CoSTCo

Abstract

Low-rank tensor factorization has been widely used for many real world tensor completion problems. While most existing factorization models assume a multilinearity relationship between tensor entries and their corresponding factors, real world tensors tend to have more complex interactions than multilinearity. In many recent works, it is observed that multilinear models perform worse than nonlinear models. We identify one potential reason for this inferior performance: the nonlinearity inside data obfuscates the underlying low-rank structure such that the tensor seems to be a high-rank tensor. Solving this problem requires a model to simultaneously capture the complex interactions and preserve the low-rank structure. In addition, the model should be scalable and robust to missing observations in order to learn from large yet sparse real world tensors. We propose a novel convolutional neural network (CNN) based model, named CoSTCo (Convolutional Sparse Tensor Completion). Our model leverages the expressive power of CNN to model the complex interactions inside tensors and its parameter sharing scheme to preserve the desired low-rank structure. CoSTCo is scalable as it does not involve computation- or memory- heavy tasks such as Kronecker product. We conduct extensive experiments on several real world large sparse tensors and the experimental results show that our model clearly outperforms both linear and nonlinear state-of-the-art tensor completion methods.