Elsevier

Information Fusion

Volume 68, April 2021, Pages 8-21
Information Fusion

Full length article
Relaxed multi-view clustering in latent embedding space

https://doi.org/10.1016/j.inffus.2020.10.013Get rights and content

Highlights

  • We propose two novel multi-view clustering methods.

  • The three key matrixes can be learned in a unified framework.

  • Extensive experiments are conducted.

Abstract

Although many multi-view clustering approaches have been developed recently, one common shortcoming of most of them is that they generally rely on the original feature space or consider the two components of the similarity-based clustering separately (i.e., similarity matrix construction and cluster indicator matrix calculation), which may negatively affect the clustering performance. To tackle this shortcoming, in this paper, we propose a new method termed Multi-view Clustering in Latent Embedding Space (MCLES), which jointly recovers a comprehensive latent embedding space, a robust global similarity matrix and an accurate cluster indicator matrix in a unified optimization framework. In this framework, each variable boosts each other in an interplay manner to achieve the optimal solution. To avoid the optimization problem of quadratic programming, we further propose to relax the constraint of the global similarity matrix, based on which an improved version termed Relaxed Multi-view Clustering in Latent Embedding Space (R-MCLES) is proposed. Compared with MCLES, R-MCLES achieves lower computational complexity with more correlations between pairs of data points. Extensive experiments conducted on both image and document datasets have demonstrated the superiority of the proposed methods when compared with the state-of-the-art.

Introduction

Multi-view clustering has become a hot research topic in machine learning in the past decade, due to the rapid emergence of a great deal of multi-view data from different areas or multiple sources [1], [2], [3], [4], [5], [6], [7], [8]. In multi-view data, the same instance can be represented by multiple views obtaining from multiple sources or different feature subsets [9], [10], [11], [12], [13], [14], [15], [16]. For instance, in a webpage, different types of data, such as texts, videos and images, can be taken into consideration as they are different aspects of the webpage. A text news can be translated into multiple languages, such as English version, Chinese version, Spanish version and so on. Considering the diversity of multiple views, it is essential to study how to integrate such kind of data efficiently and cluster them effectively.

Prior to most of the multi-view learning methods, a straightforward way to cope with the multi-view data is to concatenate all the features into a new feature vector, which is then fed into a single-view clustering method to obtain the final clustering results. However, this naive strategy neglects the different characteristics as well as the correlation among multiple views. Recently, a large number of multi-view clustering methods have been proposed to handle multi-view data by effectively considering the rich information from multiple views [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28]. For instance, to minimize the disagreement between each pair of views, a co-regularization technique was introduced in multi-view spectral clustering [19]. Inspired by the idea of co-training, Kumar et al. proposed to generate clusters that are consistent across the multiple views [18]. However, these methods can be affected by the weak or poor quality of the original views, since most of them directly work on the original features from the dataset, in which there may be lots of noise and corruptions, possibly resulting in the degraded clustering performance. To handle the potential noise, Zhang et al. performed data reconstruction based on the learned subspace [21]. Xia et al. developed a Markov chain method which takes as input a shared low-rank transition probability matrix associated with all views [20]. Nevertheless, though these methods have achieved promising clustering results, on the one hand, they generally rely on the original features in each view, still lacking the ability to discover a unified feature representation for multi-view data. On the other hand, for the similarity-based multi-view clustering methods, they mostly tend to consider the two components of similarity-based clustering (i.e., similarity matrix construction and cluster indicator matrix calculation) separately, and cannot formulate these two components simultaneously in a unified framework.

