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Mathematical Properties of Sampling and Optimal Reproducing Kernels

Research Project

Project/Area Number 21700001
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Fundamental theory of informatics
Research InstitutionHokkaido University

Principal Investigator

TANAKA Akira  北海道大学, 大学院・情報科学研究科, 准教授 (20332471)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords情報数理 / 標本化定理 / 再生核ヒルベルト空間 / 機械学習 / 標本化 / 再生核 / ヒルベルト空間 / モデル選択 / 計量 / 直交射影 / 汎化誤差 / 関数推定 / グラム行列
Research Abstract

In this work, we theoretically analyzed properties of sampling theories for reproducing kernel Hilbert spaces(RKHS's). Our main contributions are1) we gave a necessary and sufficient condition for a given RKHS and a given set of sampling points to satisfy the sampling theorem, 2) we gave an upper bound of errors in case that the sampling theorem does not hold, and3) we clarified the behavior of the solution in various machine learning problems with respect to sampling points and an adopted RKHS.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (39 results)

All 2012 2011 2010 2009 Other

All Journal Article (13 results) (of which Peer Reviewed: 4 results) Presentation (26 results)

  • [Journal Article] 画像データベースとJPEG再適用を利用したJPEG画像の画質改善2012

    • Author(s)
      河野克也, 田中章
    • Journal Title

      電子情報通信学会技術報告,回路とシステム

      Volume: Vol.111, No.465 Pages: 13-18

    • NAID

      110009545291

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Journal Article] 自己校正法における射影変換の推定精度の向上2011

    • Author(s)
      滝沢篤史, 田中章, 宮腰政明
    • Journal Title

      電子情報通信学会技術報告信号処理

      Volume: Vol.110, No.440 Pages: 229-233

    • NAID

      110008688562

    • Related Report
      2011 Final Research Report
  • [Journal Article] カーネルリッジ回帰における低計算量モデル選択法2011

    • Author(s)
      武井亨, 田中章, 宮腰政明
    • Journal Title

      電子情報通信学会技術研究報告,信号処理

      Volume: Vol.110, No.44 0 Pages: 185-190

    • NAID

      110008688554

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Journal Article] 既知の基底ベクトルを考慮したNMF2011

    • Author(s)
      天野雄太, 田中章, 宮腰政明
    • Journal Title

      電子情報通信学会技術研究報告,信号処理

      Volume: Vol.110, No.440 Pages: 137-141

    • NAID

      110008688546

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Journal Article] 固有空間BPLP法の補間精度に関する解析2011

    • Author(s)
      田中章, 小川貴弘, 長谷山美紀, 宮腰政明
    • Journal Title

      電子情報通信学会論文誌A

      Volume: Vol.J94-A, No.2 Pages: 116-126

    • NAID

      110008440906

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 自己校正法における射影変換の推定精度の向上2011

    • Author(s)
      滝沢篤史, 田中章, 宮腰政明
    • Journal Title

      電子情報通信学会技術研究報告,信号処理

      Volume: 110, 440 Pages: 229-233

    • NAID

      110008688562

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Kernel-Induced Sampling Theorem2010

    • Author(s)
      A. Tanaka, H. Imai, and M. Miyakosh i
    • Journal Title

      I EEE Transactions on Signal Processing

      Volume: Vol.58, No.7 Pages: 3569-3577

    • NAID

      120002223738

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Kernel-Induced Sampling Theorem2010

    • Author(s)
      A.Tanaka, H.Imai, M.Miyakoshi
    • Journal Title

      IEEE Transactions on Signal Processing

      Volume: 58, 7 Pages: 3569-3577

    • NAID

      120002223738

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] カーネル法を用いた回帰分析の予測精度について2009

    • Author(s)
      今井英幸, 田中章, 池田盛一
    • Journal Title

      電子情報通信学会技術研究報告,パターン認識・メディア理解

      Volume: Vol.109, No.344 Pages: 61-64

    • NAID

      110008002728

    • Related Report
      2011 Final Research Report
  • [Journal Article] パターン認識における都市伝説2009

    • Author(s)
      工藤峰一, 今井英幸, 田中章, 杉山将
    • Journal Title

      電子情報通信学会技術研究報告,パターン認識・メディア理解

      Volume: Vol.10 9, No.344 Pages: 29-34

    • NAID

      110008002721

    • Related Report
      2011 Final Research Report
  • [Journal Article] パターン認識における都市伝説2009

    • Author(s)
      工藤峰一, 今井英幸, 田中章, 杉山将
    • Journal Title

      電子情報通信学会技術研究報告, パターン認識・メディア理解 109, 344

      Pages: 29-34

    • NAID

      110008002721

    • Related Report
      2009 Annual Research Report
  • [Journal Article] カーネル法を用いた回帰分析の予測精度について2009

    • Author(s)
      今井英幸, 田中章, 池田盛一
    • Journal Title

      電子情報通信学会技術研究報告, パターン認識・メディア理解 109, 344

      Pages: 61-64

    • NAID

      110008002728

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Kernel-Induced Sampling Theorem

