Parameter-Free Consensus Embedding Learning for Multiview Graph-Based Clustering

Cross-View Approximation on Grassmann Manifold for Multiview Clustering

In existing multiview clustering research, the comprehensive learning from multiview graph and feature spaces simultaneously remains insufficient when achieving a consistent clustering structure. In addition, a postprocessing step is often required. In light of these considerations, a cross-view approximation on Grassman manifold (CAGM) model is proposed to address inconsistencies within multiview adjacency matrices, feature matrices, and cross-view combinations from the two sources. The model uses a ratio-formed objective function, enabling parameter-free bidirectional fusion. Furthermore, the CAGM model incorporates a paired encoding mechanism to generate low-dimensional and orthogonal cross-view embeddings. Through the approximation of two measurable subspaces on the Grassmann manifold, the direct acquisition of the indicator matrix is realized. Furthermore, an effective optimization algorithm corresponding to the CAGM model is derived. Comprehensive experiments on four real-world datasets are conducted to substantiate the effectiveness of our proposed method.

Joint Structured Bipartite Graph and Row-Sparse Projection for Large-Scale Feature Selection

Feature selection plays an important role in data analysis, yet traditional graph-based methods often produce suboptimal results. These methods typically follow a two-stage process: constructing a graph with data-to-data affinities or a bipartite graph with data-to-anchor affinities and independently selecting features based on their scores. In this article, a large-scale feature selection approach based on structured bipartite graph and row-sparse projection (RS2BLFS) is proposed to overcome this limitation. RS2BLFS integrates the construction of a structured bipartite graph consisting of c connected components into row-sparse projection learning with k nonzero rows. This integration allows for the joint selection of an optimal feature subset in an unsupervised manner. Notably, the c connected components of the structured bipartite graph correspond to c clusters, each with multiple subcluster centers. This feature makes RS2BLFS particularly effective for feature selection and clustering on nonspherical large-scale data. An algorithm with theoretical analysis is developed to solve the optimization problem involved in RS2BLFS. Experimental results on synthetic and real-world datasets confirm its effectiveness in feature selection tasks.

Parameter-Free Multiview K-Means Clustering With Coordinate Descent Method

Recently, more and more real-world datasets have been composed of heterogeneous but related features from diverse views. Multiview clustering provides a promising attempt at a solution for partitioning such data according to heterogeneous information. However, most existing methods suffer from hyper-parameter tuning trouble and high computational cost. Besides, there is still an opportunity for improvement in clustering performance. To this end, a novel multiview framework, called parameter-free multiview -means clustering with coordinate descent method (PFMVKM), is presented to address the above problems. Specifically, PFMVKM is completely parameter-free and learns the weights via a self-weighted scheme, which can avoid the intractable process of hyper-parameters tuning. Moreover, our model is capable of directly calculating the cluster indicator matrix, with no need to learn the cluster centroid matrix and the indicator matrix simultaneously as previous multiview methods have to do. What's more, we propose an efficient optimization algorithm utilizing the idea of coordinate descent, which can not only reduce the computational complexity but also improve the clustering performance. Extensive experiments on various types of real datasets illustrate that the proposed method outperforms existing state-of-the-art competitors and conforms well with the actual situation.

Multiview Spectral Clustering Based on Consensus Neighbor Strategy

Multiview spectral clustering, renowned for its spatial learning capability, has garnered significant attention in the data mining field. However, existing methods assume that the optimal consensus adjacency matrix is confined within the space spanned by each view's adjacency matrix. This constraint restricts the feasible domain of the algorithm and hinders the exploration of the optimal consensus adjacency matrix. To address this limitation, we propose a novel and convex strategy, termed the consensus neighbor strategy, for learning the optimal consensus adjacency matrix. This approach constructs the optimal consensus adjacency matrix by capturing the consensus local structure of each sample across all views, thereby expanding the search space and facilitating the discovery of the optimal consensus adjacency matrix. Furthermore, we introduce the concept of a correlation measuring matrix to prevent trivial solution. We develop an efficient iterative algorithm to solve the resulting optimization problem, benefitting from the convex nature of our model, which ensures convergence to a global optimum. Experimental results on 16 multiview datasets demonstrate that our proposed algorithm surpasses state-of-the-art methods in terms of its robust consensus representation learning capability. The code of this article is uploaded to https://github.com/PhdJiayiTang/Consensus-Neighbor-Strategy.git.

