This work considers a practical semi-supervised graph anomaly detection (GAD) scenario, where part of the nodes in a graph are known to be normal, contrasting to the extensively explored unsupervised setting with a fully unlabeled graph. We reveal that having access to the normal nodes, even just a small percentage of normal nodes, helps enhance the detection performance of existing unsupervised GAD methods when they are adapted to the semi-supervised setting. However, their utilization of these normal nodes is limited. In this paper, we propose a novel Generative GAD approach (namely GGAD) for the semi-supervised scenario to better exploit the normal nodes. The key idea is to generate pseudo anomaly nodes, referred to as 'outlier nodes', for providing effective negative node samples in training a discriminative one-class classifier. The main challenge here lies in the lack of ground truth information about real anomaly nodes. To address this challenge, GGAD is designed to leverage two important priors about the anomaly nodes -- asymmetric local affinity and egocentric closeness -- to generate reliable outlier nodes that assimilate anomaly nodes in both graph structure and feature representations. Comprehensive experiments on six real-world GAD datasets are performed to establish a benchmark for semi-supervised GAD and show that GGAD substantially outperforms state-of-the-art unsupervised and semi-supervised GAD methods with varying numbers of training normal nodes. Code will be made available at https://github.com/mala-lab/GGAD.
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Summary
This paper works on node anomaly detection in the novel semi-supervised setting where few labeled normal nodes are given and proposes to generate new anomaly nodes to boost the training data. The anomaly generation algorithm is inspired by the empirical observation that: (1) Anomaly nodes have lower affinity score than normal nodes (2) Feature distribution of anomaly nodes are similar to normal nodes if they share similar neighborhood patterns.
Strengths
(1) The setting is novel and aligned to the real-world situation where normal nodes are typically known compared with anomaly nodes. (2) The motivation for the proposed two regularization losses is very intuitive and clear. (3) The experimental results are very impressive.
Weaknesses
(1) The proposed two regularization losses are heavily based on the empirical analysis, which might not transfer to other anomalies in other datasets. (2) For the second prior, its assumption that anomaly nodes sharing similar local structures would share a similar feature distribution has not been empirically verified. (3) Experiments miss the comparison with diffusion-based generative anomaly detection baseline.
Questions
(1) As stated in the weakness, the core regularization loss terms are designed based on two assumptions: * The anomaly nodes have a lower affinity score than normal nodes. However, there is no comprehensive experimental verification of the other datasets on this. It might be better to provide the verification like Figure 1 but on more different datasets. * Anomaly nodes sharing similar neighborhood structures should possess similar feature distributions to their corresponding normal nodes. Although some references have been attached to justify this hypothesis, it might be better to include some empirical verification on this as well. Furthermore, there might be some contradiction between these two assumptions by themselves. First, if assumption 1 holds, it means anomaly nodes should share different local subgraphs with the normal nodes, which indicates that assumption 2 cannot hold. How do we mediate this situation? (2) Is there any difficulty when optimizing the loss according to Eq. (4) and Eq. (5) at the same time? Firstly, for Eq. (4), since the fixed terms would be embeddings of normal nodes and their neighbors, the embeddings of abnormal nodes ($\hat{\mathbf{h}}_i$ in Eq. (2)) would be optimized towards being further away from the neighbors' embeddings. However, Eq. (5) would also enforce the $\hat{\mathbf{h}}_i$ to be close to the normal one $\mathbf{h}_i$. These two directions seem to be contradictory to each other. (3) Joint optimization according to Eq. (7) does not make sense under this generative augmentation setting. Here we use a generative model to augment the training data. This therefore should be that the training model is fixed. Moreover, if we jointly optimize the anomaly detection term and the other two generative terms, it would lead to the gradient for anomaly detection leaks to classification. This is quite confusing to me and might need more clarification. (4) How many layers of the subgraphs are used in optimizing the affinity score? If we use 2-hop neighbors, it might cause the computation to consider the significantly large number of nodes. If not, how should we decide on this parameter? (5) The comparison misses the baseline [1] [1] Liu, Kay, et al. "Graph diffusion models for anomaly detection." (2024).
