaptation model.\n\n[1] Ziyue Qiao, Meng Xiao, Weiyu Guo, Xiao Luo, and Hui Xiong. Information filtering and interpolating for semi-supervised graph domain adaptation. Pattern Recognition, 153:110498, 2024.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces a novel method for graph domain adaptation tasks. This approach leverages two complementary subnetworks, an edge-oriented graph subnetwork and a path-oriented graph subnetwork, and two loss functions, domain discrepancy measurement and final score computation.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please answer the questions above, especially Q1 and Q2.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper works on active graph domain adaptation and proposes a method called DELTA that uses two encoding pathways to select informative target nodes by leveraging their inconsistencies, where the edge-oriented subnetwork/pathway uses message-passing to capture neighborhood information, and path-oriented subnetwork/pathway makes use of high-order relationships by analyzing substructures. It aggregates local semantics from the K-hop subgraph of each node, weighted by node degrees, to estimate topological uncertainty. Experiments show the efficacy of the proposed DELTA.

All three reviewers questioned the less convincing empirical evidence supporting claims made in the paper, in particular the (empirical and/or theoretical) evidence justifying the parallel design of the edge- and path-oriented subnetworks for complementary effects. The authors responded by 1) adding ablation studies, where results show that use of both the two subnetworks slightly improves the performance, and 2) a theoretical analysis on paths of different lengths contribute differently on learning (Theorem 4.1 in the revised paper). Reviewers are also concerned with other points including the less clear technical presentation of the method, the necessary motivation on the importance of the studied problem, and why the very baseline of the Random method performs quite well. The authors responded with clearer presentations. Two of the three reviewers lean to accept while reviewer czq2 favors negatively. AE agrees with the reviewers on the point that the benefits of parallel subnetworks are not justified enough; however, given completeness of the presented method and empirically verified method, the paper can be accepted according to TMLR criteria. Given acceptance, the authors need to make public their implementation and codes, since the current link has expired already. 

The authors please prepare the final version including all the revisions made in the review process, and an official webpage making public the implementation details and codes.
Decision: Accept (poster)