Iterative Deep Structural Graph Contrast Clustering for Multiview Raw Data

Multiview clustering has attracted increasing attention to automatically divide instances into various groups without manual annotations. Traditional shadow methods discover the internal structure of data, while deep multiview clustering (DMVC) utilizes neural networks with clustering-friendly data embeddings. Although both of them achieve impressive performance in practical applications, we find that the former heavily relies on the quality of raw features, while the latter ignores the structure information of data. To address the above issue, we propose a novel method termed iterative deep structural graph contrast clustering (IDSGCC) for multiview raw data consisting of topology learning (TL), representation learning (RL), and graph structure contrastive learning to achieve better performance. The TL module aims to obtain a structured global graph with constraint structural information and then guides the RL to preserve the structural information. In the RL module, graph convolutional network (GCN) takes the global structural graph and raw features as inputs to aggregate the samples of the same cluster and keep the samples of different clusters away. Unlike previous methods performing contrastive learning at the representation level of the samples, in the graph contrastive learning module, we conduct contrastive learning at the graph structure level by imposing a regularization term on the similarity matrix. The credible neighbors of the samples are constructed as positive pairs through the credible graph, and other samples are constructed as negative pairs. The three modules promote each other and finally obtain clustering-friendly embedding. Also, we set up an iterative update mechanism to update the topology to obtain a more credible topology. Impressive clustering results are obtained through the iterative mechanism. Comparative experiments on eight multiview datasets show that our model outperforms the state-of-the-art traditional and deep clustering competitors.

Efficient and Effective One-Step Multiview Clustering

Multiview clustering algorithms have attracted intensive attention and achieved superior performance in various fields recently. Despite the great success of multiview clustering methods in realistic applications, we observe that most of them are difficult to apply to large-scale datasets due to their cubic complexity. Moreover, they usually use a two-stage scheme to obtain the discrete clustering labels, which inevitably causes a suboptimal solution. In light of this, an efficient and effective one-step multiview clustering (E2OMVC) method is proposed to directly obtain clustering indicators with a small-time burden. Specifically, according to the anchor graphs, the smaller similarity graph of each view is constructed, from which the low-dimensional latent features are generated to form the latent partition representation. By introducing a label discretization mechanism, the binary indicator matrix can be directly obtained from the unified partition representation which is formed by fusing all latent partition representations from different views. In addition, by coupling the fusion of all latent information and the clustering task into a joint framework, the two processes can help each other and obtain a better clustering result. Extensive experimental results demonstrate that the proposed method can achieve comparable or better performance than the state-of-the-art methods. The demo code of this work is publicly available at https://github.com/WangJun2023/EEOMVC.

Fast Multiview Clustering by Optimal Graph Mining

Multiview clustering (MVC) aims to exploit heterogeneous information from different sources and was extensively investigated in the past decade. However, far less attention has been paid to handling large-scale multiview data. In this brief, we fill this gap and propose a fast multiview clustering by an optimal graph mining model to handle large-scale data. We mine a consistent clustering structure from landmark-based graphs of different views, from which the optimal graph based on the one-hot encoding of cluster labels is recovered. Our model is parameter-free, so intractable hyperparameter tuning is avoided. An efficient algorithm of linear complexity to the number of samples is developed to solve the optimization problems. Extensive experiments on real-world datasets of various scales demonstrate the superiority of our proposal.

CLEAR: Cluster-Enhanced Contrast for Self-Supervised Graph Representation Learning

This article studies self-supervised graph representation learning, which is critical to various tasks, such as protein property prediction. Existing methods typically aggregate representations of each individual node as graph representations, but fail to comprehensively explore local substructures (i.e., motifs and subgraphs), which also play important roles in many graph mining tasks. In this article, we propose a self-supervised graph representation learning framework named cluster-enhanced Contrast (CLEAR) that models the structural semantics of a graph from graph-level and substructure-level granularities, i.e., global semantics and local semantics, respectively. Specifically, we use graph-level augmentation strategies followed by a graph neural network-based encoder to explore global semantics. As for local semantics, we first use graph clustering techniques to partition each whole graph into several subgraphs while preserving as much semantic information as possible. We further employ a self-attention interaction module to aggregate the semantics of all subgraphs into a local-view graph representation. Moreover, we integrate both global semantics and local semantics into a multiview graph contrastive learning framework, enhancing the semantic-discriminative ability of graph representations. Extensive experiments on various real-world benchmarks demonstrate the efficacy of the proposed over current graph self-supervised representation learning approaches on both graph classification and transfer learning tasks.