Data-Adaptive Low-Rank Sparse Subspace Clustering
This work addresses the need for more flexible and effective subspace clustering algorithms in machine learning, though it is incremental as it builds on existing LRSSC frameworks.
The paper tackles the problem of low-rank sparse subspace clustering (LRSSC) by proposing a data-adaptive surrogate for the S0/L0 quasi-norm, which improves performance over existing non-adaptive methods based on Sp/Lp norms, as demonstrated on three datasets.
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.