Sparse subspace clustering algorithm with non-convex constraints

Lingling Wang; Jinping Tang; Ruyao Sun; Bo Bi

doi:10.1117/12.2680101

31 May 2023 Sparse subspace clustering algorithm with non-convex constraints

Lingling Wang, Jinping Tang, Ruyao Sun, Bo Bi

Proceedings Volume 12704, Eighth International Symposium on Advances in Electrical, Electronics, and Computer Engineering (ISAEECE 2023); 127043A (2023) https://doi.org/10.1117/12.2680101
Event: 8th International Symposium on Advances in Electrical, Electronics and Computer Engineering (ISAEECE 2023), 2023, Hangzhou, China

Abstract

Key of sparse subspace clustering is to solve an optimization problem based on sparse penalty term to obtain sparse representation coefficients. Ideal sparsity penalty term is ℓ₀-norm, but the optimization problem based on the ℓ₀-norm is NP-hard. At present, most methods for solving sparse coefficients use the convex relaxation of the ℓ₀-norm, ℓ₀-norm as a penalty term, but it can not well describe the sparsity of the representation coefficients. Therefore, In this paper, a nonconvex φ_α energy functional is used to replace the ℓ₀-norm in the objective function and a sparse subspace clustering algorithm based on non-convex φ_α energy functional is proposed, compared with the traditional ℓ₁-norm, non-convex φ_α energy functional increases the sparsity of the representation coefficients and obtains a better similarity matrix, where α ⪆ 0 is a parameter that regulates the degree of non-convex constraints. In addition, the alternating direction method of multipliers is used to solve the optimization problem with non-convex constraints. Experiments on synthetic datasets and face datasets show that the proposed algorithm reduces the error rate of clustering.

Citation Download Citation

Lingling Wang, Jinping Tang, Ruyao Sun, and Bo Bi "Sparse subspace clustering algorithm with non-convex constraints", Proc. SPIE 12704, Eighth International Symposium on Advances in Electrical, Electronics, and Computer Engineering (ISAEECE 2023), 127043A (31 May 2023); https://doi.org/10.1117/12.2680101

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KEYWORDS

Matrices

Data storage

Detection and tracking algorithms

Image processing

Machine learning

Mathematical optimization

Operating systems

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