Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.6.2022.1.02

Volume 6, Issue 1, 1 February 2022, Pages 17-36

 

Abstract. As one of the mainstream clustering methods, the spectral clustering has aroused more and more attention recently because of its good performance, especially in nonlinear data sets. However, traditional spectral clustering models have high computational complexity. Meanwhile, most of these models fail in distinguishing the noisy and useful features in practice, which leads to the limitation of clustering performance. In this paper, we propose a new fast spectral clustering with self-weighted features (FSCSWF) to achieve good clustering performance through learning and assigning optimal weights for features in a low computational complexity. Specifically, the FSCSWF selects anchors from original samples, then learns the weights of features and the similarity between anchors and samples interactively in a local structure learning framework. This interactive learning makes the learnt similarity can better measure the relationship between anchors, and samples due to the optimal weights make the data points become more discriminative. Moreover, the connectivity constraint are embedded to make sure that the connected components of bipartite graph constructed by the learnt similarity can indicate clusters directly. In this way, the FSCSWF can achieve good clustering performance and has a low computational complexity, which is linear to the number of samples. Extensive experiments on synthetic and practical data sets illustrate the effectiveness and efficiency of the FSCSWF with respect to state-of-the-art methods.

 

How to Cite this Article:
Xiang Zhu, Zhiling Cai, Ziniu Yu, Junliang Wu, William Zhu, Fast spectral clustering with self-weighted features, J. Nonlinear Var. Anal. 6 (2022), 17-36.