Study on improving algorithms for tensor decomposition based on the HPC viewpoint

2020 Fiscal Year Final Research Report

• Project/Area Number: 18K18058
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60090:High performance computing-related
• Research Institution: Hokkaido University
• Principal Investigator: Fukaya Takeshi 北海道大学, 情報基盤センター, 助教 (30633846)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Keywords: テンソル分解 / 線形計算 / 並列計算

Outline of Final Research Achievements

In this research, we aimed for improving algorithms of tensor decomposition, which is one of building blocks in data science applications. In addition to the traditional mathematical viewpoint, we investigated efficient algorithms based on the HPC viewpoint, in which the characteristics of recent computers are considered. Through this research, we found that a dominant computation in a typical tensor decomposition can be accelerated by appropriately selecting kernels depending on the conditions such as the size of a tensor. We also presented a new efficient algorithm for a matrix computation deeply related to tensor decomposition.

Free Research Field

高性能計算、数値線形代数、応用数学

Academic Significance and Societal Importance of the Research Achievements

本研究では、様々な分野での活用が期待されているデータサイエンスの基盤技術の一つであるテンソル分解の高性能化を目的とした研究を行った。また、計算機の複雑化・多様化により、数理とHPCの両方の視点が効率的な計算の実現に不可欠であり、本研究を通して、その重要性を示すことができた。国内のHPC分野におけるテンソル分解の研究事例が乏しかったので、本研究をきっかけとして、今後、様々な研究が展開されることが期待される。