Algorithm 1026: Concurrent Alternating Least Squares for Multiple Simultaneous Canonical Polyadic Decompositions

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  • Christos Psarras
  • Lars Karlsson
  • Bro, Rasmus
  • Paolo Bientinesi

Tensor decompositions, such as CANDECOMP/PARAFAC (CP), are widely used in a variety of applications, such as chemometrics, signal processing, and machine learning. A broadly used method for computing such decompositions relies on the Alternating Least Squares (ALS) algorithm. When the number of components is small, regardless of its implementation, ALS exhibits low arithmetic intensity, which severely hinders its performance and makes GPU offloading ineffective. We observe that, in practice, experts often have to compute multiple decompositions of the same tensor, each with a small number of components (typically fewer than 20), to ultimately find the best ones to use for the application at hand. In this article, we illustrate how multiple decompositions of the same tensor can be fused together at the algorithmic level to increase the arithmetic intensity. Therefore, it becomes possible to make efficient use of GPUs for further speedups; at the same time, the technique is compatible with many enhancements typically used in ALS, such as line search, extrapolation, and non-negativity constraints. We introduce the Concurrent ALS algorithm and library, which offers an interface to MATLAB, and a mechanism to effectively deal with the issue that decompositions complete at different times. Experimental results on artificial and real datasets demonstrate a shorter time to completion due to increased arithmetic intensity.

Original languageEnglish
Article number34
JournalACM Transactions on Mathematical Software
Issue number3
Number of pages20
Publication statusPublished - 2022

Bibliographical note

Funding Information:
This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—333849990/ GRK2379 (IRTG Modern Inverse Problems).

Publisher Copyright:
© 2022 Association for Computing Machinery.

    Research areas

  • CP, decomposition, high-performance, PARAFAC, Tensor

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