Bipartite graphs are widely used to model relationships between entities of different types, where vertices are divided into two disjoint sets. Biclique-preserving clustering is a fundamental operation that retrieves clusters with dense bicliques, enabling various emerging applications. However, existing methods either fail to accurately capture the unique properties of bipartite graphs or significantly overlook the informative higher-order biclique substructure, leading to compromised clustering quality. Additionally, existing methods are overly dependent on biclique enumeration, resulting in poor scalability. To address these challenges, we propose ECRC, a simple yet provable Edge-Centric Reweighting Clustering framework that provides strict approximation guarantees for any biclique. A key advantage of ECRC is its ability to leverage powerful counting instead of exhaustive enumeration, significantly reducing time and space complexity. To further improve efficiency, we propose several effective graph reduction strategies to eliminate the unqualified vertices and edges before calculating the edge-centric weight. Extensive experiments on five datasets show that our algorithms are more efficient and effective compared to six baselines.

Identifying locally dense communities closely connected to the user-initiated query node is crucial for a wide range of applications. Existing approaches either solely depend on rule based constraints or exclusively utilize deep learning technologies to identify target communities. Therefore, an important question is proposed: can deep learning be integrated with rule-based constraints to elevate the quality of community search? In this paper, we affirmatively address this question by introducing a novel approach called Neural Community Search via Attribute augmented Conductance, abbreviated as NCSAC. Specifically, NCSAC first proposes a novel concept of attribute-augmented conductance, which harmoniously blends the (internal and ex ternal) structural proximity and the attribute similarity. Then, NCSAC extracts a coarse candidate community of satisfactory quality using the proposed attribute-augmented conductance. Subsequently, NCSAC frames the community search as a graph optimization task, refining the candidate community through sophisticated reinforcement learning techniques, thereby producing high-quality results. Extensive experiments on six real world graphs and ten competitors demonstrate the superiority of our solutions in terms of accuracy, efficiency, and scalability. Notably, the proposed solution outperforms state-of-the-art methods, achieving an impressive F1-score improvement ranging from 5.3% to 42.4%. For reproducibility purposes, the source code is available at https://github.com/longlonglin/ncsac.

Bipartite graphs are widely used to model relationships between entities of different types, where nodes are divided into two disjoint sets. Similarity search, a fundamental operation that retrieves nodes similar to a given query node, plays a crucial role in various real-world applications, including machine learning and graph clustering. However, existing state of-the-art methods often struggle to accurately capture the unique structural properties of bipartite graphs or fail to incorporate the informative node attributes, leading to suboptimal performance. Besides, their high computational complexity limits scalability, making them impractical for large graphs with millions of nodes and tens of thousands of attributes. To overcome these challenges, we first introduce Attribute-augmented Hidden Personalized PageRank (AHPP), a novel random walk model designed to blend seamlessly both the higher-order bipartite structure proximity and attribute similarity. We then formulate the similarity search over attributed bipartite graphs as an approximate AHPP problem and propose two efficient push-style local algorithms with provable approximation guarantees. Finally, extensive experiments on real-world and synthetic datasets validate the effectiveness of AHPP and the efficiency of our proposed algorithms when compared with fifteen competitors.

Higher-order graph clustering partitions graphs use frequently occurring subgraphs instead of edges, proving effective in community detection and knowledge discovery. Motif conductance, known for its strong interpretability, is a leading model. However, existing motif conductance algorithms are hindered by a two-stage reweighting framework that requires enumerating motif instances to generate an edge-weighted graph for partitioning. This framework has two major drawbacks: (1) It provides only a quadratic bound for three-vertex motifs, with no provable approximation guarantees for other motifs. (2) Enumerating motif instances is computationally prohibitive for large motifs or dense graphs due to combinatorial explosions. Besides, costly spectral clustering or local graph diffusion on the edge-weighted graph limits their scalability. In this paper, we propose a novel peeling-based clustering framework, PSMC, offering a motifindependent approximation ratio for any motif. Specifically, PSMC first defines a new locally computable vertex metric Motif Resident based on the given motif. Then, it iteratively deletes vertices with the smallest motif resident using efficient dynamic update techniques, outputting a locally optimal result with approximation guarantees. Besides, we introduce several powerful optimization techniques to further reduce computational costs. Empirical results on real-world and synthetic datasets showcase our proposed solutions' superiority over ten competitors.

Network embedding has numerous practical applications and has received extensive attention in graph learning, which aims at mapping vertices into a low-dimensional and continuous dense vector space by preserving the underlying structural properties of the graph. Many network embedding methods have been proposed, among which factorization of the Personalized PageRank (PPR for short) matrix has been empirically and theoretically well supported recently. However, several fundamental issues cannot be addressed. (1) Existing methods invoke a seminal Local Push subroutine to approximate a single row or column of the PPR matrix. Thus, they have to execute n (n is the number of nodes) Local Push subroutines to obtain a provable PPR matrix, resulting in prohibitively high computational costs for large n. (2) The PPR matrix has limited power in capturing the structural similarity between vertices, leading to performance degradation. To overcome these dilemmas, we propose PSNE, an efficient spectral sParsification method for Scaling Network Embedding, which can fast obtain the embedding vectors that retain strong structural similarities. Specifically, PSNE first designs a matrix polynomial sparser to accelerate the calculation of the PPR matrix, which has a theoretical guarantee in terms of the Frobenius norm. Subsequently, PSNE proposes a simple but effective multiple-perspective strategy to enhance further the representation power of the obtained approximate PPR matrix. Finally, PSNE applies a randomized singular value decomposition algorithm on the sparse and multiple-perspective PPR matrix to get the target embedding vectors. Experimental evaluation of real-world and synthetic datasets shows that our solutions are indeed more efficient, effective, and scalable compared with ten competitors.

