A Survey on High-Dimensional Subspace Clustering

Wentao Qu, Xianchao Xiu, Huangyue Chen and Lingchen Kong ()
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Wentao Qu: School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China
Xianchao Xiu: School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China
Huangyue Chen: Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Lingchen Kong: School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China

Mathematics, 2023, vol. 11, issue 2, 1-39

Abstract: With the rapid development of science and technology, high-dimensional data have been widely used in various fields. Due to the complex characteristics of high-dimensional data, it is usually distributed in the union of several low-dimensional subspaces. In the past several decades, subspace clustering (SC) methods have been widely studied as they can restore the underlying subspace of high-dimensional data and perform fast clustering with the help of the data self-expressiveness property. The SC methods aim to construct an affinity matrix by the self-representation coefficient of high-dimensional data and then obtain the clustering results using the spectral clustering method. The key is how to design a self-expressiveness model that can reveal the real subspace structure of data. In this survey, we focus on the development of SC methods in the past two decades and present a new classification criterion to divide them into three categories based on the purpose of clustering, i.e., low-rank sparse SC, local structure preserving SC, and kernel SC. We further divide them into subcategories according to the strategy of constructing the representation coefficient. In addition, the applications of SC methods in face recognition, motion segmentation, handwritten digits recognition, and speech emotion recognition are introduced. Finally, we have discussed several interesting and meaningful future research directions.

Keywords: high-dimensional data; kernel learning; machine learning; sparse optimization; subspace clustering (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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