Efficient Alternating Least Squares Algorithms for Low Multilinear Rank Approximation of Tensors

The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for approximation usually rely directly on matrix SVD, therefore often suffer from notorious intermediate data explosion issue and are not easy to parallelize, especially when input tensor is large. In this paper, we propose a new class of HOSVD algorithms based alternating least squares (ALS) efficiently computing proposed ALS-based approaches able eliminate redundant computations singular vectors matrices free explosion. Also, more flexible with adjustable convergence tolerance intrinsically parallelizable high-performance computers. Theoretical analysis reveals ALS iteration q-linear convergent relatively wide region. Numerical experiments large-scale tensors both synthetic real-world demonstrate can substantially reduce total cost original ones highly scalable parallel computing.