A Novel Hierarchical Deep Matrix Completion Method

The matrix completion technique based on matrix factorization for recovering missing items is widely used in collaborative filtering, image restoration, and other applications. We proposed a new matrix completion model called hierarchical deep matrix completion (HDMC), where we assume that the variables lie in hierarchically organized groups. HDMC explicitly expresses either shallow or high-level hierarchical structures, such as taxonomy trees, by embedding a series of so-called structured sparsity penalties in a framework to encourage hierarchical relations between compact representations and reconstructed data. Moreover, HDMC considers the group-level sparsity of neurons in a neural network to obtain a pruning effect and compact architecture by enhancing the relevance of within-group neurons while neglecting the between-group neurons. Since the optimization of HDMC is a nonconvex problem, to avoid converting the framework of the HDMC models into separate optimized formulations, we unify a generic optimization by applying a smoothing proximal gradient strategy in dual space. HDMC is compared with state-of-the-art matrix completion methods on applications with simulated data, MRI image datasets, and gene expression datasets. The experimental results verify that HDMC achieves higher matrix completion accuracy.