Nonlinear Subspace Clustering via Adaptive Graph Regularized Autoencoder

Most existing subspace clustering methods focus on learning a meaningful (e.g., sparse or low-rank) representation of the data. However, they have the following two problems which greatly limit the performance: 1) They neglect the intrinsic local geometrical structures within the data to result in locality preserving property be missing. 2) They neglect the feature learning of the raw data which is usually so complex that the learned representation coefficient is not an optimal graph for clustering. This paper addresses the above problems and proposes a novel nonlinear subspace clustering model via adaptive graph regularized autoencoder (NSC-AGA). This model unifies feature learning, locality preserving, and representation matrix learning into a framework, and a new adaptive graph regularizer is introduced, which takes the representation coefficient matrix as a learnable similarity graph imposed on the Euclidean distance matrix of the deep features. Two matrices interact with each other to make the representation coefficient matrix reflect both the global linear correlation and the local geometric distance relationship. A number of experimental results on the five public image database demonstrate that the proposed NSC-AGA model achieves superior clustering performance compared with the state-of-the-art methods.