Data-Adaptive Low-Rank Sparse Subspace Clustering
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910827594907648 |
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| author | Kopriva, Ivica |
| author_facet | Kopriva, Ivica |
| contents | Low-rank sparse subspace clustering (LRSSC) algorithms built on self-expressive model effectively capture both the global and local structure of the data. However, existing solutions, primarily based on proximal operators associated with Sp/Lp , p e {0, 1/2, 2/3, 1}, norms are not data-adaptive. In this work, we propose an LRSSC algorithm incorporating a data-adaptive surrogate for the S0/L0 quasi-norm. We provide a numerical solution for the corresponding proximal operator in cases where an analytical expression is unavailable. The proposed LRSSC algorithm is formulated within the proximal mapping framework, and we present theoretical proof of its global convergence toward a stationary point. We evaluate the performance of the proposed method on three well known datasets, comparing it against LRSSC algorithms constrained by Sp/Lp, p e {0, 1/2, 2/3, 1}, norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data-Adaptive Low-Rank Sparse Subspace Clustering Kopriva, Ivica Machine Learning 68W05, 68U10, 65Y99 F.2.1; G.1.6; I.5.3 Low-rank sparse subspace clustering (LRSSC) algorithms built on self-expressive model effectively capture both the global and local structure of the data. However, existing solutions, primarily based on proximal operators associated with Sp/Lp , p e {0, 1/2, 2/3, 1}, norms are not data-adaptive. In this work, we propose an LRSSC algorithm incorporating a data-adaptive surrogate for the S0/L0 quasi-norm. We provide a numerical solution for the corresponding proximal operator in cases where an analytical expression is unavailable. The proposed LRSSC algorithm is formulated within the proximal mapping framework, and we present theoretical proof of its global convergence toward a stationary point. We evaluate the performance of the proposed method on three well known datasets, comparing it against LRSSC algorithms constrained by Sp/Lp, p e {0, 1/2, 2/3, 1}, norms. |
| title | Data-Adaptive Low-Rank Sparse Subspace Clustering |
| topic | Machine Learning 68W05, 68U10, 65Y99 F.2.1; G.1.6; I.5.3 |
| url | https://arxiv.org/abs/2502.10106 |