Scaled Simplex Representation for Subspace Clustering

The self-expressive property of data points, that is, each data point can be linearly represented by the other data points in the same subspace, has proven effective in leading subspace clustering (SC) methods. Most self-expressive methods usually construct a feasible affinity matrix from a coeffici...

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Bibliographic Details
Published in:IEEE transactions on cybernetics Vol. 51; no. 3; pp. 1493 - 1505
Main Authors: Xu, Jun, Yu, Mengyang, Shao, Ling, Zuo, Wangmeng, Meng, Deyu, Zhang, Lei, Zhang, David
Format: Journal Article
Language:English
Published: United States IEEE 01.03.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Affinity
Algorithms
Clustering
Clustering algorithms
Coefficients
Computational modeling
Constraints
Correlation
Data models
Data points
Iterative methods
Mathematical analysis
Matrix methods
Optimization
Representations
Scaled simplex representation (SSR)
self-expressiveness
Statistical analysis
subspace clustering (SC)
Subspaces
ISSN:2168-2267, 2168-2275, 2168-2275
Online Access:Get full text
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Summary:The self-expressive property of data points, that is, each data point can be linearly represented by the other data points in the same subspace, has proven effective in leading subspace clustering (SC) methods. Most self-expressive methods usually construct a feasible affinity matrix from a coefficient matrix, obtained by solving an optimization problem. However, the negative entries in the coefficient matrix are forced to be positive when constructing the affinity matrix via exponentiation, absolute symmetrization, or squaring operations. This consequently damages the inherent correlations among the data. Besides, the affine constraint used in these methods is not flexible enough for practical applications. To overcome these problems, in this article, we introduce a scaled simplex representation (SSR) for the SC problem. Specifically, the non-negative constraint is used to make the coefficient matrix physically meaningful, and the coefficient vector is constrained to be summed up to a scalar <inline-formula> <tex-math notation="LaTeX">s < 1 </tex-math></inline-formula> to make it more discriminative. The proposed SSR-based SC (SSRSC) model is reformulated as a linear equality-constrained problem, which is solved efficiently under the alternating direction method of multipliers framework. Experiments on benchmark datasets demonstrate that the proposed SSRSC algorithm is very efficient and outperforms the state-of-the-art SC methods on accuracy. The code can be found at https://github.com/csjunxu/SSRSC .
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2019.2943691