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

Research Project

Project/Area Number 18K18058
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 60090:High performance computing-related
Research InstitutionHokkaido 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
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsテンソル分解 / 線形計算 / 並列計算 / 高性能計算 / 線形計算アルゴリズム
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.

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。

Report

(4 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (15 results)

All 2020 2019 2018 Other

All Int'l Joint Research (1 results) Journal Article (3 results) (of which Int'l Joint Research: 1 results,  Open Access: 2 results,  Peer Reviewed: 1 results) Presentation (11 results) (of which Int'l Joint Research: 6 results)

  • [Int'l Joint Research] University of Oxford(英国)

    • Related Report
      2020 Annual Research Report
  • [Journal Article] 縦長行列のQR分解に対する各種アルゴリズムの比較:Oakforest-PACS上での性能評価2020

    • Author(s)
      深谷 猛
    • Journal Title

      東京大学情報基盤センター スーパーコンピューティングニュース

      Volume: 22 Pages: 28-39

    • Related Report
      2020 Annual Research Report
    • Open Access
  • [Journal Article] Shifted Cholesky QR for Computing the QR Factorization of Ill-Conditioned Matrices2020

    • Author(s)
      Takeshi Fukaya, Ramaseshan Kannan, Yuji Nakatsukasa, Yusaku Yamamoto, Yuka Yanagisawa
    • Journal Title

      SIAM Journal on Scientific Computing

      Volume: 42 Issue: 1 Pages: A477-A503

    • DOI

      10.1137/18m1218212

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] マルチコアCPU環境における密テンソル向けALS法の性能評価2018

    • Author(s)
      深谷猛
    • Journal Title

      情報処理学会研究報告:ハイパフォーマンスコンピューティング

      Volume: 2018-HPC-167 Pages: 1-9

    • Related Report
      2018 Research-status Report
  • [Presentation] 縦長行列の列ピボット付きQR分解に対するコレスキーQR型アルゴリズムの検討2020

    • Author(s)
      深谷 猛, 中務 佑治, 山本 有作
    • Organizer
      日本応用数理学会2020年度年会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Shifted CholeskyQR3 for High Performance Tall-Skinny QR Factorization2020

    • Author(s)
      Takeshi Fukaya, Ramaseshan Kannan, Yuji Nakatsukasa, Yusaku Yamamoto, Yuka Yanagisawa
    • Organizer
      2020 SIAM Conference on Parallel Processing for Scientific Computing (SIAM PP20)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] テンソル分解におけるMTTKRPのスレッド並列化に関する考察2019

    • Author(s)
      深谷 猛
    • Organizer
      第24回計算工学講演会
    • Related Report
      2019 Research-status Report
  • [Presentation] ALS法を用いた密テンソルのCP分解におけるMTTKRPの性能評価2019

    • Author(s)
      深谷 猛
    • Organizer
      The 3rd cross-disciplinary Workshop on Computing Systems, Infrastructures, and Programming (xSIG2019)
    • Related Report
      2019 Research-status Report
  • [Presentation] HPC視点に基づくテンソル分解アルゴリズムの高性能化2019

    • Author(s)
      深谷 猛
    • Organizer
      第11回 自動チューニング技術の現状と応用に関するシンポジウム(ATTA2019)
    • Related Report
      2019 Research-status Report
  • [Presentation] Recent progress of the Cholesky QR factorization2019

    • Author(s)
      Takeshi Fukaya
    • Organizer
      2019 Mini-Workshop on Computational Science (MWCS2019)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Shifted Cholesky QR algorithm for computing the QR factorization of ill-conditioned matrices2019

    • Author(s)
      Takeshi Fukaya, Ramaseshan Kannan, Yuji Nakatsukasa, Yusaku Yamamoto, Yuka Yanagisawa
    • Organizer
      2019 Conference on Advanced Topics and Auto Tuning in High-Performance Scientific Computing (ATAT2019)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] High performance QR factorization of ill-conditioned matrices based on the Cholesky QR algorithm2019

    • Author(s)
      Takeshi Fukaya, Ramaseshan Kannan, Yuji Nakatsukasa, Yusaku Yamamoto, Yuka Yanagisawa
    • Organizer
      2019 SIAM Conference on Computational Science and Engineering (CSE19)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] 密テンソルに対するALS法の実装方法に関する考察2018

    • Author(s)
      深谷猛
    • Organizer
      日本応用数理学会2018年度年会
    • Related Report
      2018 Research-status Report
  • [Presentation] An overview of various algorithms for computing tall-skinny QR factorization2018

    • Author(s)
      Takeshi Fukaya, Yusaku Yamamoto
    • Organizer
      he 37th JSST Annual International Conference on Simulation Technology (JSST2018)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Performance Evaluation of the Shifted Cholesky QR Algorithm for Ill-Conditioned Matrices2018

    • Author(s)
      Takeshi Fukaya, Ramaseshan Kannan, Yuji Nakatsukasa, Yusaku Yamamoto, Yuka Yanagisawa
    • Organizer
      SC’18: The International Conference for High Performance Computing, Networking, Storage, and Analysis
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research

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Published: 2018-04-23   Modified: 2022-01-27  

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