Rating
5
Confidence
4
Soundness
3
Presentation
3
Contribution
3
Limitations
In addition to the limitations mentioned by the author, there are some other limitations worth addressing: (1) The currently proposed anomaly generation method is still operated in the embedding space. As admitted by the author anomaly behavior is heavily based on interactional behaviors, therefore, it is also helpful to consider directly characterizing/generating anomaly in the graph space. (2) The comparison misses one generative-based baseline [1] [1] Liu, Kay, et al. "Graph diffusion models for anomaly detection." (2024).
Response to Reviewer 7mdh
We greatly appreciate your further comments and it's great to know that our response has helped address some of your questions. Please find our point-by-point response to your follow-up questions as follows. >**Questions #1** Why would adding Gaussian noise make the outlier distribution like a single bar? We'd like to clarify that the Gaussian noise works like a hyperparameter in the feature interpolation in Eq. (5) to diversify the outlier nodes in the feature representation space. Changes of this noise distribution do not affect the superiority of the detection performance of GGAD over the competing methods (please see the results in Table A1 in our response to Reviewer JEU8 for empirical justification). Further, the outliers are generated based on the neighbors of some sampled normal nodes, so the number of the outlier nodes is far less than that of all normal samples, leading to a relatively sparse distribution of the outlier nodes in the affinity density map compared to the normal nodes in the figure. However, this does not affect their effectiveness in serving as negative samples for training the one-class classifier. >**Questions #2** Concern on two constraints We achieve the mediation of two constraints by jointly minimizing $L_{ala} $ and $L_{ec}$. The mediation leads to a result where the generated outlier nodes lie at the fringe of the normal nodes in the feature representation space, as illustrated in Fig. 1(b) and Fig. 3(c). Such outlier nodes meet the two criteria evenly you mentioned in the above comment. In terms of optimization, from Fig.3 in the uploaded **pdf**, we can see that the overall loss and the two individual losses gradually converge at around similar epochs where both constants are satisfied for the generated outliers; not unstable or fluctuated bounces are found after these epochs. Thus, we didn't experience any difficulty in the optimization of GGAD across all the datasets used. >**Questions #3** How do we select the initial normal nodes? As mentioned in lines 202-204, We randomly sample a set of *S* normal nodes and respectively generate an outlier node for each of them based on its ego network. In line 300, we indicate the size of the generated outlier node S is set to 5\% of by default. As shown in Fig. 6 and Fig. 7 in App C.1 of the paper, the performance of GGAD generally remains stable w.r.t the number of the generated outlier nodes. We hope the above replies help address your concerns. We're more than happy to engage in more discussion with you to address any further concerns you may have. Thank you very much for helping enhance our paper again!
Follow-up further
**Question #1: Why would adding Gaussian noise make the outlier distribution like a single bar?** My question here is not whether tweaking the Gaussian noise would enhance previous baseline performance but more like if we can tweak the added Gaussian noise, would the motivation figure also suffer from this issue (the distribution of generated outliers in previous methods are further away than ground truth ones compared to the proposed methods)? However, since the presented results show significantly better performance of the proposed method, I guess it should be that no matter what level of Gaussian noise we add, they would still not be more like the ones generated by the proposed method. **Question #3: How do we select the initial normal nodes?** This makes sense to me. Thanks! **Question #2 Concern with two constraints** I am still confused here and would hear more guidance on this point. Because neighbors embeddings and original node embeddings are fixed and assuming we are working on the homophily social networks (which is a widely adopted property in real-world datasets), how could we enforce the generated outlier node embeddings to be further away from neighbors but at the same time be close to the original center node. Although I still have questions on **Question #2 Concern with two constraints**. Overall, I appreciate the authors' response and think the observation of this paper would still be useful in future research in anomaly detection. I increase my score but hope authors could further address my questions here **Question #2 Concern with two constraints**.
