Title: Semi-supervised Graph Anomaly Detection via Robust Homophily Learning
Venue: NeurIPS 2025
Accepted: yes
Keywords: Graph Anomaly Detection

Adaptive Graph Neural Networks

Frequency

One-class classification
Abstract: Current semi-supervised graph anomaly detection (GAD) methods utilizes a small set of labeled normal nodes to identify abnormal nodes from a large set of unlabeled nodes in a graph. These methods posit that 1) normal nodes share a similar level of homophily and 2) the labeled normal nodes can well represent the homophily patterns in the entire normal class. However, this assumption often does not hold well since normal nodes in a graph can exhibit diverse homophily in real-world GAD datasets. In this paper, we propose RHO, namely Robust Homophily Learning, to adaptively learn such homophily patterns. RHO consists of two novel modules, adaptive frequency response filters (AdaFreq) and graph normality alignment (GNA). AdaFreq learns a set of adaptive spectral filters that capture different frequency components of the labeled normal nodes with varying homophily in the channel-wise and cross-channel views of node attributes. GNA is introduced to enforce consistency between the channel-wise and cross-channel homophily representations to robustify the normality learned by the filters in the two views. Experiments on eight real-world GAD datasets show that RHO can effectively learn varying, often under-represented, homophily in the small labeled node set and substantially outperforms state-of-the-art competing methods. Code is available at \url{https://github.com/mala-lab/RHO}.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work proposes a novel framework, Robust Homophily Learning (RHO), for semi-supervised graph anomaly detection (GAD). RHO incorporates two novel designs: AdaFreq, which captures diverse frequency components of labeled normal nodes across channel-wise and cross-channel views of node attributes; and GNA, which enforces consistency between two views to robustly model node normality, accounting for varying levels of homophily among normal nodes. Experiments on eight real-world GAD datasets demonstrate the effectiveness of RHO.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n \n1. The paper is well written and easy to follow.\n\n2. The motivation for the proposed RHO is novel, and theoretical analysis supports the design of the adaptive filter. The visualization in Figure 3 is intuitive.\n\n3. The experiments and theory are sufficient to demonstrate the effectiveness.\n\n**Weaknesses and Questions:**\n\n1. According to the algorithm design of RHO, the centers $c$ in the two views are dynamically updated during training, which differs from the static center design used in previous works. What is the motivation behind this dynamic update? If the centers are set as static, how would it affect the model's performance?\n\n2. The description of symbols are unclear. What is the difference between the convolution kernel $g$ in Line 145 and convolution kernel $g\\_\\theta$ in Line 146.\n\n3. Figure 1a presents the statistics of the homophily rate for normal nodes. The formula provided for computing node-level homophily (Lines 128–129) is more appropriate than using graph-level homophily.\n\n4. RHO achieves significant improvements on some datasets, but demonstrates competitive performance on Reddit and Amazon. What could be the possible reasons behind this?\n\nQUESTIONS:\nPlease refer to Weaknesses.\n\nLIMITATIONS:\nPlease refer to Weaknesses.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes RHO, a semi‐supervised graph anomaly detection (GAD) method that learns heterogeneous homophily patterns from a small set of labeled normal nodes. RHO combines two novel modules:  \n1. AdaFreq: adaptive spectral filters with trainable frequency‐response parameter $k$, applied in both cross‐channel and channel‐wise views to capture diverse low‐ and high‐frequency components of normal nodes.  \n2. Graph Normality Alignment (GNA): a contrastive alignment loss that enforces consistency between the two views’ representations.\n\nSTRENGTHS AND WEAKNESSES:\n### **Strengths**\nThe proposed method:\n1. Leveraging both cross‐channel and channel‐wise perspectives captures complementary homophily patterns.\n2. The GNA module effectively aligns the two views, improving robustness.\n\n### **Weaknesses**\n\n#### **1. The analyses are confusing at times:**\n\n**In Theorem 1:**\n\n1.  **\"assuming $β_m > 0$\":** It is unclear why all projection coefficients \\(\\beta_m\\) must be positive. What if \\(\\beta_m<0\\)? Does the result still hold or collapse? Any justification or empirical evidence for this assumption is missing. \n2.  **Motivation for the filter design:** The manuscript states “According to Theorem 1, … by training the parameter $k$.” However, Theorem 1’s statement involves $g(\\lambda_m)$ under an assumption on $\\beta_m$ The definition of $g(\\lambda)$in Theorem 1 differs from Eq. (2) (where $g(\\lambda)=1-k\\lambda$), so it is unclear how Theorem 1 *motivates* the choice of this linear filter form.  \n3. **\"When k = 0, g(λ) retains raw frequency signals.\":** The claim “When $k=0$, $g(\\lambda)$ retains raw frequency signals” seems contradictory: if $g(\\lambda)=1$, then the output is constant across all eigenvalues, not the original signal $\\lambda$. Should raw frequency signal be $\\lambda$ rather than 1?  \n\n#### **2. Adaptive filters are well-studied in the graph learning field. What's new (advantages) in your method over existing ones?**\n\n### Minor Issues  \n1. “which is simultaneously applies on” → should be “which is simultaneously applied to” (Sec. 4.1).  \n2. “AUROCassesses the model’s overall ability...” → missing space: “AUROC assesses…” (Sec. 5.1).