Unified One-Step Multi-View Spectral Clustering

Abstract

Multi-view spectral clustering, which exploits the complementary information among graphs of diverse views to obtain superior clustering results, has attracted intensive attention recently. However, most existing multi-view spectral clustering methods obtain the clustering partitions in a two-step scheme, i.e., spectral embedding and subsequent k-means. This two-step scheme inevitably seeks sub-optimal clustering results due to the information loss during the two-steps processes. Besides, existing multi-view spectral clustering methods do not jointly utilize the information of graphs and embedding matrices, which also degrades final clustering results. To solve these issues, we propose a unified one-step multi-view spectral clustering method, which integrates the spectral embedding and <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$k$</tex></formula> -means into a unified framework to obtain discrete clustering labels with a one-step strategy. Under the observation that the inner product of the embedding matrix is a low-rank approximation of the graph, we combine graphs and embedding matrices of different views to obtain a unified graph. Then, we directly capture the discrete clustering indicator matrix from the unified graph. Furthermore, we design an effective optimization algorithm to solve the resultant problem. Finally, a set of experiments on various datasets are conducted to verify the effectiveness of the proposed method. The demo code of this work is publicly available at https://github.com/guanyuezhen/UOMvSC.