Double Self-weighted Multi-view Clustering via Adaptive View Fusion

Multi-view clustering has been applied in many real-world applications where original data often contain noises. Some graph-based multi-view clustering methods have been proposed to try to reduce the negative influence of noises. However, previous graph-based multi-view clustering methods treat all features equally even if there are redundant features or noises, which is obviously unreasonable. In this paper, we propose a novel multi-view clustering framework Double Self-weighted Multi-view Clustering (DSMC) to overcome the aforementioned deficiency. DSMC performs double self-weighted operations to remove redundant features and noises from each graph, thereby obtaining robust graphs. For the first self-weighted operation, it assigns different weights to different features by introducing an adaptive weight matrix, which can reinforce the role of the important features in the joint representation and make each graph robust. For the second self-weighting operation, it weights different graphs by imposing an adaptive weight factor, which can assign larger weights to more robust graphs. Furthermore, by designing an adaptive multiple graphs fusion, we can fuse the features in the different graphs to integrate these graphs for clustering. Experiments on six real-world datasets demonstrate its advantages over other state-of-the-art multi-view clustering methods

Consensus graph and spectral representation for one-step multi-view kernel based clustering

Recently, multi-view clustering has received much attention in the fields of machine learning and pattern recognition. Spectral clustering for single and multiple views has been the common solution. Despite its good clustering performance, it has a major limitation: it requires an extra step of clustering. This extra step, which could be the famous k-means clustering, depends heavily on initialization, which may affect the quality of the clustering result. To overcome this problem, a new method called Multiview Clustering via Consensus Graph Learning and Nonnegative Embedding (MVCGE) is presented in this paper. In the proposed approach, the consensus affinity matrix (graph matrix), consensus representation and cluster index matrix (nonnegative embedding) are learned simultaneously in a unified framework. Our proposed method takes as input the different kernel matrices corresponding to the different views. The proposed learning model integrates two interesting constraints: (i) the cluster indices should be as smooth as possible over the consensus graph and (ii) the cluster indices are set to be as close as possible to the graph convolution of the consensus representation. In this approach, no post-processing such as k-means or spectral rotation is required. Our approach is tested with real and synthetic datasets. The experiments performed show that the proposed method performs well compared to many state-of-the-art approaches

Scalable Incomplete Multi-View Clustering with Structure Alignment

The success of existing multi-view clustering (MVC) relies on the assumption that all views are complete. However, samples are usually partially available due to data corruption or sensor malfunction, which raises the research of incomplete multi-view clustering (IMVC). Although several anchor-based IMVC methods have been proposed to process the large-scale incomplete data, they still suffer from the following drawbacks: i) Most existing approaches neglect the inter-view discrepancy and enforce cross-view representation to be consistent, which would corrupt the representation capability of the model; ii) Due to the samples disparity between different views, the learned anchor might be misaligned, which we referred as the Anchor-Unaligned Problem for Incomplete data (AUP-ID). Such the AUP-ID would cause inaccurate graph fusion and degrades clustering performance. To tackle these issues, we propose a novel incomplete anchor graph learning framework termed Scalable Incomplete Multi-View Clustering with Structure Alignment (SIMVC-SA). Specially, we construct the view-specific anchor graph to capture the complementary information from different views. In order to solve the AUP-ID, we propose a novel structure alignment module to refine the cross-view anchor correspondence. Meanwhile, the anchor graph construction and alignment are jointly optimized in our unified framework to enhance clustering quality. Through anchor graph construction instead of full graphs, the time and space complexity of the proposed SIMVC-SA is proven to be linearly correlated with the number of samples. Extensive experiments on seven incomplete benchmark datasets demonstrate the effectiveness and efficiency of our proposed method. Our code is publicly available at https://github.com/wy1019/SIMVC-SA

Louvain-like Methods for Community Detection in Multi-Layer Networks

In many complex systems, entities interact with each other through complicated patterns that embed different relationships, thus generating networks with multiple levels and/or multiple types of edges. When trying to improve our understanding of those complex networks, it is of paramount importance to explicitly take the multiple layers of connectivity into account in the analysis. In this paper, we focus on detecting community structures in multi-layer networks, i.e., detecting groups of well-connected nodes shared among the layers, a very popular task that poses a lot of interesting questions and challenges. Most of the available algorithms in this context either reduce multi-layer networks to a single-layer network or try to extend algorithms for single-layer networks by using consensus clustering. Those approaches have anyway been criticized lately. They indeed ignore the connections among the different layers, hence giving low accuracy. To overcome these issues, we propose new community detection methods based on tailored Louvain-like strategies that simultaneously handle the multiple layers. We consider the informative case, where all layers show a community structure, and the noisy case, where some layers only add noise to the system. We report experiments on both artificial and real-world networks showing the effectiveness of the proposed strategies.Comment: 16 pages, 4 figure