    • Author(s)
      A.Tanaka, H.Imai, M.Miyakoshi
    • Journal Title

      IEEE Transactions on Signal Processing ((印刷中))

    • NAID

      120002223738

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Variance Analyses for Kernel Regresso rs with Nested Reproducing Kernel Hilb ert Spaces2012

    • Author(s)
      A. Ta naka, H. Imai, and K. Takamiya
    • Organizer
      2012 IEEE International Co nference on Acoustics, Speech, and Sign al Processing(ICASSP2012)
    • Place of Presentation
      国立京都国際会館(京都)
    • Year and Date
      2012-03-28
    • Related Report
      2011 Final Research Report
  • [Presentation] Variance Analyses for Kernel Regressors with Nested Reproducing Kernel Hilbert Spaces2012

    • Author(s)
      A.Tanaka, H.Imai, K.Takamiya
    • Organizer
      2012 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP2012)
    • Place of Presentation
      国立京都国際会館(京都)
    • Year and Date
      2012-03-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] トレース正規化による非負定値エルミート行列の同時対角化の性能改善2011

    • Author(s)
      田中章
    • Organizer
      第26回信号処理シンポジウム
    • Place of Presentation
      札幌コンベンションセンター(札幌)
    • Year and Date
      2011-11-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] Non-negative Matrix Factorization Considering Given Vectors in a Basis2011

    • Author(s)
      Y. Amano, A. Tanaka, and M. Miyako shi
    • Organizer
      2011 IEEE International Conference on Granular Computing(GrC2011)
    • Place of Presentation
      Garden Villa Hotel(台湾)
    • Year and Date
      2011-11-08
    • Related Report
      2011 Final Research Report
  • [Presentation] Performance Improvement of Me tric Reconstruction Based on Partial Joi nt Diagonalization2011

    • Author(s)
      A. Takizawa, A. Tanaka, and M. Miya koshi
    • Organizer
      2011 IEEE Internat ional Conference on Granular Computin g(GrC2011)
    • Place of Presentation
      Garden Vill a Hotel(台湾)
    • Year and Date
      2011-11-08
    • Related Report
      2011 Final Research Report
  • [Presentation] Performance Improvement of Metric Reconstruction Based on Partial Joint Diagonalization2011

    • Author(s)
      A.Takizawa, A.Tanaka, M.Miyakoshi
    • Organizer
      2011 IEEE International Conference on Granular Computing (GrC2011)
    • Place of Presentation
      Garden Villa Hotel(台湾)
    • Year and Date
      2011-11-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] Non-negative Matrix Factorization Considering Given Vectors in a Basis2011

    • Author(s)
      Y.Amano, A.Tanaka, M.Miyakoshi
    • Organizer
      2011 IEEE International Conference on Granular Computing (GrC2011)
    • Place of Presentation
      Garden Villa Hotel(台湾)
    • Year and Date
      2011-11-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] Music Interpolation by Wiener Filter and Its Application to Music Arrangement2011

    • Author(s)
      Y.Mizuno, A.Tanaka, M.Miyakoshi
    • Organizer
      2011 IEEE International Conference on Granular Computing (GrC2011)
    • Place of Presentation
      Garden Villa Hotel(台湾)
    • Year and Date
      2011-11-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] Theoretical Analyses on a Class of Nested RKHS's2011

    • Author(s)
      A. Tanaka, H. Imai, M. Kudo, and M. Miyakoshi
    • Organizer
      2011 IEEE International Conference on Acoustics, Speech, and Signal Processing(ICASSP2011)
    • Place of Presentation
      Prague Congress Center(チェコ)
    • Year and Date
      2011-05-25
    • Related Report
      2011 Final Research Report
  • [Presentation] Theoretical Analyses on a Class of Nested RKHS's2011

    • Author(s)
      A.Tanaka, H.Imai, M.Kudo, M.Miyakoshi
    • Organizer
      2011 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP2011)
    • Place of Presentation
      Prague Congress Center(チェコ)
    • Year and Date
      2011-05-25
    • Related Report
      2011 Annual Research Report
  • [Presentation] Analyses on Kernel-Specific Generalization Ability for Kernel Regressors2010

    • Author(s)
      A. Tanaka, M. Miyakoshi
    • Organizer
      10th International Symposium on Signal Processing and Information Technology(ISSPIT2010)
    • Place of Presentation
      Hotel Steinberger Nile Palace(エジプト)
    • Year and Date
      2010-12-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Analyses on Kernel-Specific Generalization Ability for Kernel Regressors2010

    • Author(s)
      A.Tanaka, M.Miyakoshi
    • Organizer
      10th International Symposium on Signal Processing and Information Technology (ISSPIT2010)
    • Place of Presentation
      エジプト、ルクソール
    • Year and Date
      2010-12-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] 未知観測に対する二次制約を考慮した線形系逆問題2010

    • Author(s)
      田中章, 滝沢篤史, 宮腰政明
    • Organizer
      第25回SIPシンポジウム
    • Place of Presentation
      奈良、奈良女子大学
    • Year and Date
      2010-11-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] 一般標本化定理における最良近似関数の誤差解析2010

