Parallel randomly compressed cubes: A scalable distributed architecture for big tensor decomposition

Nicholas D. Sidiropoulos, Evangelos E. Papalexakis, Christos Faloutsos

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

Abstract

This article combines a tutorial on state-of-the-art tensor decomposition as it relates to big data analytics, with original research on parallel and distributed computation of low-rank decomposition for big tensors, and a concise primer on Hadoop?MapReduce. A novel architecture for parallel and distributed computation of low-rank tensor decomposition that is especially well suited for big tensors is proposed. The new architecture is based on parallel processing of a set of randomly compressed, reduced-size replicas of the big tensor. Each replica is independently decomposed, and the results are joined via a master linear equation per tensor mode. The approach enables massive parallelism with guaranteed identifiability properties: if the big tensor is of low rank and the system parameters are appropriately chosen, then the rank-one factors of the big tensor will indeed be recovered from the analysis of the reduced-size replicas. Furthermore, the architecture affords memory/storage and complexity gains of order for a big tensor of size of rank F with No sparsity is required in the tensor or the underlying latent factors, although such sparsity can be exploited to improve memory, storage, and computational savings.

Original languageEnglish (US)
Article number6879586
Pages (from-to)57-70
Number of pages14
JournalIEEE Signal Processing Magazine
Volume31
Issue number5
DOIs
StatePublished - 2014

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