Canonical polyadic decomposition (CPD) of big tensors with low multilinear rank

Tensor decomposition methods have been widely applied to big data analysis as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most existing approaches are not designed to meet the challenges posed by big data dilemma. This paper attempts to improve the scalability of tensor decompositions and makes two contributions: A flexible and fast algorithm for the CP decomposition (FFCP) of tensors based on their Tucker compression; A distributed randomized Tucker decomposition approach for arbitrarily big tensors but with relatively low multilinear rank. These two algorithms can deal with huge tensors, even if they are dense. Extensive simulations provide empirical evidence of the validity and efficiency of the proposed algorithms.