A Versatile Framework for Attributed Network Clustering via K-Nearest Neighbor Augmentation

Attributed networks containing entity-specific information in node attributes are ubiquitous in modeling social networks, e-commerce, bioinformatics, etc. Their inherent network topology ranges from simple graphs to hypergraphs with high-order interactions and multiplex graphs with separate layers. An important graph mining task is node clustering, aiming to partition the nodes of an attributed network into k disjoint clusters such that intra-cluster nodes are closely connected and share similar attributes, while inter-cluster nodes are far apart and dissimilar. It is highly challenging to capture multi-hop connections via nodes or attributes for effective clustering on multiple types of attributed networks. In this paper, we first present AHCKA as an efficient approach to attributed hypergraph clustering (AHC). AHCKA includes a carefully-crafted K-nearest neighbor augmentation strategy for the optimized exploitation of attribute information on hypergraphs, a joint hypergraph random walk model to devise an effective AHC objective, and an efficient solver with speedup techniques for the objective optimization. The proposed techniques are extensible to various types of attributed networks, and thus, we develop ANCKA as a versatile attributed network clustering framework, capable of attributed graph clustering (AGC), attributed multiplex graph clustering (AMGC), and AHC. Moreover, we devise ANCKA with algorithmic designs tailored for GPU acceleration to boost efficiency. We have conducted extensive experiments to compare our methods with 19 competitors on 8 attributed hypergraphs, 16 competitors on 6 attributed graphs, and 16 competitors on 3 attributed multiplex graphs, all demonstrating the superb clustering quality and efficiency of our methods.

Effective Edge-wise Representation Learning in Edge-Attributed Bipartite Graphs

Graph representation learning (GRL) is to encode graph elements into informative vector representations, which can be used in downstream tasks for analyzing graph-structured data and has seen extensive applications in various domains. However, the majority of extant studies on GRL are geared towards generating node representations, which cannot be readily employed to perform edge-based analytics tasks in edge-attributed bipartite graphs (EABGs) that pervade the real world, e.g., spam review detection in customer-product reviews and identifying fraudulent transactions in user-merchant networks. Compared to node-wise GRL, learning edge representations (ERL) on such graphs is challenging due to the need to incorporate the structure and attribute semantics from the perspective of edges while considering the separate influence of two heterogeneous node sets U and V in bipartite graphs. To our knowledge, despite its importance, limited research has been devoted to this frontier, and existing workarounds all suffer from sub-par results. Motivated by this, this paper designs EAGLE, an effective ERL method for EABGs. Building on an in-depth and rigorous theoretical analysis, we propose the factorized feature propagation (FFP) scheme for edge representations with adequate incorporation of long-range dependencies of edges/features without incurring tremendous computation overheads. We further ameliorate FFP as a dual-view FFP by taking into account the influences from nodes in U and V severally in ERL. Extensive experiments on 5 real datasets showcase the effectiveness of the proposed EAGLE models in semi-supervised edge classification tasks. In particular, EAGLE can attain a considerable gain of at most 38.11% in AP and 1.86% in AUC when compared to the best baselines.

Efficient Topology-aware Data Augmentation for High-Degree Graph Neural Networks

In recent years, graph neural networks (GNNs) have emerged as a potent tool for learning on graph-structured data and won fruitful successes in varied fields. The majority of GNNs follow the message-passing paradigm, where representations of each node are learned by recursively aggregating features of its neighbors. However, this mechanism brings severe over-smoothing and efficiency issues over high-degree graphs (HDGs), wherein most nodes have dozens (or even hundreds) of neighbors, such as social networks, transaction graphs, power grids, etc. Additionally, such graphs usually encompass rich and complex structure semantics, which are hard to capture merely by feature aggregations in GNNs. Motivated by the above limitations, we propose TADA, an efficient and effective front-mounted data augmentation framework for GNNs on HDGs. Under the hood, TADA includes two key modules: (i) feature expansion with structure embeddings, and (ii) topology- and attribute-aware graph sparsification. The former obtains augmented node features and enhanced model capacity by encoding the graph structure into high-quality structure embeddings with our highly-efficient sketching method. Further, by exploiting task-relevant features extracted from graph structures and attributes, the second module enables the accurate identification and reduction of numerous redundant/noisy edges from the input graph, thereby alleviating over-smoothing and facilitating faster feature aggregations over HDGs. Empirically, TADA considerably improves the predictive performance of mainstream GNN models on 8 real homophilic/heterophilic HDGs in terms of node classification, while achieving efficient training and inference processes.

