A Similarity Matrix Low-Rank Approximation and Inconsistency Separation Fusion Approach for Multiview Clustering

Abstract

In recent years, multiview clustering algorithms have achieved promising performance by exploiting the complementarity and consistency of different views. However, many multiview spectral clustering methods only focus on the consistent information of views, and the time cost of feature decomposition is expensive. Moreover, these methods also require postprocessing (e.g., k-means) to obtain the final clustering results. To overcome these limitations simultaneously, we propose a novel multiview clustering algorithm. First, the method removes the inconsistent information of the views through cross-view measurement to maintain consistent information. These inconsistencies may be caused by noise, corruptions, or view-specific properties and will affect the quality of the similarity matrix. Then, we learn a consensus embedding matrix with nonnegative constraints by performing a low-rank decomposition of the consistency information. In this way, we can replace the eigendecomposition of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\times }$</tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> Laplacian matrix in spectral clustering with the singular value decomposition of a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\times }$</tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> low-rank matrix to reduce the computational burden, where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\ll }$</tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> . Furthermore, due to the nonnegative constraint, we can directly obtain the clustering results. Also, to consider the diversity of views, adaptive weighting is applied to different view data. Compared to state-of-the-art multiview clustering methods on five benchmark multiview datasets, we demonstrate the superiority and effectiveness of our approach. We release the source code at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/hulu88/FAMvC</uri> .

Topics & Concepts