Response to Reviewer 7mdh
Thank you very much for raising the score. We greatly appreciate your further comments and it's great to know that our response has addressed most of your questions. Please find our response to this concern. >**Follow-up question with Question #1** Why would adding Gaussian noise make the outlier distribution like a single bar? Yes, your understanding is correct. Changing the level of Gaussian noise in the generation of the outlier nodes in the baseline methods does not affect the detection performance of the baseline methods AEGIS and GAAN, since they still suffer from the absence of considering graph structure information in their generation model. >**Follow-up question with Question #2** Concern with two constraints We agree that in the homophily graph, the nodes tend to connect with the nodes from the same class, leading to the relatively high similarity between the embeddings of the target node and their neighbors. However, this does not affect the learning of the outlier nodes our method aims to obtain. This is because, given the embeddings of a fixed target node and their neighbors, minimizing the two proposed losses jointly would result in a mediation in the feature representation space where the generated outlier nodes are close to, yet separable from, the target normal node and its neighbors. Thus, these outlier nodes can be thought as `hard anomalies` that lie at the fringe of normal nodes in the feature representation space. If the egocentric closeness loss is removed, the generated outliers would become `trivial anomalies` that distribute far away from the normal nodes (see Fig. 3(a) in the paper). On the other hand, if the local affinity loss is removed, the generated outliers would then become `misleading/false anomalies` that lie inside the normal nodes in the feature representation space (see Fig. 3(b) in the paper). We hope the above reply helps address your follow-up questions. We will clarify this point in our final version. We're more than happy to engage in more discussion with you to address any further questions you may have. Thank you very much for helping enhance our paper again!
Summary
The paper proposes a novel approach called GGAD aimed at improving anomaly detection in graphs under a semi-supervised framework. GGAD generates pseudo anomaly nodes that serve as negative samples for training a one-class classifier. This method is built on two key priors: asymmetric local affinity and egocentric closeness, which help in generating reliable outlier nodes that mimic real anomalies in terms of both graph structure and feature representation. Extensive experimental results demonstrate the effectiveness of the method across diverse graph anomaly detection datasets.
Strengths
1.The method is innovative. The proposed graph anomaly detection method can exploit the feature and structure information of normal nodes more effectively in the studied semi-supervised scenario compared to existing methods. The proposed two priors provide a meaningful characterization of desired properties of outliers in this semi-supervised setting and can be utilized to explore other beneficial priors further. 2.The experiments in the paper are comprehensive and thorough.
Weaknesses
1. The model relies on prior knowledge to generate anomaly points. This prior knowledge can limit the model’s application scenarios. The model performs best only when the real anomalies align with this prior knowledge. For anomaly types that do not conform to the prior knowledge, the model may not effectively detect them. 2.The model does not perform best on the Photo dataset in Table 1, and the article lacks an explanation of the results at the overall data level. 3. This model employs a semi-supervised approach that uses some positive samples for training. However, it does not consider the issue of noise interference within the positive samples, namely, how the model overcomes interference when some positive samples are mislabeled. 4. During the initialization step, only the initial feature of outliers are obtained while the connections between the outliers and normal nodes are not well illustrated in the paper. From Figure 2, one outlier is connected to more than one normal node while the feature of the outlier is generated according to single normal node. The neighborhood of outliers is important since the it involves the computation of node affinity score of outliers.
Questions
see weakness
Rating
6
Confidence
3
Soundness
3
Presentation
3
Contribution
3
Limitations
yes, the authors point out that some anomalies whose characteristics may not be captured by the two priors used
Summary
This paper introduces a novel generative-based GAD approach, named GGAD, tailored for the semi-supervised scenario. Unlike existing GAD frameworks, the authors highlight the feasibility and importance of a semi-supervised setting where labels for normal nodes are relatively easy to obtain during training, but labeled abnormal nodes are very limited. In this context, the paper proposes generating pseudo-anomaly nodes to serve as substitutes for real anomaly nodes in training, thus aiding in anomaly detection. These pseudo-anomalies are generated through two unique loss-guidance mechanisms. Experimental results demonstrate the effectiveness of GGAD. However, the description of the semi-supervised setting in this paper lacks clarity and unconvincing. Additionally, there is minimal differentiation between the proposed method and existing works that generate pseudo-anomaly samples for data augmentation. I think this paper's novelty is limited. I still think that doing unsupervised GAD is more necessary, and if the authors can prove that the pseudo-outlier proposed by GGAD can benefit unsupervised GAD as a general module, I can up my score.
Strengths
1.The complete experiment shows the effectiveness of the method and the necessity of each component. 2.Some visual illustrations help the reader understand, although the shapes of the images seem to be compressed.
