Affinity adaptive sparse subspace clustering via constrained Laplacian rank

Subspace clustering typically clusters data by performing spectral clustering to an affinity matrix constructed in some deterministic ways of self-representation coefficient matrix. Therefore, the quality of the affinity matrix is vital to their performance. However, traditional deterministic ways only provide a feasible affinity matrix but not the most suitable one for showing data structures. Besides, post-processing commonly on the coefficient matrix also affects the affinity matrix’s quality. Furthermore, constructing the affinity matrix is separate from optimizing the coefficient matrix and performing spectral clustering, which can not guarantee the optimal overall result. To this end, we propose a new method, affinity adaptive sparse subspace clustering (AASSC), by adding Laplacian rank constraint into a subspace sparse-representation model to adaptively learn a high-quality affinity matrix having accurate p-connected components from a sparse coefficient matrix without post-processing, where p represents categories. In addition, by relaxing the Laplacian rank constraint into a trace minimization, AASSC naturally combines the operations of the coefficient matrix, affinity matrix, and spectral clustering into a unified optimization, guaranteeing the overall optimal result. Extensive experimental results verify the proposed method to be effective and superior.