Effective Clustering on Large Attributed Bipartite Graphs

Attributed bipartite graphs (ABGs) are an expressive data model for describing the interactions between two sets of heterogeneous nodes that are associated with rich attributes, such as customer-product purchase networks and author-paper authorship graphs. Partitioning the target node set in such graphs into k disjoint clusters (referred to as k-ABGC) finds widespread use in various domains, including social network analysis, recommendation systems, information retrieval, and bioinformatics. However, the majority of existing solutions towards k-ABGC either overlook attribute information or fail to capture bipartite graph structures accurately, engendering severely compromised result quality. The severity of these issues is accentuated in real ABGs, which often encompass millions of nodes and a sheer volume of attribute data, rendering effective k-ABGC over such graphs highly challenging. In this paper, we propose TPO, an effective and efficient approach to k-ABGC that achieves superb clustering performance on multiple real datasets. TPO obtains high clustering quality through two major contributions: (i) a novel formulation and transformation of the k-ABGC problem based on multi-scale attribute affinity specialized for capturing attribute affinities between nodes with the consideration of their multi-hop connections in ABGs, and (ii) a highly efficient solver that includes a suite of carefully-crafted optimizations for sidestepping explicit affinity matrix construction and facilitating faster convergence. Extensive experiments, comparing TPO against 19 baselines over 5 real ABGs, showcase the superior clustering quality of TPO measured against ground-truth labels. Moreover, compared to the state of the arts, TPO is often more than 40x faster over both small and large ABGs.

SlotGAT: Slot-based Message Passing for Heterogeneous Graph Neural Network

Heterogeneous graphs are ubiquitous to model complex data. There are urgent needs on powerful heterogeneous graph neural networks to effectively support important applications. We identify a potential semantic mixing issue in existing message passing processes, where the representations of the neighbors of a node $v$ are forced to be transformed to the feature space of $v$ for aggregation, though the neighbors are in different types. That is, the semantics in different node types are entangled together into node $v$'s representation. To address the issue, we propose SlotGAT with separate message passing processes in slots, one for each node type, to maintain the representations in their own node-type feature spaces. Moreover, in a slot-based message passing layer, we design an attention mechanism for effective slot-wise message aggregation. Further, we develop a slot attention technique after the last layer of SlotGAT, to learn the importance of different slots in downstream tasks. Our analysis indicates that the slots in SlotGAT can preserve different semantics in various feature spaces. The superiority of SlotGAT is evaluated against 13 baselines on 6 datasets for node classification and link prediction. Our code is at https://github.com/scottjiao/SlotGAT_ICML23/.

Efficient High-Quality Clustering for Large Bipartite Graphs

A bipartite graph contains inter-set edges between two disjoint vertex sets, and is widely used to model real-world data, such as user-item purchase records, author-article publications, and biological interactions between drugs and proteins. k-Bipartite Graph Clustering (k-BGC) is to partition the target vertex set in a bipartite graph into k disjoint clusters. The clustering quality is important to the utility of k-BGC in various applications like social network analysis, recommendation systems, text mining, and bioinformatics, to name a few. Existing approaches to k-BGC either output clustering results with compromised quality due to inadequate exploitation of high-order information between vertices, or fail to handle sizable bipartite graphs with billions of edges. Motivated by this, this paper presents two efficient k-BGC solutions, HOPE and HOPE+, which achieve state-of-the-art performance on large-scale bipartite graphs. HOPE obtains high scalability and effectiveness through a new k-BGC problem formulation based on the novel notion of high-order perspective (HOP) vectors and an efficient technique for low-rank approximation of HOP vectors. HOPE+ further elevates the k-BGC performance to another level with a judicious problem transformation and a highly efficient two-stage optimization framework. Two variants, HOPE+ (FNEM) and HOPE+ (SNEM) are designed when either the Frobenius norm or spectral norm is applied in the transformation. Extensive experiments, comparing HOPE and HOPE+ against 13 competitors on 10 real-world datasets, exhibit that our solutions, especially HOPE+, are superior to existing methods in terms of result quality, while being up to orders of magnitude faster. On the largest dataset MAG with 1.1 billion edges, HOPE+ is able to produce clusters with the highest clustering accuracy within 31 minutes, which is unmatched by any existing solution for k-BGC.

Efficient and Effective Similarity Search over Bipartite Graphs

Similarity search over a bipartite graph aims to retrieve from the graph the nodes that are similar to each other, which finds applications in various fields such as online advertising, recommender systems etc. Existing similarity measures either (i) overlook the unique properties of bipartite graphs, or (ii) fail to capture high-order information between nodes accurately, leading to suboptimal result quality. Recently, Hidden Personalized PageRank (HPP) is applied to this problem and found to be more effective compared with prior similarity measures. However, existing solutions for HPP computation incur significant computational costs, rendering it inefficient especially on large graphs. In this paper, we first identify an inherent drawback of HPP and overcome it by proposing bidirectional HPP (BHPP). Then, we formulate similarity search over bipartite graphs as the problem of approximate BHPP computation, and present an efficient solution Approx-BHPP. Specifically, Approx-BHPP offers rigorous theoretical accuracy guarantees with optimal computational complexity by combining deterministic graph traversal with matrix operations in an optimized and non-trivial way. Moreover, our solution achieves significant gain in practical efficiency due to several carefully-designed optimizations. Extensive experiments, comparing BHPP against 8 existing similarity measures over 7 real bipartite graphs, demonstrate the effectiveness of BHPP on query rewriting and item recommendation. Moreover, Approx-BHPP outperforms baseline solutions often by up to orders of magnitude in terms of computational time on both small and large datasets.