Weaknesses
1. I am still confused about the motivation for performing semi-supervised GAD. Why do most methods emphasize unsupervised scenarios? The cost of labeling normal nodes seems too expensive, as the authors themselves state on lines 268 to 269, yet they assert again on line 31 that labels for normal nodes are easy to obtain.This inconsistency hinders a clear understanding of the necessity and practical applications of semi-supervised GAD, which significantly undermines the motivation for this work. 2. While the first loss function proposed by the authors appears intuitively valid, the second loss function aims to generate outliers similar to normal nodes. In my opinion, optimizing these two losses together is unreasonable because they conflict with each other. It seems that they should correspond to different outlier generation processes 3. The paper validates the improvement of unsupervised GAD using labeled normal nodes and claims that GGAD remains superior. I think the authors ignore the fact that unsupervised methods do not obtain this outlier like GGAD and this comparison is not reasonable.
Questions
1. why semi-supervised GAD is more important than unsupervised GAD, How do you overcome the labeling cost? 2. If unsupervised GAD methods use outliers in GGAD, is it beneficial for them? 3. why Eq.5 need Gaussian noise? 4.In addition to the outlier generation methods mentioned on lines 376-396 (they seem overly simplistic), are there more advanced methods for generating outliers similar to GGAD? How does GGAD compare to them?
Rating
5
Confidence
5
Soundness
2
Presentation
3
Contribution
2
Limitations
No limitation need to discuss
Response to Reviewer JEU8
Thank you for raising the score. Please find our point-by-point replies as follows. > **Questions #1** Ignore the fact that many anomaly detection methods are based on the structure of the graph, which may affect the scope of the method (it cannot be used on graphs without attributes) As mentioned above, our GGAD generates outlier nodes that assimilate the real anomaly nodes in both graph structure and feature representations, where the structure information of the graph has been fully considered in our methodology design (i.e., through Eqs. (2) and (3) in the asymmetric local structural affinity prior). As emphasized in many GAD studies, anomalies in the graph are primarily reflected in the relationships of a node to its neighboring nodes immediately connected to themselves [Ref1-2] and many other methods reviewed in [Ref3]. That's why we consider generating the outlier nodes based on the egonet of target normal nodes. Currently, to our best knowledge, most GAD methods are focused on attributed graph datasets (please see the survey and benchmark papers in [Ref3-5] for more details). As for the graph without attributes, the methods for attributed graphs can be applied by augmenting the graph with node attributes based on, e.g., one-hot encoding based on neighborhood information or feature construction using graph structure information (see [Ref3]). Thus, this should not be seen as a limitation of our method and numerous existing GAD methods. > **Questions #2** The implementation of Gaussian noise This simple perturbation can help maintain the affinity separability while enforcing the egocentric closeness constraint. It is a hyperparameter in GGAD and the default value was presented in the implementation. Gaussian noise-based perturbation is commonly used in existing feature interpolation techniques, including those in GAD methods [Ref6-7], and it is used as a way to diversify the generated outlier nodes only, not having catastrophic impacts on the performance of GGAD. This is justified by the newly added results in Table A1 below where we change the mean and variance of the Gaussian noise and replace the Gaussian noise with uniform noise. The results show that, regardless of the distribution of the noise, GGAD remains very effective, demonstrating similar superiority over the competing methods in Table 1 in the paper. ``` Table A1. The performance of GGAD under different scales of Gaussian noise and uniform noise (AUPRC/AUROC). ``` |**Data**| **Amazon**|**Elliptic**|**Photo**| |:---- |:----: |:----: |:----: | | mean=0, std = 0 | 0.7343 / 0.9192 | 0.2107 / 0.7060 | 0.1325/0.6432 | | mean=0.005, std = 0.001 | 0.7475 / 0.9233 | 0.2240 / 0.7110 | 0.1401/0.6444 | | mean=0.01, std = 0.005 | 0.7834 / 0.9324 | 0.2425 / 0.7290 | 0.1442/0.6476 | |uniform noise(a=0, b=0.01) | 0.7434 / 0.9142 | 0.2173 /0.7163 | 0.1407/0.6526 | Overall, in our paper and the rebuttal here, we have examined the feasibility of a very wide range of methods that are related to our method GGAD from diverse aspects, e.g., different