GRACE: A General Graph Convolution Framework for Attributed Graph Clustering

Graphs are one of the popular models for effective representation of complex structured huge data and the similarity search for graphs has become a fundamental research problem in Graph Mining. In this paper initially, the preliminary graph related basic theorems are brushed and showcased on with various research sub domains such as Graph Classification, Graph Searching, Graph Indexing, and Graph Clustering. These are discussed with few of the most dominant algorithms in their respective sub domains. Finally a model is proposed along with various algorithms with their future projection.

Deep graph clustering with multi-level subspace fusion

Discovering dense subgraphs and understanding the relations among them is a fundamental problem in graph mining. We want to not only identify dense subgraphs, but also build a hierarchy among them (e.g., larger but sparser subgraphs formed by two smaller dense subgraphs). Peeling algorithms ( k -core, k -truss, and nucleus decomposition) have been effective to locate many dense subgraphs. However, constructing a hierarchical representation of density structure, even correctly computing the connected k -cores and k -trusses, have been mostly overlooked. Keeping track of connected components during peeling requires an additional traversal operation, which is as expensive as the peeling process. In this paper, we start with a thorough survey and point to nuances in problem formulations that lead to significant differences in runtimes. We then propose efficient and generic algorithms to construct the hierarchy of dense subgraphs for k -core, k -truss, or any nucleus decomposition. Our algorithms leverage the disjoint-set forest data structure to efficiently construct the hierarchy during traversal. Furthermore, we introduce a new idea to avoid traversal. We construct the subgraphs while visiting neighborhoods in the peeling process, and build the relations to previously constructed subgraphs. We also consider an existing idea to find the k -core hierarchy and adapt for our objectives efficiently. Experiments on different types of large scale real-world networks show significant speedups over naive algorithms and existing alternatives. Our algorithms also outperform the hypothetical limits of any possible traversal-based solution.

Finding dense subgraphs of a large graph is a standard problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications. In this paper we introduce a new family of dense subgraph objectives, parameterized by a single parameter $p$, based on computing generalized means of degree sequences of a subgraph. Our objective captures both the standard densest subgraph problem and the maximum $k$-core as special cases, and provides a way to interpolate between and extrapolate beyond these two objectives when searching for other notions of dense subgraphs. In terms of algorithmic contributions, we first show that our objective can be minimized in polynomial time for all $p \geq 1$ using repeated submodular minimization. A major contribution of our work is analyzing the performance of different types of peeling algorithms for dense subgraphs both in theory and practice. We prove that the standard peeling algorithm can perform arbitrarily poorly on our generalized objective, but we then design a more sophisticated peeling method which for $p \geq 1$ has an approximation guarantee that is always at least $1/2$ and converges to 1 as $p \rightarrow \infty$. In practice, we show that this algorithm obtains extremely good approximations to the optimal solution, scales to large graphs, and highlights a range of different meaningful notions of density on graphs coming from numerous domains. Furthermore, it is typically able to approximate the densest subgraph problem better than the standard peeling algorithm, by better accounting for how the removal of one node affects other nodes in its neighborhood.

Attributed graph clustering is a basic yet essential method for graph data exploration. Recent efforts over graph contrastive learning have achieved impressive clustering performance. However, we observe that the commonly adopted InfoMax operation tends to capture redundant information, limiting the downstream clustering performance. To this end, we develop a novel method termed attributed graph clustering with dual redundancy reduction (AGC-DRR) to reduce the information redundancy in both input space and latent feature space. Specifically, for the input space redundancy reduction, we introduce an adversarial learning mechanism to adaptively learn a redundant edge-dropping matrix to ensure the diversity of the compared sample pairs. To reduce the redundancy in the latent space, we force the correlation matrix of the cross-augmentation sample embedding to approximate an identity matrix. Consequently, the learned network is forced to be robust against perturbation while discriminative against different samples. Extensive experiments have demonstrated that AGC-DRR outperforms the state-of-the-art clustering methods on most of our benchmarks. The corresponding code is available at https://github.com/gongleii/AGC-DRR.