Effective and Scalable Clustering on Massive Attributed Graphs

Given a graph G where each node is associated with a set of attributes, and a parameter k specifying the number of output clusters, k-attributed graph clustering (k-AGC) groups nodes in G into k disjoint clusters, such that nodes within the same cluster share similar topological and attribute characteristics, while those in different clusters are dissimilar. This problem is challenging on massive graphs, e.g., with millions of nodes and billions of edges. For such graphs, existing solutions either incur prohibitively high costs, or produce clustering results with compromised quality. In this paper, we propose ACMin, an effective approach to k-AGC that yields high-quality clusters with cost linear to the size of the input graph G. The main contributions of ACMin are twofold: (i) a novel formulation of the k-AGC problem based on an attributed multi-hop conductance quality measure custom-made for this problem setting, which effectively captures cluster coherence in terms of both topological proximities and attribute similarities, and (ii) a linear-time optimization solver that obtains high-quality clusters iteratively, based on efficient matrix operations such as orthogonal iterations, an alternative optimization approach, as well as an initialization technique that significantly speeds up the convergence of ACMin in practice. Extensive experiments, comparing 11 competitors on 6 real datasets, demonstrate that ACMin consistently outperforms all competitors in terms of result quality measured against ground-truth labels, while being up to orders of magnitude faster. In particular, on the Microsoft Academic Knowledge Graph dataset with 265.2 million edges and 1.1 billion attribute values, ACMin outputs high-quality results for 5-AGC within 1.68 hours using a single CPU core, while none of the 11 competitors finish within 3 days.

Active Learning for Node Classification: The Additional Learning Ability from Unlabelled Nodes

Node classification on graph data is an important task on many practical domains. However, it requires labels for training, which can be difficult or expensive to obtain in practice. Given a limited labelling budget, active learning aims to improve performance by carefully choosing which nodes to label. Our empirical study shows that existing active learning methods for node classification are considerably outperformed by a simple method which randomly selects nodes to label and trains a linear classifier with labelled nodes and unsupervised learning features. This indicates that existing methods do not fully utilize the information present in unlabelled nodes as they only use unlabelled nodes for label acquisition. In this paper, we utilize the information in unlabelled nodes by using unsupervised learning features. We propose a novel latent space clustering-based active learning method for node classification (LSCALE). Specifically, to select nodes for labelling, our method uses the K-Medoids clustering algorithm on a feature space based on the dynamic combination of both unsupervised features and supervised features. In addition, we design an incremental clustering module to avoid redundancy between nodes selected at different steps. We conduct extensive experiments on three public citation datasets and two co-authorship datasets, where our proposed method LSCALE consistently and significantly outperforms the state-of-the-art approaches by a large margin.

Realtime Index-Free Single Source SimRank Processing on Web-Scale Graphs

Given a graph G and a node u in G, a single source SimRank query evaluates the similarity between u and every node v in G. Existing approaches to single source SimRank computation incur either long query response time, or expensive pre-computation, which needs to be performed again whenever the graph G changes. Consequently, to our knowledge none of them is ideal for scenarios in which (i) query processing must be done in realtime, and (ii) the underlying graph G is massive, with frequent updates. Motivated by this, we propose SimPush, a novel algorithm that answers single source SimRank queries without any pre-computation, and at the same time achieves significantly higher query processing speed than even the fastest known index-based solutions. Further, SimPush provides rigorous result quality guarantees, and its high performance does not rely on any strong assumption of the underlying graph. Specifically, compared to existing methods, SimPush employs a radically different algorithmic design that focuses on (i) identifying a small number of nodes relevant to the query, and subsequently (ii) computing statistics and performing residue push from these nodes only. We prove the correctness of SimPush, analyze its time complexity, and compare its asymptotic performance with that of existing methods. Meanwhile, we evaluate the practical performance of SimPush through extensive experiments on 8 real datasets. The results demonstrate that SimPush consistently outperforms all existing solutions, often by over an order of magnitude. In particular, on a commodity machine, SimPush answers a single source SimRank query on a web graph containing over 133 million nodes and 5.4 billion edges in under 62 milliseconds, with 0.00035 empirical error, while the fastest index-based competitor needs 1.18 seconds.