ways of exploiting graph structure information, generating outlier nodes, implementing GGAD with various alternative methods, and utilizing the generated outlier nodes in unsupervised/semi-supervise settings, etc. Thus, we would greatly appreciate if you could provide other unexplored directions for us to further evaluate the effectiveness of our method GGAD. We would kindly request your reconsideration of your current rating of our paper if otherwise. Thank you very much again! **References**: - [Ref1] Addressing Heterophily in Graph Anomaly Detection: A Perspective of Graph Spectrum, WWW2023 - [Ref2] Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detection, NIPS2023 - [Ref3] A comprehensive survey on graph anomaly detection with deep learning, TKDE 2021 - [Ref4] GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection, NIPS2023 - [Ref5] BOND: Benchmarking Unsupervised Outlier Node Detection on Static Attributed Graphs NIPS2022 - [Ref6] Perturbation learning based anomaly detection, NIPS2022 - [Ref7] DAGAD: Data Augmentation for Graph Anomaly Detection， ICDM2022 - [Ref8] Consistency Training with Learnable Data Augmentation for Graph Anomaly Detection with Limited Supervision, ICLR2024
Dear Authors: Thanks for your reply! As you said, for graphs without attributes, you can add hand-crafted features, which is normal and not a shortcoming of GGAD. My initial concern was that it seemed unreasonable to let the generated abnormal nodes share the same neighbors as the normal nodes. I read the paper again, and I thought that the loss in Eq 4 might solve this problem. I can accept the author's explanation. But with Gaussian noise, If you say it's "a way to diversify the generated outlier nodes only, not having catastrophic impacts on the performance of GGAD. "Then I still don't think it's the most necessary. To sum up, the loss in Eq 4 is good and dispels my confusion, but the loss in Eq 5 weakens the novelty, so I'm sorry that I can't improve the score.
Dear Reviewer JEU8, Thanks a lot for the prompt reply. We apologize that we don't understand why the use of the loss in Eq. 5 weakens the novelty of our method, given the fact that you find good novelty in Eq. 4. As demonstrated by our ablation study results in Table 2 in the paper, the adding of the loss in Eq. 5 to our method leads to very significant performance improvement across all the datasets in both AUROC and AUPRC. Moreover, as shown in the newly added results in Table A1 above, the loss in Eq. 5 works well regardless of different prior distribution used to specify the noise. We would really appreciate if you could kindly advise why the additional major contribution made by the loss in Eq. 5 is considered as a negative part of our model design. Thank you!
Dear Authors: I'm sorry for the misunderstanding caused by my reply. I don't think Loss in Eq. 5 is considered as a negative part of our model design. I acknowledge that your experiments prove its effectiveness, I read the paper again, my opinion is, if you are aim to generate nodes that are less like anomaly nodes, more like normal nodes, then I think you need to select the failed nodes instead of computing on all nodes as in Eq. 5.
Dear Reviewer JEU8, Thanks for the prompt clarification. However, we believe there are some major misunderstanding here. - First of all, our goal is always to generate outlier nodes assimilating real anomaly nodes, but we focus more on generating the `hard' anomaly nodes that lie at the fringe of the normal nodes in the feature representation space, corresponding to our egocentric closeness prior. This is why the loss in Eq. 5 plays a crucial role in our outlier generation. Conversely, if we remove the loss in Eq. 5 from our objective function, the generated outliers would be simply trivial outlier nodes that are far away from the normal nodes, which are not that helpful for learning a discriminative one-class classifier, as supported by our results in Fig. 3 and ablation study results in Table 2 in the paper. - Secondly, the number of normal nodes or the type of normal nodes we use in Eq. 5 does not really affect the performance. This is because the normal nodes in the feature representation space are generally closed to each other. Please also note that the normal nodes used in Eq. 5 are randomly sampled from the labeled normal node set. Increasing or decreasing the number of normal nodes has limited impact on the performance of GGAD, as shown in Fig. 6 and Fig. 7 in App C.1 of the paper. We hope these clarifications help sort out the possible misunderstanding you might have before. We apologize for the confusion and will clarify these points in our final paper. Thank you very much again!