Late Fusion Multi-view Clustering via Global and Local Alignment Maximization

Multi-view clustering (MVC) optimally integrates complementary information from different views to improve clustering performance. Although demonstrating promising performance in various applications, most of existing approaches directly fuse multiple pre-specified similarities to learn an optimal similarity matrix for clustering, which could cause over-complicated optimization and intensive computational cost. In this paper, we propose late fusion MVC via alignment maximization to address these issues. To do so, we first reveal the theoretical connection of existing k-means clustering and the alignment between base partitions and the consensus one. Based on this observation, we propose a simple but effective multi-view algorithm termed LF-MVC-GAM. It optimally fuses multiple source information in partition level from each individual view, and maximally aligns the consensus partition with these weighted base ones. Such an alignment is beneficial to integrate partition level information and significantly reduce the computational complexity by sufficiently simplifying the optimization procedure. We then design another variant, LF-MVC-LAM to further improve the clustering performance by preserving the local intrinsic structure among multiple partition spaces. After that, we develop two three-step iterative algorithms to solve the resultant optimization problems with theoretically guaranteed convergence. Further, we provide the generalization error bound analysis of the proposed algorithms. Extensive experiments on eighteen multi-view benchmark datasets demonstrate the effectiveness and efficiency of the proposed LF-MVC-GAM and LF-MVC-LAM, ranging from small to large-scale data items. The codes of the proposed algorithms are publicly available at https://github.com/wangsiwei2010/latefusionalignment

Contribution to Graph-based Multi-view Clustering: Algorithms and Applications

185 p.In this thesis, we study unsupervised learning, specifically, clustering methods for dividing data into meaningful groups. One major challenge is how to find an efficient algorithm with low computational complexity to deal with different types and sizes of datasets.For this purpose, we propose two approaches. The first approach is named "Multi-view Clustering via Kernelized Graph and Nonnegative Embedding" (MKGNE), and the second approach is called "Multi-view Clustering via Consensus Graph Learning and Nonnegative Embedding" (MVCGE). These two approaches jointly solve four tasks. They jointly estimate the unified similarity matrix over all views using the kernel tricks, the unified spectral projection of the data, the clusterindicator matrix, and the weight of each view without additional parameters. With these two approaches, there is no need for any postprocessing such as k-means clustering.In a further study, we propose a method named "Multi-view Spectral Clustering via Constrained Nonnegative Embedding" (CNESE). This method can overcome the drawbacks of the spectral clustering approaches, since they only provide a nonlinear projection of the data, on which an additional step of clustering is required. This can degrade the quality of the final clustering due to various factors such as the initialization process or outliers. Overcoming these drawbacks can be done by introducing a nonnegative embedding matrix which gives the final clustering assignment. In addition, some constraints are added to the targeted matrix to enhance the clustering performance.In accordance with the above methods, a new method called "Multi-view Spectral Clustering with a self-taught Robust Graph Learning" (MCSRGL) has been developed. Different from other approaches, this method integrates two main paradigms into the one-step multi-view clustering model. First, we construct an additional graph by using the cluster label space in addition to the graphs associated with the data space. Second, a smoothness constraint is exploited to constrain the cluster-label matrix and make it more consistent with the data views and the label view.Moreover, we propose two unified frameworks for multi-view clustering in Chapter 9. In these frameworks, we attempt to determine a view-based graphs, the consensus graph, the consensus spectral representation, and the soft clustering assignments. These methods retain the main advantages of the aforementioned methods and integrate the concepts of consensus and unified matrices. By using the unified matrices, we enforce the matrices of different views to be similar, and thus the problem of noise and inconsistency between different views will be reduced.Extensive experiments were conducted on several public datasets with different types and sizes, varying from face image datasets, to document datasets, handwritten datasets, and synthetics datasets. We provide several analyses of the proposed algorithms, including ablation studies, hyper-parameter sensitivity analyses, and computational costs. The experimental results show that the developed algorithms through this thesis are relevant and outperform several competing methods