VEST: Very sparse tucker factorization of large-scale tensors

Abstract

Given a large tensor, how can we decompose it to sparse core tensor and factor matrices without reducing the accuracy? Existing approaches either output dense results or have scalability issues. In this paper, we propose VEST, a tensor factorization method for large partially observable data to output a very sparse core tensor and factor matrices. VEST performs initial decomposition and iteratively determines unimportant entries in the decomposition results, removes the unimportant entries, and updates the remaining entries. To determine unimportant entries of factor matrices and core tensor, we define and use the entry-wise 'responsibility' of the current decomposition. For scalable computation, the entries are updated iteratively using a carefully derived coordinate descent rule in parallel. Also, VEST automatically searches for the best sparsity ratio that results in a balanced trade-off between sparsity and accuracy. Extensive experiments show that our method VEST produces more accurate results compared to the best performing competitors for all tested real-life datasets.