\n\nQUESTIONS:\nSee weaknesses above\n\nLIMITATIONS:\nThe proposed method only applies to node-level anomaly detection. Also, the authors do not provide interpretation of the learned $k$.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a novel semi-supervised graph anomaly detection framework named RHO, which aims to address the challenge of homophily among normal nodes—i.e., the fact that normal nodes may have either high or low homophily in graph structure. To tackle this, the authors introduce AdaFreq, an adaptive frequency-response filter that adjusts graph signal propagation strengths based on learnable frequency parameters, applied in both a cross-channel view (aggregating all features) and a channel-wise view (learning distinct filters per feature channel). To unify these two complementary views, the paper further proposes a Graph Normality Alignment (GNA) module that encourages consistent representations across views through a contrastive alignment objective. Experimental results and visualizations demonstrate that RHO effectively captures diverse normal patterns and improves anomaly detection robustness compared to existing methods.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n\n1. **Novel problem formulation**: The paper identifies an important yet underexplored issue in graph anomaly detection named *heterogeneous homophily among normal nodes*, and it designs the model explicitly to address this challenge.\n\n2. **Methodological originality**: The introduction of AdaFreq, a learnable frequency-response filter applied to both cross-channel and channel-wise views, is a compelling design. Especially, using channel-wise frequency modulation to model per-feature homophily variation is a fresh perspective.\n\n3. **Effective view alignment strategy**: The proposed Graph Normality Alignment (GNA) module employs a contrastive objective to reconcile representations from different views, leading to more robust normality modeling.\n\n4. **Strong empirical results**: The paper presents comprehensive experiments with both quantitative metrics and qualitative visualizations (e.g., t-SNE, anomaly score histograms), which together provide strong support for the method’s effectiveness.\n\n5. **Clarity of exposition**: The paper is clearly written and logically structured. Design motivations are well-justified, and ablation studies are provided to isolate the impact of each module.\n\n**Weaknesses:**\n\n1. While the paper focuses on per-feature adaptive filtering, it does not explore potential interactions across multiple feature combinations (e.g., pairwise or group-wise channel dependencies), which may limit its capacity to capture complex homophily patterns.\n\n2. Some modules, such as GNA, introduce additional complexity. A more detailed runtime or scalability analysis would further strengthen the paper.\n\nQUESTIONS:\n1. In the channel-wise view, each feature dimension is propagated independently using a dedicated frequency filter. Have the authors considered modeling interactions between feature dimensions (e.g., pairwise or grouped channels)? Would such multi-dimensional interactions further enhance the model’s capacity to capture complex homophily patterns?\n\n2. In the experiments, most baseline methods are from earlier years, with only a few from 2024. \n\n3. The GNA module focuses on aligning representations across the cross-channel and channel-wise views. Within the channel-wise view, however, each feature dimension is processed independently. Is there any mechanism to encourage consistency or coordination among individual feature channels?\n\nLIMITATIONS:\nSee above.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces RHO, a robust homophily learning framework for semi-supervised graph anomaly detection that adaptively captures diverse normal patterns by learning spectral filters tailored to varying homophily levels. It proposes two key modules—AdaFreq, which learns channel-wise and cross-channel adaptive frequency-response filters, and GNA, which aligns their representations via contrastive learning to ensure consistency. Extensive experiments on eight real-world datasets show that RHO consistently outperforms state-of-the-art methods in detecting anomalies across heterogeneous homophily settings.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- The RHO framework’s adaptive spectral filters effectively capture diverse normal patterns across varying homophily levels.\n- The integration of AdaFreq and GNA modules ensures both frequency-wise adaptation and representation consistency through contrastive learning.\n- Evaluation on eight real-world datasets demonstrates RHO’s superior anomaly-detection performance.\n\nWeaknesses:\n- The paper is missing recent baselines such as PMP [1] and ConsisGAD [2].\n- The term \"cross-channel\" is confusing: in this paper it refers to sharing across channels, but readers may interpret it as fusion among channels.\n- Important sections, such as the complexity analysis, should be included in the main text rather than relegated to the appendix.\n\n[1] Wei Zhuo, Zemin Liu, Bryan Hooi, Bingsheng He, Guang Tan, Rizal Fathony, and Jia Chen. \"Partitioning Message Passing for Graph Fraud Detection.\" In The Twelfth International Conference on Learning Representations.\n\n[2] Nan Chen, Zemin Liu, Bryan Hooi, Bingsheng He, Rizal Fathony, Jun Hu, and Jia Chen. \"Consistency training with learnable data augmentation for graph anomaly detection with limited supervision.\" In The Twelfth International Conference on Learning Representations. 2024.\n\nQUESTIONS:\nSee Weaknesses.\n\nLIMITATIONS:\nSee Weaknesses.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}