Neuron-Enhanced AutoEncoder Matrix Completion and Collaborative Filtering: Theory and Practice

Neural networks have shown promising performance in collaborative filtering and matrix completion but the theoretical analysis is limited and there is still room for improvement in terms of the accuracy of recovering missing values. This paper presents a neuron-enhanced autoencoder matrix completion (AEMC-NE) method and applies it to collaborative filtering. Our AEMC-NE adds an element-wise autoencoder to each output of the main autoencoder to enhance the reconstruction capability. Thus it can adaptively learn an activation function for the output layer to approximate possibly complicated response functions in real data. We provide theoretical analysis for AEMC-NE as well as AEMC to investigate the generalization ability of autoencoder and deep learning in matrix completion, considering both missing completely at random and missing not at random. We show that the element-wise neural network has the potential to reduce the generalization error bound, the data sparsity can be useful, and the prediction performance is closely related to the difference between the numbers of variables and samples. The numerical results on synthetic data and five benchmark datasets demonstrated the effectiveness of AEMC-NE in comparison to many baselines.