Shared Memory Parallelization of MTTKRP for Dense Tensors

2017/08/29 by Koby Hayashi, Hayashi, Koby, Grey Ballard +5 · 1 citation
Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Distributed #FOS: Computer and information sciences #Parallel #Parallel Computing and Optimization Techniques #Tensor decomposition and applications #and Cluster Computing (cs.DC)

paper · pdf · doi:10.48550/arxiv.1708.08976

openalex publication_date 2017/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The matricized-tensor times Khatri-Rao product (MTTKRP) is the computational bottleneck for algorithms computing CP decompositions of tensors. In this paper, we develop shared-memory parallel algorithms for MTTKRP involving dense tensors. The algorithms cast nearly all of the computation as matrix operations in order to use optimized BLAS subroutines, and they avoid reordering tensor entries in memory. We benchmark sequential and parallel performance of our implementations, demonstrating high sequential performance and efficient parallel scaling. We use our parallel implementation to compute a CP decomposition of a neuroimaging data set and achieve a speedup of up to 7.4× over existing parallel software.

Citations

• Tensor Decompositions and Applications
• Tensor Decomposition for Signal Processing and Machine Learning

Cited by

• Comparison of Accuracy and Scalability of Gauss-Newton and Alternating Least Squares for CP Decomposition

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