Multi-View Spectral Clustering With Incomplete Graphs

Chenping Hou,Wenzhang Zhuge,Dongyun Yi,Hong Tao,Tingjin Luo

doi:10.1109/access.2020.2997755

Chenping Hou, Wenzhang Zhuge + Show 3 more

Open Access

https://doi.org/10.1109/access.2020.2997755

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Abstract

Traditional multi-view learning usually assumes each instance appears in all views. However, in real-world applications, it is not an uncommon case that a number of instances suffer from some view samples missing. How to effectively cluster this kind of partial multi-view data has attracted much attention. In this paper, we propose an incomplete multi-view clustering method, namely Multi-view Spectral Clustering with Incomplete Graphs (MSCIG), which connects processes of spectral embedding and similarity matrix completion to achieve better clustering performance. Specifically, MSCIG recovers missing entries of each similarity matrix based on multiplications of a common representation matrix and corresponding view-specific representation matrix, and in turn learns these representation matrices based on the complete similarity matrices. Besides, MSCIG adopts the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -th root integration strategy to incorporate losses of multiple views, which characterizes the contributions of different views. Moreover, we develop an iterative algorithm with proved convergence to solve the resultant problem of MSCIG, which updates the common representation matrix, view-specific representation matrices, similarity matrices, and view weights alternatively. We conduct extensive experiments on 9 benchmark datasets to compare the proposed algorithm with existing state-of-the-art incomplete multi-view clustering methods. Experimental results validate the effectiveness of the proposed algorithm.

Highlights

With the development of data collection techniques, in many practical applications such as image retrieval and cross-language document categorization, data appear in multiple modalities or naturally come from multiple sources, which are named as multi-view data
In real applications, it is not a uncommon case that a number of instances suffer from some view representations missing, which results in partial multi-view data
We propose Multi-view Spectral Clustering with Incomplete Graphs (MSCIG) to handle incomplete multi-view clustering problem

Summary

Introduction

With the development of data collection techniques, in many practical applications such as image retrieval and cross-language document categorization, data appear in multiple modalities or naturally come from multiple sources, which are named as multi-view data. A common assumption adopted by conventional multi-view learning methods is that each data point appears in all views. In real applications, it is not a uncommon case that a number of instances suffer from some view representations missing, which results in partial multi-view data. Another example is cross-language document categorization, it is often the case that a document is translated into several but not all languages. Since it is an often case that every view of this kind of data suffers from some samples missing, traditional single-view or multi-view clustering methods may fail to obtain the clustering results of all data points directly. The transpose, the Frobenius norm, and the trace of matrix M are denoted by MT , ||M||F , and tr(M), respectively. The 2-norm of vector mi is denoted by ||mi||

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