    • Author(s)
      田中章, 宮腰政明
    • Organizer
      日本音響学会2010年秋季研究発表会
    • Place of Presentation
      大阪、関西大学
    • Year and Date
      2010-09-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] 一般標本化定理における最良近似関数の誤差解析2010

    • Author(s)
      田中章,宮腰政明
    • Organizer
      日本音響学会2010年秋季研究発表会
    • Place of Presentation
      関西大学(大阪)
    • Year and Date
      2010-09-06
    • Related Report
      2011 Final Research Report
  • [Presentation] A Relationship Between Generalization Error and Training Samples in Kernel Regressors2010

    • Author(s)
      A. Tanaka, H. Imai, M. Kudo, and M. Miyakoshi
    • Organizer
      20th International Conference on Pattern Recognition(ICPR2010)
    • Place of Presentation
      Istanbul Convention & Exhibition Centre(トルコ)
    • Year and Date
      2010-08-24
    • Related Report
      2011 Final Research Report
  • [Presentation] A Relationship Between Generalization Error and Training Samples in Kernel Regressors2010

    • Author(s)
      A.Tanaka, H.Imai, M.Kudo, M.Miyakoshi
    • Organizer
      20th International Conference on Pattern Recognition (ICPR2010)
    • Place of Presentation
      トルコ、イスタンブール
    • Year and Date
      2010-08-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] Theoretical Analyses for a Class of Kernels with an Invariant Metric2010

    • Author(s)
      A. Tanaka, M. Miyakoshi
    • Organizer
      2010 IEEE International Conference on Acoustics, Speech, and Signal Processing
    • Place of Presentation
      Sheraton Dallas Hotel(米国)
    • Year and Date
      2010-03-17
    • Related Report
      2011 Final Research Report
  • [Presentation] Theoretical Analyses for a Class of Kernels with an Invariant Metric2010

    • Author(s)
      田中章, 宮腰政明
    • Organizer
      2010 IEEE International Conference on Acoustics, Speech, and Signal Processing
    • Place of Presentation
      Sheraton Dallas Hotel(Dallas, Texas, USA)
    • Year and Date
      2010-03-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] 再生核ヒルベルト空間に対する標本化定理2010

    • Author(s)
      田中章, 今井英幸, 宮腰政明
    • Organizer
      日本音響学会2010年春季研究発表会
    • Place of Presentation
      電気通信大学(東京)
    • Year and Date
      2010-03-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] Performance Improvement of Second-Order-Statistics-Based Noisy BSS2010

    • Author(s)
      田中章, 宮腰政明
    • Organizer
      7^<th> IASTED International Conference on Signal Processing, Pattern Recognition and Applications
    • Place of Presentation
      Congress Innsbruck(Innsbruck, Austria)
    • Year and Date
      2010-02-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] 再生核ヒルベルト空間における標本化定理2009

    • Author(s)
      田中章,今井英幸,宮腰政明
    • Organizer
      第24回信号処理シンポジウム
    • Place of Presentation
      鹿児島サンロイヤルホテル(鹿児島)
    • Year and Date
      2009-11-25
    • Related Report
      2011 Final Research Report 2009 Annual Research Report
  • [Presentation] Analysis on Blind Decorrelation of Isotropic Noise Correlation Matrices Based on Symmetric Decomposition2009

    • Author(s)
      A. Tanaka, M. Miyakoshi, N. Ono
    • Organizer
      IEEE Statistical Signal Processing Workshop 2009
    • Place of Presentation
      Cardiff University(英国)
    • Year and Date
      2009-09-02
    • Related Report
      2011 Final Research Report
  • [Presentation] Analysis on Blind Decorrelation of Isotropic Noise Correlation Matrices Based on Symmetric Decomposition2009

    • Author(s)
      A.Tanaka, M.Miyakoshi, N.Ono
    • Organizer
      IEEE Statistical Signal Processing Workshop 2009
    • Place of Presentation
      Cardiff University(Cardiff, UK)
    • Year and Date
      2009-09-02
    • Related Report
      2009 Annual Research Report
  • [Presentation] Joint Estimation of Signal and Noise Correlation Matrices and Its Application to Inverse Filtering2009

    • Author(s)
      A. Tanaka, M. Miyakoshi
    • Organizer
      2009 IEEE International Conference on Acoustics, Speech, and Signal Processing(ICASSP2009)
    • Place of Presentation
      Taipei International Convention Center(台湾)
    • Year and Date
      2009-04-21
    • Related Report
      2011 Final Research Report
  • [Presentation] Joint Estimation of Signal and Noise Correlation Matrices and Its Application to Inverse Filtering2009

    • Author(s)
      田中章, 宮腰政明
    • Organizer
      2009 IEEE International Conference on Acoustics, Speech, and Signal Processing
    • Place of Presentation
      Taipei International Convention Center(Taipei, Taiwan)
    • Year and Date
      2009-04-21
    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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