Dear Authors: I agree with your explanation this time, and I think you need to add the difference between "hard" outliers and "trivial" outliers to the manuscript, which is the key motivation of Eq 5 in my opinion. I will raise my score to 5, and I hope my suggestion will be helpful to improve the quality of the paper.
Dear Reviewer JEU8, We're very pleased that our clarification is helpful, and thank you for increasing the rating to an acceptance score. We will add the intuition of "hard" outlier nodes and its difference to "trivial" outlier nodes in Sec. 3.4 to clarify why the loss in Eq. 5 is important in our method. The discussions have been very helpful for enhancing our paper. Many thanks again for your time and effort on our paper. We're happy to take any further questions you might have.
Summary
This paper explores the problem of semi-supervised graph anomaly detection (GAD), where some nodes are known to be normal, in contrast to the typical unsupervised setting with no labeled data. The authors show that even a small percentage of labeled normal nodes can improve the performance of existing unsupervised GAD methods when adapted to the semi-supervised scenario. The paper proposes a novel Generative GAD approach (GGAD) to better exploit normal nodes by generating pseudo anomaly nodes, called 'outlier nodes', to provide effective negative samples for training a one-class classifier. GGAD generates these outlier nodes using priors about anomaly nodes, such as asymmetric local affinity and egocentric closeness, to mimic anomalies in structure and features. Experiments on six real-world GAD datasets show that GGAD outperforms state-of-the-art methods in both unsupervised and semi-supervised settings.
Strengths
+ This paper studies a new problem of semi-supervised GAD that has not been widely studied. + The proposed method is simple and effective from the empirical perspective. + The experiments are extensive including effectiveness and efficiency analyses and the method has been tested on real-world large-scale graphs to verify the scalability.
Weaknesses
- The two priors that are used to generate outlier nodes are heuristic or based on empirical evidence. There is no theoretical analysis provided to better guarantee the effectiveness of the proposed method. - It will be more interesting and helpful to show the generated outlier nodes can capture the characteristics of anomalous nodes in addition to comparing their representations. - The experimental settings of anomaly contamination are not very clear: how the contamination is introduced? - Overall experimental settings. What hardware has been used in the experiments, e.g., memory, and why are the experiments conducted on CPUs?
Questions
1. Theoretical analysis of the proposed method, especially these two priors. 2. Experimental settings including hardware and anomaly contamination. 3. Analysis of the generated outlier nodes.
Rating
5
Confidence
3
Soundness
2
Presentation
3
Contribution
2
Limitations
The authors have adequately addressed the limitations
Summary
The paper studies an under-explored graph anomaly detection problem where the detection models have access to a set of labeled normal nodes. To tackle this problem, it introduces a generative approach namely GGAD that generates pseudo anomaly nodes, called outlier nodes, to support the training of a discriminative one-class classifier. The key idea underlying this approach is to generate the outlier nodes in a way that can well simulate real anomaly nodes in both graph structure and feature representation perspectives. To achieve this, GGAD defines and incorporates two priors, including asymmetric local affinity and egocentric closeness, into its optimization objectives, with the former prior focusing on the alignment on the graph structure aspect and the latter on the feature representation aspect. The method is evaluated on six large real-world datasets and shows impressive detection performance compared to existing state-of-the-art methods.
Strengths
- The paper is generally well-written and easy-to-follow. - The problem setting is practical since labeled normal samples are easy to obtain in many real-world applications. Compared to the commonly studied unsupervised setting, this semi-supervised setting often results in better detection performance. - The proposed method GGAD is novel. There have been many generative anomaly detection methods, but as far as I know, they are unable to consider the graph structure and the neighboring nodes’ representations. By introducing the two new priors, GGAD addresses this issue well. Fig.1 and Fig. 3 help demonstrate this effect. - The method is compared with a range of unsupervised and semi-supervised methods on 6 real-world datasets with diverse genuine anomalies, and gains largely improved detection performance over these competing methods. - The ablation study is plausible and justifies the contribution of each proposed prior.
Weaknesses
- The outlier node generation in GGAD may cause non-trivial computational overhead. - Despite better performance than the competing methods, GGAD gains an AUC of only around 0.6 on some datasets, such as DGraph and Reddit. - In Fig. 4 (b), GGAD shows a fast AUPRC growth with increasing training size, but the other methods have a flat performance trend. What would be the reason behind?
