K-BEST subspace clustering: kernel-friendly block-diagonal embedded and similarity-preserving transformed subspace clustering

Abstract

Subspace clustering methods, employing sparse and low-rank models, have demonstrated efficacy in clustering high-dimensional data. These approaches typically assume the separability of input data into distinct subspaces, a premise that does not hold true in general. Furthermore, prevalent low-rank and sparse methods relying on self-expression exhibit effectiveness primarily with linear structure data, facing limitations in processing datasets with intricate nonlinear structures. While kernel subspace clustering methods excel in handling nonlinear structures, they may compromise similarity information during the reconstruction of original data in kernel space. Additionally, these methods may fall short of attaining an affinity matrix with an optimal block-diagonal property. In response to these challenges, this paper introduces a novel subspace clustering approach named Similarity Preserving Kernel Block Diagonal Representation based Transformed Subspace Clustering (KBD-TSC). KBD-TSC contributes in three key aspects: (1) integration of a kernelized version of transform learning within a subspace clustering framework, introducing a block diagonal representation term to generate an affinity matrix with a block-diagonal structure. (2) Construction and integration of a similarity preserving regularizer into the model by minimizing the discrepancy between inner products of the original data and those of the reconstructed data in kernel space. This facilitates enhanced preservation of similarity information between the original data points. (3) Proposal of KBD-TSC by integrating the block diagonal representation term and similarity preserving regularizer into a kernel self-expressing model. The optimization of the proposed model is efficiently addressed through the alternating direction method of multipliers. This study validates the effectiveness of the proposed KBD-TSC method through experimental results obtained from nine datasets, showcasing its potential in addressing the limitations of existing subspace clustering techniques.