Decomposition of Big Tensors With Low Multilinear Rank
arXiv:1412.1885
Abstract
Tensor decompositions are promising tools for big data analytics 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 major challenges posed by big data analytics. This paper attempts to improve the scalability of tensor decompositions and provides 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.
Cited by in corpus (8)
- Parallel Tensor Compression for Large-Scale Scientific Data
- Efficient Nonnegative Tucker Decompositions: Algorithms and Uniqueness
- Randomized Tensor Ring Decomposition and Its Application to Large-scale Data Reconstruction
- Low-Rank Tucker Approximation of a Tensor From Streaming Data
- Fast and Accurate Randomized Algorithms for Low-rank Tensor Decompositions
- Randomized algorithms for the low multilinear rank approximations of tensors
- Efficient parallel CP decomposition with pairwise perturbation and multi-sweep dimension tree
- PASTA: A Parallel Sparse Tensor Algorithm Benchmark Suite