Recent advances in satellite tracking technologies can provide huge amount of data for biologists to understand continuous long movement patterns of wild bird species. In particular, highly correlated habitat areas are of great biological interests. Biologists can use this information to strive potential ways for controlling highly pathogenic avian influenza. We convert these biological problems into graph mining problems. Traditional models for frequent graph mining assign each vertex label with equal weight. However, the weight difference between vertexes can make strong impact on decision making by biologists. In this paper, by considering different weights of individual vertex in the graph, we develop a new algorithm, Helen, which focuses on identifying cliques with high weights. We introduce “graph-weighted support framework” to reduce clique candidates, and then filter out the low weighted cliques. We evaluate our algorithm on real life birds’ migration data sets, and show that graph mining can be very helpful for ecologists to discover unanticipated bird migration relationships.KeywordsGraph MiningBirds MigrationBirds Flues H5N1Scientific dataQinghai Lake

Attributed graph clustering aims to partition nodes of a graph structure into different groups. Recent works usually use variational graph autoencoder (VGAE) to make the node representations obey a specific distribution. Although they have shown promising results, how to introduce supervised information to guide the representation learning of graph nodes and improve clustering performance is still an open problem. In this article, we propose a Collaborative Decision-Reinforced Self-Supervision (CDRS) method to solve the problem, in which a pseudo node classification task collaborates with the clustering task to enhance the representation learning of graph nodes. First, a transformation module is used to enable end-to-end training of existing methods based on VGAE. Second, the pseudo node classification task is introduced into the network through multitask learning to make classification decisions for graph nodes. The graph nodes that have consistent decisions on clustering and pseudo node classification are added to a pseudo-label set, which can provide fruitful self-supervision for subsequent training. This pseudo-label set is gradually augmented during training, thus reinforcing the generalization capability of the network. Finally, we investigate different sorting strategies to further improve the quality of the pseudo-label set. Extensive experiments on multiple datasets show that the proposed method achieves outstanding performance compared with state-of-the-art methods. Our code is available at https://github.com/Jillian555/TNNLS_CDRS.

Spectral embedding network for attributed graph clustering

Due to the explosive growth of graph data, attributed graph clustering has received increasing attention recently. Although deep neural networks based graph clustering methods have achieved impressive performance, the huge amount of training parameters make them time-consuming and memory- intensive. Moreover, real-world graphs are often noisy or incomplete and are not optimal for the clustering task. To solve these problems, we design a graph learning framework for the attributed graph clustering task in this study. We firstly develop a shallow model for learning a fine-grained graph from smoothed data, which sufficiently exploits both node attributes and topology information. A regularizer is also designed to flexibly explore the high-order information hidden in the data. To further reduce the computation complexity, we then propose a linear method with respect to node number n, where a smaller graph is learned based on importance sampling strategy to select m(m≪n) anchors. Extensive experiments on six benchmark datasets demonstrate that our proposed methods are not only effective but also more efficient than state-of-the-art techniques. In particular, our method surpasses many recent deep learning approaches.

Community detection for attributed graphs, also called attributed graph clustering, is a new challenging issue in data mining due to the increasing emergence of different kinds of real-word networks with rich attributes. The existing works for the attributed graph clustering can be divided into two classes, namely distanced-based approaches and model-based approaches. In this paper, we focus on a model-based approach called clustered attributed graph model proposed by Xu et al. [12]. Instead of the original variational Bayes EM algorithm (VBEM) for solving this model, we propose a new variational EM algorithm (VEM). Comparing with the VBEM algorithm, our proposed VEM algorithm can reduce the number of parameters when fitting the model, which brings the lower computational complexity and easier implementation in practice. Additionally, a good model selection criterion ICL can be easily derived under the VEM framework. Our proposed VEM algorithm is demonstrated to perform competitively over the existing state of the art VBEM algorithm in terms of the extensive simulations and the real data.

Submodular function optimization is a fundamental tool in modeling complex interactions in machine learning and graph mining problems. We propose to study constrained submodular optimization to improve the current state of the art. Our goals are to design evolutionary algorithms with stronger approximation guarantees, the study of submodular maximization under submodular constraints, fairness in submodular optimization, and k-submodular optimization. We begin by exploring a basic submodular maximization problem in the context of viral marketing/information diffusion in social networks. From there, we broaden our scope to include a broader range of scenarios and formulate them into more optimization problems. Looking ahead, we plan to tackle scalable submodular optimization problems in fairness, dynamic constraints, dynamic streams, and distributed fashion. Lastly, we discuss a series of real-world applications that can be formulated as submodular optimization problems. In the future, we aim to apply algorithmic ideas to solve more real-world problems.

