Studies on principal component analysis for three-way data of inputs and outputs

• Project/Area Number: 20500256
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: Osaka University
• Principal Investigator: ADACHI Kohei 大阪大学, 大学院・人間科学研究科, 教授 (60299055)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 行動計量分析 / 多変量解析 / 主成分分析 / 三相データ / 入出力データ / 回転 / ネットワーク / モデル選択 / 同時プロクラステス法 / 多変量解析法 / 主成分分析法 / 同時プロクラステス分析 / 正準相関分析 / 単純構造

Research Abstract

The principal component analysis(PCA) procedures were studied which can be applied to three-way data arrays of inputs by outputs by individuals for finding the components intermediating between inputs and outputs. These studies allowed us to find the procedure to find the optimal model among the PCA models considered and develop the method for optimally transforming the PCA solutions to useful ones of simple structures.

Research Products

• [Journal Article] Three-way Tucker2 component analysis solutions of stimuli×responses×individuals data with simple structure and the fewest core differences (2011)
  • Author(s): Adachi, K
  • Journal Title: Psychometrika Volume: vol.76 Issue: 2 Pages: 285-305
  • DOI: 10.1007/s11336-011-9208-6
  • Peer Reviewed
• [Journal Article] 最小二乗置換によるサイズ固定クラスタリング (2011)
  • Author(s): 足立浩平
  • Journal Title: データ分析の理論と応用 Volume: 1巻 Pages: 11-22
  • NAID: 130007828583
  • Peer Reviewed
• [Journal Article] Constrained principal component analysis of standardized data for biplots with unit-length variable vectors (2011)
  • Author(s): Adachi, K
  • Journal Title: Advances in Data Analysis and Classification Volume: vol.5 Issue: 1 Pages: 23-36
  • DOI: 10.1007/s11634-010-0081-4
  • Peer Reviewed
• [Journal Article] Three-way Tucker2 component analysis solutions of stimuli×responses×individuals data with simple structure and the fewest core differences (2011)
  • Author(s): Kohei Adachi
  • Journal Title: Psychometrika Volume: 76 Pages: 285-305
  • Peer Reviewed
• [Journal Article] Constrained principal component analysis of standardized data for biplots with unit-length variable vectors (2011)
  • Author(s): Kohei Adachi
  • Journal Title: Advances in Data Analysis and Classification Volume: 5 Pages: 23-36
  • Peer Reviewed
• [Journal Article] Joint Procrustes Analysis for Simultaneous Nonsingular Transformation of Component Score and Loading Matrices (2009)
  • Author(s): Adachi, K
  • Journal Title: Psychometrika Volume: vol.74 Issue: 4 Pages: 667-683
  • DOI: 10.1007/s11336-009-9131-2
  • Peer Reviewed
• [Journal Article] Joint Procrustes Analysis for Simultaneous Nonsingular Transformation of Component Score and Loading Matrices (2009)
  • Author(s): Kohei Adachi
  • Journal Title: Psychometrika 74 Pages: 667-683
  • Peer Reviewed
• [Journal Article] Joint Procrustes Analysis : Minimizing a LS Function of a Nonsingular Matrix and Its Inverse Matrix with SVD Reparameterization (2008)
  • Author(s): Adachi, K
  • Journal Title: The Proceedings of International Association of Statistical Computing(IASC) Volume: (CD-ROM版) Pages: 32-39
• [Journal Article] Correspondence Analysis as Reduced Rank Approximation of Quantified Indicator Matrices (2008)
  • Author(s): Adachi, K. & Murakami, T.
  • Journal Title: The Proceedings of International Association of Statistical Computing(IASC) Volume: (CD-ROM版) Pages: 40-49
• [Journal Article] Joint Procrustes Analysis : Minimizing a LS Function of a Nonsingular Matrix and Its Inverse Matrix with SVD Reparameterization (2008)
  • Author(s): Kohei Adachi
  • Journal Title: The Proceedings of International Association of Statistical Computing (IASC)2008 巻番号なし(CD-ROM版) Pages: 32-39
• [Journal Article] Multiple Correspondence Analysis as Reduced Rank Approximation of Quantified Indicator Matrices (2008)
  • Author(s): Kohei Adachi, Takashi Murakami
  • Journal Title: The Proceedings of International Association of statistical Computing (IASC)2008 巻番号なし(CD-ROM版) Pages: 40-49
• [Presentation] Nonsingular Transformation of Tucker2 Solutions for Representing Stimulus-Response Relationships by Sparse Networks (2011)
  • Author(s): Adachi, K.
