Learnable low-rank latent dictionary for subspace clustering

Recently, Self-Expressive-based Subspace Clustering (SESC) has been widely applied in pattern clustering and machine learning as it aims to learn a representation that can faithfully reflect the correlation between data points. However, most existing SESC methods directly use the original data as the dictionary, which miss the intrinsic structure (e.g., low-rank and nonlinear) of the real-word data. To address this problem, we propose a novel Projection Low-Rank Subspace Clustering (PLRSC) method by integrating feature extraction and subspace clustering into a unified framework. In particular, PLRSC learns a projection transformation to extract the low-dimensional features and utilizes a low-rank regularizer to ensure the informative and important structures of the extracted features. The extracted low-rank features effectively enhance the self-expressive property of the dictionary. Furthermore, we extend PLRSC to a nonlinear version (i.e., NPLRSC) by integrating a nonlinear activator into the projection transformation. NPLRSC cannot only effectively extract features but also guarantee the data structure of the extracted features. The corresponding optimization problem is solved by the Alternating Direction Method (ADM), and we also prove that the algorithm converges to a stationary point. Experimental results on the real-world datasets validate the superior of our model over the existing subspace clustering methods.