Recently, due to the rapid growth of electronic data having graph structures such as HTML and XML texts and chemical compounds, many researchers have been interested in data mining and machine learning techniques for finding useful patterns from graph-structured data (graph data). Since graph data contain a huge number of substructures and it tends to be computationally expensive to decide whether or not such data have given structural features, graph mining problems face computational difficulties. Let ${\mathcal{C}}$ be a graph class which satisfies a connected hereditary property and contains infinitely many different biconnected graphs, and for which a special kind of the graph isomorphism problem can be computed in polynomial time. In this paper, we consider learning and mining problems for ${\mathcal{C}}$ . Firstly, we define a new graph pattern, which is called a block preserving graph pattern (bp-graph pattern) for ${\mathcal{C}}$ . Secondly, we present a polynomial time algorithm for deciding whether or not a given bp-graph pattern matches a given graph in ${\mathcal{C}}$ . Thirdly, by giving refinement operators over bp-graph patterns, we present a polynomial time algorithm for finding a minimally generalized bp-graph pattern for ${\mathcal{C}}$ . Outerplanar graphs are planar graphs which can be embedded in the plane in such a way that all of vertices lie on the outer boundary. Many pharmacologic chemical compounds are known to be represented by outerplanar graphs. The class of connected outerplanar graphs ${\mathcal{O}}$ satisfies the above conditions for ${\mathcal{C}}$ . Next, we propose two incremental polynomial time algorithms for enumerating all frequent bp-graph patterns with respect to a given finite set of graphs in ${\mathcal{O}}$ . Finally, by reporting experimental results obtained by applying the two graph mining algorithms to a subset of the NCI dataset, we evaluate the performance of the two graph mining algorithms.

Multi-label node classification is an important yet under-explored domain in graph mining as many real-world nodes belong to multiple categories rather than just a single one. Although a few efforts have been made by utilizing Graph Convolution Networks (GCNs) to learn node representations and model correlations between multiple labels in the embedding space, they still suffer from the ambiguous feature and ambiguous topology induced by multiple labels, which reduces the credibility of the messages delivered in graphs and overlooks the label correlations on graph data. Therefore, it is crucial to reduce the ambiguity and empower the GCNs for accurate classification. However, this is quite challenging due to the requirement of retaining the distinctiveness of each label while fully harnessing the correlation between labels simultaneously. To address these issues, in this paper, we propose a Correlation-aware Graph Convolutional Network (CorGCN) for multi-label node classification. By introducing a novel Correlation-Aware Graph Decomposition module, CorGCN can learn a graph that contains rich label-correlated information for each label. It then employs a Correlation-Enhanced Graph Convolution to model the relationships between labels during message passing to further bolster the classification process. Extensive experiments on five datasets demonstrate the effectiveness of our proposed CorGCN.

Graph clustering is a prevalent issue associated with social networks, data mining, and machine learning; its objective is to detect communities or groups in networks. Inspired by the recent success of deep learning (DL), new DL-based graph clustering methods have achieved promising results. However, a deep neural network involves a large number of training parameters. Moreover, existing methods typically select the similarity metric by an ad hoc approach, which considerably affects the resulting output. In this study, we propose a principled graph learning perspective, fine-grained attributed graph clustering. Based on a shallow approach, the proposed method sufficiently exploits both node features and structure information by benefiting from graph convolution. Consequently, a fine-grained graph encoded higher-order relations is automatically learned. Comprehensive experiments on benchmark datasets demonstrate the superiority of the proposed method over state-of-the-art algorithms, including several DL methods.

The development of big data has brought changes to society and brought us challenges. How to extract useful information from complex data has become the focus of research in recent years. Personalized recommendation as an effective solution has received widespread attention in academia and industry. Collaborative filtering has been widely used by finding users with similar user behaviors as the preferences of similar users. However, the existing methods ignore the interaction information between the user and the item during feature extraction, which leads to imperfect feature extraction and affects the algorithm effect. This paper proposes a graph convolution collaborative filtering model based on the attention model, which uses the graph convolution network to embed user and item interaction information into feature vectors, and uses the attention model to highlight the relatively important interaction information among them, so as to obtain more excellent feature vector. The experimental results show that the model has a good effect on the two commonly used evaluation metrics: recall and normalized discounted cumulative gain(NDCG).