  • Organizer: International Meeting of Psychometric Society
  • Place of Presentation: 香港教育学院
  • Year and Date: 2011-07-19
• [Presentation] Three Kinds of Hierarchical Relations among PCA, Nonmetric PCA, and Multiple Correspondence Analysis (2011)
  • Author(s): Adachi, K. & Murakami, T.
  • Organizer: International Meeting of Psychometric Society
  • Place of Presentation: 香港教育学院
  • Year and Date: 2011-07-19
• [Presentation] Three Kinds of Hierarchical Relations among PCA, Nonmetric PCA, and Multiple Correspondence Analysis (2011)
  • Author(s): Kohei Adachi, Takashi Murakami
  • Organizer: International Meeting of Psychometric Society, 2011
  • Place of Presentation: 香港教育学院(香港)(招待講演)
  • Year and Date: 2011-07-19
• [Presentation] Nonsingular Transformation of Tucker2 Solutions for Representing Stimulus-Response Relationships by Sparse Networks (2011)
  • Author(s): Kohei Adachi
  • Organizer: International Meeting of Psychometric Society, 2011
  • Place of Presentation: 香港教育学院(香港)
  • Year and Date: 2011-07-19
• [Presentation] Singular Value Reparameter-ization with Its Applications to Least Squares Computations (2010)
  • Author(s): Adachi, K.
  • Organizer: The 3rd International Conference on COMPUTING & STATISTICS
  • Place of Presentation: ロンドン大学
  • Year and Date: 2010-12-11
• [Presentation] Singular Value Reparameterization with Its Applications to Least Squares Computations (2010)
  • Author(s): Kohei Adachi
  • Organizer: 3rd International Conference on COMPUTING & STATISTICS
  • Place of Presentation: ロンドン大学(イギリス)(招待講演)
  • Year and Date: 2010-12-11
• [Presentation] A Factor Analysis Procedure for Jpintly Estimating Factors, Loadings, and Specificitie (2010)
  • Author(s): Adachi, K.
  • Organizer: 第10回中国日本統計シンポジウム
  • Place of Presentation: 西南財経大学
  • Year and Date: 2010-10-16
• [Presentation] A Factor Analysis Procedure for Jpintly Estimating Factors, Loadings, and Specificities (2010)
  • Author(s): Kohei Adachi
  • Organizer: 第10回中国日本統計シンポジウム
  • Place of Presentation: 西南財経大学(中国)
  • Year and Date: 2010-10-16
• [Presentation] PCAの基礎:幾種かの最小二乗行列近似によるPCAの定式化 (2010)
  • Author(s): 足立浩平
  • Organizer: 「データ縮約のトレンドを追う-PCAとSDA-」ワークショップ
  • Place of Presentation: 統計数理研究所(東京都)(招待講演)
  • Year and Date: 2010-09-17
• [Presentation] PCAの3種の拡張:非計量PCA(数量化)と三相PCAと因子分析 (2010)
  • Author(s): 足立浩平
  • Organizer: 「データ縮約のトレンドを追う-PCAとSDA-」ワークショップ
  • Place of Presentation: 統計数理研究所(東京都)(招待講演)
  • Year and Date: 2010-09-17
• [Presentation] A constrained condition-number LS algorithm with its applications to reverse component analysis and generalized oblique Procrustes rotation (2010)
  • Author(s): Adachi, K.
  • Organizer: 19th Symposium of IASC on Computational Statistics(COMPSAT 2010)
  • Place of Presentation: パリ国際会議場
  • Year and Date: 2010-08-26
• [Presentation] A constrained condition-number LS algorithm with its applications to reverse component analysis and generalized oblique Procrustes rotation (2010)
  • Author(s): Kohei Adachi
  • Organizer: 19th Symposium of IASC on Computational Statistics (COMPSAT 2010)
  • Place of Presentation: パリ国際会議場(フランス)
  • Year and Date: 2010-08-26
• [Presentation] A New Formulation of Factor Analysis with Fixed Common and Specific Factors (2010)
  • Author(s): Adachi, K.
  • Organizer: The 75th Meeting of Psychometric Society
  • Place of Presentation: ジョージア大学
  • Year and Date: 2010-07-09
• [Presentation] A New Formulation of Factor Analysis with Fixed Common and specific Factors (2010)
  • Author(s): Kohei Adachi
  • Organizer: The 75th Meeting of Psychometric Society
  • Place of Presentation: ジョージア大学(アメリカ)
  • Year and Date: 2010-07-09
• [Presentation] Singular Value Reparameterization with Its Applications to Rank Preserving Computation, Procrustes Transformation, and Factor Analysis (2010)
  • Author(s): Adachi, K.
