Sparse Dual Graph-Regularized Deep Nonnegative Matrix Factorization for Image Clustering

Abstract

Deep nonnegative matrix factorization (Deep NMF) as an emerging technique for image clustering has attracted more and more attention. This is because it can effectively reduce high-dimensional data and reveal the latent hierarchical information of the complex data. However, two limitations may still deteriorate their performances: (1) the local invariance of the input data is insufficiently explored, that is, the intrinsic geometrical structures of the original data in the data and feature spaces are not considered simultaneously; (2) the sparseness that can greatly improve the ability of learning parts is also ignored. In this paper, we propose a novel approach to address the above two problems, referred to as Sparse Dual Graph-regularized Deep Nonnegative Matrix Factorization (SDG Deep NMF), which can learn sparse and informative deep features while sufficiently exploring the local invariance of the data to discover valuable information underlying the input data. Specifically, SDG Deep NMF learns the informative deep features by performing the dual graph regularization in the deep NMF framework, which can respect the intrinsic geometrical structures of the input data in the data and feature spaces while mining the data information in hidden layers. Meanwhile, SDG Deep NMF also imposes sparse constraints on the basis matrix during the feature learning to improve the part-based learning capabilities. Moreover, we construct the objective function of SDG Deep NMF in the form of the Euclidean distance for convenience, the iterative updating scheme is chosen to optimize it. Comprehensive experiments on four benchmark datasets can demonstrate the effectiveness of the proposed approach in image clustering.