Questions
See the weakness
Rating
7
Confidence
4
Soundness
4
Presentation
3
Contribution
3
Limitations
NA
The reply has addressed my questions.
The reply has addressed my questions.
We're very pleased that our response has addressed your questions. Thank you very much for the positive comments and appreciation of our work.
Dear Authors: On the semi-supervised question, I assume that you only use a subset of nodes in the original dataset as normal samples and use the generated abnormal samples (similar to data augmentation?) to train a classifier, if that's the case, I think it's reasonable and would be willing to boost my score to 4. However, I think the process of generating abnormal nodes seems too simple, I can understand the intention of Eq(4), but how to use abnormal nodes to calculate Eq(3), how do you determine what their neighbors have? I think that's critical. Eq (5) is more like a regularization term and I think its contribution is small.
Response to Reviewer JEU8
We greatly appreciate your further comments and it's great to know that our response has helped address your questions. Please find our point-by-point replies as follows. **(0)** Setting. Yes, the studied setting assumes the availability of a small set of labeled normal nodes during training. To train a discriminative one-class classifier, our method GGAD utilizes these normal nodes to generate pseudo abnormal nodes that assimilate real anomaly nodes in both graph structure and feature representations. **(1)** Similar to data augmentation? Current data augmentation methods for GAD like DAGAD and DIFAD [Ref1-2] and imbalanced graph learning like GraphSMOTE and GraphMixup [Ref3-4] require both labeled abnormal nodes and normal nodes, making them not applicable to the studied semi-supervised setting where only the labels of partial normal nodes are available during training. Unlike these graph data augmentation methods, our GGAD is a generative method that generates pseudo abnormal nodes by leveraging the two abnormality-related priors using only a small set of normal nodes. Furthermore, from the ablation study results in Table 3 in the paper, commonly used graph data augmentation methods like the random sampling or mixing up normal nodes with noise cannot work. Besides, the newly added results of existing popular generative methods in Table 1 in the upload **pdf** further demonstrate the unique effectiveness of the proposed generative method in our GGAD. **(2)** The calculation of Eq(3) for abnormal nodes ? As mentioned in lines 202-204, and shown in Fig. 1 left in the paper, we sample some normal nodes as the target location for outlier node generation, in which the outlier nodes share the same neighbors with the sampled target normal nodes. The affinity calculation of the generated abnormal nodes is based on the neighbors of these target normal nodes. **(3)** Eq. (5) is more like a regularization term and I think its contribution is small. Eq. (5) is designed to incorporate our egocentric closeness-based abnormality prior, through which we aim to pull the representations of generated outliers close to the node representations in its egonet in the feature representation space, as shown in Fig. 3(c). Without this loss, the generated abnormal nodes only meet one abnormality prior, which do not provide sufficient discriminative information for the one-class classifier. Thus, the contribution of this loss is significant: it is not only reflected in its own design but also in the collaboration with the other prior implemented via Eq. (4). This collaborative effect helps generate the pseudo abnormal nodes which can serve as effective negative samples for training a tight decision boundary of the one-class classifier. As the very first work to explore the semi-supervised GAD setting, we introduce a simple yet effective way to generate pseudo abnormal nodes for training an accurate one-class classifier for GAD, offering a novel principled framework for semi-supervised GAD. Further, our method GGAD can also perform well in anomaly-contaminated training data; as also pointed out by you and justified by our newly added results, the generated abnormal nodes can also help improve unsupervised GAD methods in the popular unsupervised setting. All these lead to a piece of work that has significant contributions to GAD in the newly introduced semi-supervised setting and the widely-explored unsupervised setting. In terms of methodology, all modules in our method are novel for GAD, and as far as we know, GGAD is the very first method that can generate pseudo abnormal nodes assimilating real anomaly nodes in both graph structure and feature representations. It is true that GGAD is simple, but as per Occam's razor, simpler models are preferred over more complex ones. Thus, we argue that our method is technically solid and expected to have moderate-to-high impact in the GAD community. We're more than happy to engage in more discussion with you to address any further concerns you may have. Thank you very much for helping enhance our paper! **References**: - [Ref1] DAGAD: Data Augmentation for Graph Anomaly Detection， ICDM2022 - [Ref2] NEW RECIPES FOR GRAPH ANOMALY DETECTION: FORWARD DIFFUSION DYNAMICS AND GRAPH GENERATION, 2024 - [Ref3] G-Mixup: Graph Data Augmentation for Graph Classification ICML2022 - [Ref4] GraphSMOTE: Imbalanced Node Classification on Graphs with Graph Neural Networks WSDM2021
Dear Authors: Thank you for your reply. I am glad that my understanding of problem setting is consistent with yours. If you only use a small number of normal nodes as the training set, I think it is reasonable and i will raise my score. I acknowledge Occam's razor and the fact that it is critical to an ML-based model, especially one based on neural networks. However, I still have some concerns about the current neighbor selection, and the fact that many anomaly detection methods are based on the structure of the graph, which you ignore, may affect the scope of the method (it cannot be used on graphs without attributes).Also, regarding Gaussian noise, I think there is a lack of a mathematically explanation, which further adds to my concerns about the method. To sum up, I think anomaly detection is an important area, so I would like to critically examine the reasonability and feasibility of related methods, for which I do not support accepting this paper, I will keep my score: 4
Appreciate your response!