Aiming to address the above limitation, in this paper, we propose a novel framework termed Multi-view Clustering in Latent Embedding Space (MCLES) according to the underlying assumption that multiple views are originated from one underlying latent representation, which reveals the shared latent structure among different views. The proposed method jointly learns the latent embedding representation matrix, the global similarity matrix and the cluster indicator matrix in a unified model. Specifically, the latent embedding representation matrix learned from the multi-view features is able to explore the relationships among different samples and avoid the possible corruption as well as the curse of dimensionality. With the idea of self-expression, the global similarity matrix is constructed based on the learned latent embedding representation rather than the original features of data. Further, the cluster indicator matrix is directly learned without the additional procedure of spectral clustering. Furthermore, by expanding on our previous work, we further propose a Relaxed Multi-view Clustering in Latent Embedding Space (R-MCLES), which avoids the optimization problem of quadratic programming by relaxing the constraint of the global similarity matrix. Theoretical analysis has been provided to confirm the rationale of the relaxation in the supplementary material, which leads to lower computational complexity while achieving more correlations between pairs of data points. Extensive experiments conducted on both image and document datasets have demonstrated the superiority of the proposed approaches when compared with the state-of-the-art approaches.

The main contributions of this paper are summarized as follows:

  • We propose a novel multi-view clustering approach termedMCLES, which jointly learns a comprehensive latent embedding representation matrix, a robust global similarity matrix and an accurate cluster indicator matrix in a unified framework.

  • By leveraging the intrinsic interactions among them, our framework extracts the global similarity matrix based on the learned latent embedding representation, and further acquires the cluster indicator matrix based on the global similarity matrix.

  • In addition to exploring the MCLES method, we further propose the Relaxed Multi-view Clustering in Latent Embedding Space (R-MCLES) to avoid the quadratic programming optimization problem and achieve more correlations between pairs of data points.

  • The proposed R-MCLES method is efficiently settled by the alternating optimization scheme without involving the quadratic programming optimization problem.

The rest of this paper is organized as follows. In Section 2, we briefly review related works, which motivate the present work. The proposed MCLES and R-MCLES methods are described in Section 3 in which the complexity and convergence analysis is provided. In Section 4, the experimental results are reported where ten benchmark datasets are used and eight state-of-the-art methods are compared. Finally, the paper is concluded in Section 5. Some results in this paper were first presented in [29].

Section snippets

Related work

In the past few years, many multi-view clustering methods have been proposed to cope with the ubiquitous multi-view data. Some of the existing multi-view clustering methods are the graph-based models [1], [18], [19], [20], [30]. For instance, as one of the early approaches, De Sa proposed to construct a bipartite graph to connect the features in two views [30]. Based on the co-training technique, Kumar and Daumé proposed to seek for the clusters which agree across the multiple views [18].

Overview

In this section, we first provide an overview of the proposed framework. For clarity, the proposed model is illustrated in Fig. 1.

In multi-view clustering, the input is a set of multi-view observations consisting of n samples represented by V different views, denoted as X=X1;;XVRv=1Vdv×n, where XvRdv×n is the feature matrix of the vth view with dv being its dimensionality. Our proposed methods aim to discover a latent embedding representation, which encodes the complementary information

Experiments

In this section, extensive experiments are conducted on ten widely used image and document datasets to validate the superiority of the proposed MCLES and R-MCLES methods.

Conclusion

In this paper, a novel Multi-view Clustering in Latent Embedding Space (MCLES) is proposed to jointly learn a latent embedding representation matrix, a robust global similarity matrix and an accurate cluster indicator matrix in a unified optimization framework. Within this unified framework, the latent embedding representation discovered from multiple views is more comprehensive than each single view by effectively integrating the complementary information from the multi-view data, and

CRediT authorship contribution statement

Man-Sheng Chen: Design and implement the algorithms, and write the paper. Ling Huang: Design and implement the algorithms, and write the paper. Chang-Dong Wang: Ensured that the descriptions are accurate and agreed by all authors, Provide very detailed supervision of this work. Dong Huang: Provide very detailed supervision of this work. Jian-Huang Lai: Provide very detailed supervision of this work.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by NSFC, China (61876193, 61976097), Guangdong Natural Science Funds for Distinguished Young Scholar, China (2016A030306014) and National Key Research and Development Program of China (2018YFC0809700).

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