  • Organizer: The 19th International Workshop on Matrices and Statistics
  • Place of Presentation: 上海金融学院
  • Year and Date: 2010-06-06
• [Presentation] Singular Value Reparameterization with Its Applications to Rank Preserving Computation, Procrustes Transformation, and Factor Analysis (2010)
  • Author(s): Kohei Adachi
  • Organizer: The 19th International Workshop on Matrices and Statistics
  • Place of Presentation: 上海金融学院(中国)
  • Year and Date: 2010-06-06
• [Presentation] Reduced Condition Number Regression and its Alternating Least Squares Algorithm with Singular Value Reparameterization (2009)
  • Author(s): 足立浩平
  • Organizer: 科学研究費(基盤研究(B) 18300094)シンポジウム「多変量データ解析法への計算機統計学・行動計量学的アプローチの新展開」
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-12-04
• [Presentation] Reduced Condition Number Regression and its Alternating Least Squares Algorithm with Singular Value Reparameterization (2009)
  • Author(s): 足立浩平
  • Organizer: 科学研究費 (基盤研究(B)18300094) シンポジウム「多変量データ解析法への計算機統計学・行動計量学的アプローチの新展開」
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-12-04
• [Presentation] 入出力データの三相主成分分析-Tucker2の成分と核行列の同時変換- (2009)
  • Author(s): 足立浩平
  • Organizer: 日本計算機統計学会第23回シンポジウム
  • Place of Presentation: 札幌学院大学
  • Year and Date: 2009-11-07
• [Presentation] 入出力データの三相主成分分析-Tucker 2の成分と核行列の同時変換- (2009)
  • Author(s): 足立浩平
  • Organizer: 日本計算機統計学会第23回シンポジウム
  • Place of Presentation: 札幌学院大学
  • Year and Date: 2009-11-07
• [Presentation] パーセプトロンとしての三相主成分分析-刺激・主成分・反応のネットワーク表現- (2009)
  • Author(s): 足立浩平
  • Organizer: 2009年度統計関連学会連合大会
  • Place of Presentation: 同志社大学
  • Year and Date: 2009-09-08
• [Presentation] 4層パーセプトロンとしての三相主成分分析 (2009)
  • Author(s): 足立浩平
  • Organizer: 日本心理学会第73回大会ワークショップ「日本における数理心理学の展開XVI」
  • Place of Presentation: 立命館大学
  • Year and Date: 2009-08-26
• [Presentation] パームティミン回転-最小二乗行置換による因子負荷行列の単純構造化- (2009)
  • Author(s): 足立浩平
  • Organizer: 日本行動計量学会第37回大会
  • Place of Presentation: 大分大学
  • Year and Date: 2009-08-05
• [Presentation] Permutimin : Factor Rotation to Specified Simple Structure with Least Squares Permutation (2009)
  • Author(s): Adachi, K.
  • Organizer: International Meeting of Psychometric Society
  • Place of Presentation: ケンブリッジ大学
  • Year and Date: 2009-07-22
• [Presentation] Permutimin : Factor Rotation to Specified Simple Structure with Least Squares Permutation (2009)
  • Author(s): 足立浩平
  • Organizer: International Meeting of Psychometric Society, 2009
  • Place of Presentation: ケンブリッジ大学 英国
  • Year and Date: 2009-07-22
• [Presentation] Joint Procrustes Algorithm for Nonsingular and Compensatory Transformation of Component and Loading Matrices (2009)
  • Author(s): Adachi, K.
  • Organizer: The 1st Institute of Mathematical Statistics Asia PacificRim Meetings
  • Place of Presentation: ソウル国立大学
  • Year and Date: 2009-06-29
• [Presentation] Joint Procrustes Algorithm for Nonsingular and Compensatory Transformation of Component and Loading Matrices (2009)
  • Author(s): 足立浩平
  • Organizer: The 1st Institute of Mathematical Statistics Asia Pacific Rim Meetings
  • Place of Presentation: ソウル国立大学韓国
  • Year and Date: 2009-06-29
• [Presentation] 最小二乗パーミュテイションの因子回転とサイズ固定クラスタリングへの応用 (2009)
  • Author(s): 足立浩平
  • Organizer: 日本計算機統計学会第23回大会
  • Place of Presentation: 福岡女子大学
  • Year and Date: 2009-05-17
• [Presentation] Joint Procrustes Analysis : Minimizing a LS Function of a Nonsingular Matrix and Its Inverse Matrix with SVD Reparameterization (2008)
  • Author(s): Adachi, K.