Thank you for more analysis. I have follow-up questions as follows: **Weaknesses #2 and Questions #1 More verification on more datasets and empirical verification of the second prior**: after seeing more visualization of normal/abnormal/gaussian-generated outliers distributions, I have the following questions: why would adding Gaussian noise make the outlier distribution like a single bar? **Weaknesses #3 and Limitations #2 and Questions #5**: thank you for the clarification and it is reasonable. **Questions #2 How do we mediate the two assumptions that might be some contradiction and is there any difficulty in optimization?**: I am not so convinced about the reply. Still, my initial concern is - (1) One optimization is to make the generated node embedding itself similar to the original node embedding. - (2) The other optimization is to make the generated node embedding itself have a lower affinity score than the neighbors of the original nodes Let's assume (1) works and the generated node embeddings become further away from neighbor embeddings, then how would (2) still hold given that the original node embeddings have a higher affinity score to the neighbors? Furthermore, I want to add on top of my above questions with another question given that this designed method needs to select normal nodes to generate abnormal nodes. How do we select the initial normal nodes? Do we use all of them or randomly sample them? Without further addressing my above concern, I cannot further raise my score.
Kindly Request for Reviewer's Feedback
Dear Reviewer yDqR, Since the End of author/reviewer discussions is coming in ONE day, may we know if our response addresses your main concerns? If so, we kindly ask for your reconsideration of the score. Should you have any further advice on the paper and/or our rebuttal, please let us know and we will be more than happy to engage in more discussion and paper improvements. Thank you so much for devoting time to improving our paper!
Thanks for the rebuttal
I appreciate the efforts of the authors during the rebuttal phase. These responses addressed most of my concerns. But I still have some concerns for W4 and Q2: to make a fair comparison, why CPU is selected? Because of the large memory requirement to load a large graph?
Response to Reviewer yDqR
We're very pleased to know that our response has addressed most of your concerns. We really appreciate your further comments. Please find our response to your follow-up question as follows. >**Follow-up question with Question #1** To make a fair comparison, why CPU is selected? Because of the large memory requirement to load a large graph? Yes, your understanding is correct. A number of baselines like DOMINANT, AnomalyDAE, and TAM require large memory to handle large-scale graph datasets. However, we lack GPUs with a sufficiently large memory size to perform experiments on these large datasets using GPUs. Thus, in order to obtain the runtime results for all methods across all data sets using the same computing environment, we obtained the runtime results based on a consistent CPU-based setting. We hope the above reply helps address this follow-up question. We will clarify this point in our final version. We're more than happy to engage in more discussion with you to address any further concerns you may have. Thank you very much for helping enhance our paper again!
Thanks for the clarification
I appreciate the clarification from the authors. Now my concerns have been addressed and I would like to increase the rating.
Dear Reviewer yDqR, Thank you very much for your consideration of our replies and for the rating increase to an acceptance score. We're very pleased to know that our response has addressed your concerns. Please kindly let us know if there are any further questions. Thanks again.
Decision
Accept (poster)