古典的多次元尺度構成法の視点からの関連性データの非対称性への対処  [in Japanese] Handling Asymmetry of Relational Data from a Viewpoint of Classical Multidimensional Scaling  [in Japanese]

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Author(s)

Abstract

非対称な関連性データに対し,対称部を距離として従来の古典的MDSで扱いつつ,歪対称部を分析・表示する方法を提案する.その中で,以前提案した定式化との類似性に触れ,相違点を明らかにする.さらに,関連性データを複素数表示した場合,複素ベクトルを用いてデータを表現できることを示し,距離的な関連性データが与えられている場合に,従来研究が分析対象とする内積的な関連性データに変換できることを示す.

A method is proposed, which analyzes and represents anti-symmetric part of asymmetric relational data, dealing simultaneously with symmetric part as distance by the classical MDS. The similarity to the author's previous formulation is mentioned and the difference is clarified. Furthermore, it is shown that the data can be represented by complex vectors when relational data is given as complex numbers and that the data can be transformed to inner product-like relational data as analyzed in former researches when it is given as distance-like relational data.

Journal

  • Transactions of the Japan Society for Industrial and Applied Mathematics

    Transactions of the Japan Society for Industrial and Applied Mathematics 21(2), 165-174, 2011

    The Japan Society for Industrial and Applied Mathematics

References:  12

Codes

  • NII Article ID (NAID)
    110008673566
  • NII NACSIS-CAT ID (NCID)
    AN10367166
  • Text Lang
    JPN
  • Article Type
    NOT
  • ISSN
    09172246
  • NDL Article ID
    11171441
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z15-727
  • Data Source
    CJP  NDL  NII-ELS  J-STAGE 
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