Multi-view clustering has attracted increasing attention in data mining communities. Despite superior clustering performance, we observe that existing multi-view subspace clustering methods directly fuse multi-view information in the similarity level by merging noisy affinity matrices; and isolate the processes of affinity learning, multiple information fusion and clustering. Both factors may cause insufficient utilization of multi-view information, leading to unsatisfying clustering performance. This paper proposes a novel consensus one-step multi-view subspace clustering (COMVSC) method to address these issues. Instead of directly fusing affinity matrices, COMVSC optimally integrates discriminative partition-level information, which is helpful in eliminating noise among data. Moreover, the affinity matrices, consensus representation and final clustering labels are learned simultaneously in a unified framework. Extensive experiment results on benchmark datasets demonstrate the superiority of our method over other state-of-the-art approaches.

Multi-view spectral clustering can effectively reveal the intrinsic cluster structure among data by performing clustering on the learned optimal embedding across views. Though demonstrating promising performance in various applications, most of existing methods usually linearly combine a group of pre-specified first-order Laplacian matrices to construct the optimal Laplacian matrix, which may result in limited representation capability and insufficient information exploitation. Also, storing and implementing complex operations on the{$n\times n}$Laplacian matrices incurs intensive storage and computation complexity. To address these issues, this paper first proposes a multi-view spectral clustering algorithm that learns a high-order optimal neighborhood Laplacian matrix, and then extends it to the late fusion version for accurate and efficient multi-view clustering. Specifically, our proposed algorithm generates the optimal Laplacian matrix by searching the neighborhood of the linear combination of both the first-order and high-order base Laplacian matrices simultaneously. By this way, the representative capacity of the learned optimal Laplacian matrix is enhanced, which is helpful to better utilize the hidden high-order connection information among data, leading to improved clustering performance. We design an efficient algorithm with proved convergence to solve the resultant optimization problem. Extensive experimental results on nine datasets demonstrate the superiority of the proposed algorithm

Multiple kernel clustering (MKC) algorithm aims to group data into different categories by optimally integrating information from a group of pre-specified kernels. Though demonstrating superiorities in various applications, we observe that existing MKC algorithms usuallydo not sufficiently consider the local density around individual data samplesandexcessively limit the representation capacity of the learned optimal kernel, leading to unsatisfying performance. In this paper, we propose an algorithm, called optimal neighborhood MKC with adaptive local kernels (ON-ALK), to address the two issues. In specific, we construct adaptive local kernels to sufficiently consider the local density around individual data samples, where different numbers of neighbors are discriminatingly selected on each sample. Further, the proposed ON-ALK algorithm boosts the representation of the learned optimal kernel via relaxing it into the neighborhood area of weighted combination of the pre-specified kernels. To solve the resultant optimization problem, a three-step iterative algorithm is designed and theoretically proven to be convergent. After that, we also study the generalization bound of the proposed algorithm. Extensive experiments have been conducted to evaluate the clustering performance. As indicated, the algorithm significantly outperforms state-of-the-art methods in recent literatures on six challenging benchmark datasets, verifying its advantages and effectiveness.

Although demonstrating great success, previous multi-view unsupervised feature selection (MV-UFS) methods often construct a view-specific similarity graph and characterize the local structure of data within each single view. In such a way, the cross-view information could be ignored. In addition, they usually assume that different feature views are projected from a latent feature space while the diversity of different views cannot be fully captured. In this work, we resent a MV-UFS model via cross-view local structure preserved diversity and consensus learning, referred to as CvLP-DCL briefly. In order to exploit both the shared and distinguishing information across different views, we project each view into a label space, which consists of a consensus part and a view-specific part. Therefore, we regularize the fact that different views represent same samples. Meanwhile, a cross-view similarity graph learning term with matrix-induced regularization is embedded to preserve the local structure of data in the label space. By imposing the$l_{2,1}$-norm on the feature projection matrices for constraining row sparsity, discriminative features can be selected from different views. An efficient algorithm is designed to solve the resultant optimization problem and extensive experiments on six publicly datasets are conducted to validate the effectiveness of the proposed CvLP-DCL.

Multi-view clustering has attracted increasing attention in multimedia, machine learning and data mining communities. As one kind of the essential multi-view clustering algorithm, multi-view subspace clustering (MVSC) becomes more and more popular due to its strong ability to reveal the intrinsic low dimensional clustering structure hidden across views. Despite superior clustering performance in various applications, we observe that existing MVSC methodsdirectly fuse multi-view information in the similarity level by merging noisy affinity matrices; andisolate the processes of affinity learning, multi-view information fusion and clustering. Both factors may cause insufficient utilization of multi-view information, leading to unsatisfying clustering performance. This paper proposes a novel consensus one-step multi-view subspace clustering (COMVSC) method to address these issues. Instead of directly fusing multiple affinity matrices, COMVSC optimally integrates discriminative partition-level information, which is helpful to eliminate noise among data. Moreover, the affinity matrices, consensus representation and final clustering labels matrix are learned simultaneously in a unified framework. By doing so, the three steps can negotiate with each other to best serve the clustering task, leading to improved performance. Accordingly, we propose an iterative algorithm to solve the resulting optimization problem. Extensive experiment results on benchmark datasets demonstrate the superiority of our method against other state-of-the-art approaches.

Feature extraction and feature selection have been regarded as two independent dimensionality reduction methods in most of the existing literature. In this paper, we propose to integrate both approaches into a unified framework and design an unsupervised linear feature selective projection (FSP) for feature extraction with low-rank embedding and dual Laplacian regularization, with the aim to exploit the intrinsic relationship among data and suppress the impact of noise. Specifically, a projection matrix with an l2,1-norm regularization is introduced to project original high dimensional data points into a new subspace with lower dimension, where the l2,1-norm regularization can endow the projection with good interpretability. We deploy a coefficient matrix with low rank constraint to reconstruct the data points and the l2,1-norm is imposed to regularize the data reconstruction errors in the low-dimensional subspace and make FSP robust to noise. Furthermore, a dual graph Laplacian regularization term is imposed on the low dimensional data and data reconstruction matrix for preserving the local manifold geometrical structure of data. Finally, an alternatively iterative algorithm is carefully designed for solving the proposed optimization model. Theoretical convergence and computational complexity analysis of the algorithm are also provided. Comprehensive experiments on various benchmark datasets have been carried out to evaluate the performance of the proposed FSP. As indicated, our algorithm significantly outperforms other state-of-the-art methods for feature extraction.