Higher-order graph clustering aims to partition the graph using frequently occurring subgraphs (i.e., motifs), instead of the lower-order edges, as the atomic clustering unit, which has been recognized as the state-of-the-art solution in ground truth community detection and knowledge discovery. Motif conductance is one of the most promising higher-order graph clustering models due to its strong interpretability. However, existing motif conductance based graph clustering algorithms are mainly limited by a seminal two-stage reweighting computing framework, needing to enumerate all motif instances to obtain an edge-weighted graph for partitioning. However, such a framework has two-fold vital defects: (1) It can only provide a quadratic bound for the motif with three vertices, and whether there is provable clustering quality for other motifs is still an open question. (2) The enumeration procedure of motif instances incurs prohibitively high costs against large motifs or large dense graphs due to combinatorial explosions. Besides, expensive spectral clustering or local graph diffusion on the edge-weighted graph also makes existing methods unable to handle massive graphs with millions of nodes. To overcome these dilemmas, we propose a Provable and Scalable Motif Conductance algorithm PSMC, which has a fixed and motif-independent approximation ratio for any motif. Specifically, PSMC first defines a new vertex metric Motif Resident based on the given motif, which can be computed locally. Then, it iteratively deletes the vertex with the smallest motif resident value very efficiently using novel dynamic update technologies. Finally, it outputs the locally optimal result during the above iterative process. To further boost efficiency, we propose several effective bounds to estimate the motif resident value of each vertex, which can greatly reduce computational costs. Empirical results on real-life and synthetic demonstrate that our proposed algorithms achieve 3.2-32 times speedup and improve the quality by at least 12 times than the state-of-the art baselines.

Deep learning has achieved outstanding performance in natural language processing, but actuality has witnessed its fragility against adversarial attacks. Synonyms-based attacks are most disastrous since their generated samples approximate raw inputs. Several countermeasures have been proposed in the literature, but the defense effectiveness is unsatisfactory because of the clumsy single-granularity synonyms clustering. To mitigate this dilemma, we propose a Granular-Ball Sample Enhancement-based defense Framework (GBSEF) for text adversarial attacks. Specifically, GBSEF first adopts an effective general synonyms clustering algorithm, which can adaptively adjust the granularity of synonym sets (i.e., granular-balls) for diverse datasets. Regarding each ball as a dot, the function consisting of most dots well fits the original data distribution, resulting in the relationships among words being well presented by the granular-balls. GBSEF then replaces each input word with the center vector of its subordinate ball, to construct robust samples preserving syntax and semantic information simultaneously. Finally, GBSEF combines a random substitution mechanism with granular-balls. This way can prompt GBSEF to take full advantage of the multi-granularity feature of granular-balls, to get more diverse valid samples. GBSEF obtains great performance through training on these samples. Abundant evaluations demonstrate the robustness and effectiveness of GBSEF against adversarial attacks, albeit with a slight performance decrease under normal scenarios without attacks. Meanwhile, GBSEF has good transferability against adversarial samples. Compared with state-of-art defense countermeasures, under multiple attacks on four neural network models (i.e., CNN, LSTM, Bi-LSTM, BERT), GBSEF always outperforms existing baselines.

Most natural language processing tasks rely on massive labeled data to train an outstanding neural network model. However, the label noise (i.e., wrong label) is inevitably introduced when annotating large-scale text datasets, which significantly degrades the performance of neural network models. To overcome this dilemma, we propose a novel Granular-B all based tRAINing framework, named GBRAIN, to realize robust coarse-grained representation learning, thus combating label noises in diverse text tasks. Specifically, considering that most samples in the dataset are precisely labeled, GBRAIN first proposes a dynamic granular-ball clustering algorithm to blend seamlessly into the traditional neural network model. A striking feature of the clustering algorithm is that it can adaptively group the embedding vectors of similar data into the same set (hereafter referred to as a granular-ball). The embedding vectors and labels of all samples from the same set will be coarse-grainedly represented by the center vector and the label of the granular-ball, respectively. Consequently, noise labels can be rectified through the labels of most of the labeled data. Moreover, we introduce a new gradient backpropagation mechanism compatible with our framework, which can help optimize coarse-grained embedding vectors with iterative training. Empirical results on text classification and name entity recognition tasks demonstrate that our proposal GBRAIN is indeed effective in contrast to the state-of-the-art baselines.

Graph Neural Networks (GNNs) have achieved remarkable performance in various applications, including social media analysis, computer vision, and natural language processing. Decoupled GNNs are a ubiquitous framework because of their high efficiency. However, existing decoupled GNNs suffer from the following several defects. (1) Their studies on GNN feature propagation are isolated, with each study emphasizing a user-specified propagation matrix. (2) They still have high computation costs to achieve provable performance on massive graphs with millions of nodes and billions of edges. (3) Their feature propagation steps are uniform, which makes it difficult for them to escape the dilemmas of over-smoothing. In this paper, we propose GSD-GNN, a Generalized and Scalable Decoupled GNN framework based on the spectral graph theory, which offers the following advantages. Firstly, through minor parameter adjustments, it can degenerate into most existing Decoupled GNNs, such as APPNP, GDC, SGC, etc. Secondly, it efficiently computes an arbitrary propagation matrix with near-linear time complexity and theoretical guarantees. Thirdly, it customizes the adaptive feature propagation mechanism for each node to mitigate the over-smoothing dilemma. Finally, extensive experiments on massive graphs demonstrate that the proposed GSD-GNN indeed is effective, scalable, and flexible.