  • Organizer: International Associa-tion of Statistical Computing
  • Place of Presentation: パシィフィコ横浜
  • Year and Date: 2008-12-08
• [Presentation] Joint Procrustes Analysis : Minimizing a LS Function of a Nonsingular Matrix and Its Inverse Matrix with SVD Reparameterization (2008)
  • Author(s): Kohei Adachi
  • Organizer: International Association of Statistical Computing, 2008
  • Place of Presentation: パシィフィコ横浜
  • Year and Date: 2008-12-08
• [Presentation] Multiple Correspondence Analysis as Reduced Rank Approximation of Quantified Indicator Matrices (2008)
  • Author(s): Adachi, K. & Murakami, T.
  • Organizer: International Association of Statistical Computing
  • Place of Presentation: パシィフィコ横浜
  • Year and Date: 2008-12-06
• [Presentation] Multiple Correspondence Analysis as Reduced Rank Approximation of Quantified Indicator Matrices (2008)
  • Author(s): Kohei Adachi, Takashi Murakami
  • Organizer: International Association of Statistical Computing, 2008
  • Place of Presentation: パシイフイコ横浜
  • Year and Date: 2008-12-06
• [Presentation] 心理統計学と実験心理学のねじれた関係 (2008)
  • Author(s): 足立浩平
  • Organizer: 日本心理学会第72回大会
  • Place of Presentation: 北海道大学
  • Year and Date: 2008-09-21
• [Presentation] 負荷行列の列ではなく行のノルムを1と制約した主成分分析の性質-アダマール積vech演算子を用いた考察- (2008)
  • Author(s): 足立浩平
  • Organizer: 2008年度統計関連学会連合大会
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2008-09-08
• [Presentation] 負荷行列の列ではなく行のノルムを1と制約した主成分分析の性質-アダマール積とvech演算子を用いた考察- (2008)
  • Author(s): 足立浩平
  • Organizer: 2008年度統計関連学会連合大会
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2008-09-08
• [Presentation] 多変量データ解析法のタクソノミー (2008)
  • Author(s): 足立浩平
  • Organizer: 日本行動計量学会第36回大会
  • Place of Presentation: 成蹊大学
  • Year and Date: 2008-09-04
• [Presentation] Reformulation of Multiple Correspondence Analysis as Reduced Rank Approximation of Quantified Indicator Matrices (2008)
  • Author(s): 足立浩平, 村上隆
  • Organizer: 日本行動計量学会第36回大会
  • Place of Presentation: 成蹊大学
  • Year and Date: 2008-09-03
• [Presentation] Joint Procrustes Component Analysis for Exploring the Perceptual and Semantic Structures in Three-Way Semantic Differential Data (2008)
  • Author(s): Adachi, K.
  • Organizer: International Congress of Psychology
  • Place of Presentation: ICC Berlin
  • Year and Date: 2008-07-24
• [Presentation] Joint Procrustes Component Analysis for Exploring the Perceptual and Semantic Structures in Three-Way Semantic Differential Data (2008)
  • Author(s): Kohei Adachi
  • Organizer: International Congress of Psychology, 2008
  • Place of Presentation: ICC Berlin
  • Year and Date: 2008-07-24
• [Presentation] Joint Procrustes Analysis with Constrained Simplimax Rotation : Nonsingular Transformation of Component Score and Loading Matrices Toward Simple Structure (2008)
  • Author(s): Adachi, K.
  • Organizer: The 32nd Annual Conference of the German Classification Society
  • Place of Presentation: HELMUT-SCHMIDT-UNIVERSITAT
  • Year and Date: 2008-07-16
• [Presentation] Joint Procrusts Analysis in the S-O-R Framework (2008)
  • Author(s): Adachi, K.
  • Organizer: International Meeting of Psychometric Society
  • Place of Presentation: University of New Hampsire
  • Year and Date: 2008-07-01
• [Presentation] Joint Procrusts Analysis in the S-O-R Framework (2008)
  • Author(s): Kohei Adachi
  • Organizer: International Meeting of Psychometric Society, 2008
  • Place of Presentation: University of New Hampsire
  • Year and Date: 2008-07-01
• [Book] 心理学フロンティア(I章15節 : 多次元尺度法, 16節 : 構造方程式モデリング) (2008)
  • Author(s): 足立浩平
  • Total Pages: 8
  • Publisher: 新曜社
• [Book] 非計量多変量解析法-主成分分析から多重対応分析へ-
  • Author(s): 足立浩平・村上隆
  • Total Pages: 171
  • Publisher: 朝倉書店
• [Book] 心理学フロンティア(I章15節:多次元尺度法, 16節:構造方程式モデリング)
  • Author(s): 足立浩平
  • Total Pages: 8
  • Publisher: 新曜社
• [Remarks]
• [Remarks]
  • URL: http://www.dma.jim.osaka-u.ac.jp/kg-portal/aspi/RX0011D.asp?UNO=14131&page=