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How to Use HFM for Asymmetric MDS

In: Structure and Dynamics of Asymmetric Interactions

Author

Listed:
  • Naohito Chino

    (Aichi Gakuin University, Emeritus Professor)

Abstract

In this sectionMultidimensional scaling (MDS) we shall introduce HFMHermitian Form Model (HFM) for the analysis of asymmetric (dis)similarity matrix, which was proposed by Chino and Shiraiwa (Chino and Shiraiwa in Behaviormetrika 39:127–165, 1993). Let us first suppose that we have an observedAsymmetric Similarity Matrix (ASM) asymmetric similaritySimilarity (similarities) matrix $${\varvec{S}} = \left[ {{\varvec{s}}_{{{\varvec{jk}}}} } \right]$$ S = s jk , whose element $${\varvec{s}}_{{{\varvec{jk}}}}$$ s jk denotes the intensity of the similarity from object j to object k among N objects. Therefore, matrix S is N by N, and is in general asymmetric. We shall hereafter abbreviate the Asymmetric Similarity MatrixAsymmetric Similarity Matrix (ASM) as ASM.

Suggested Citation

  • Naohito Chino, 2025. "How to Use HFM for Asymmetric MDS," Springer Books, in: Structure and Dynamics of Asymmetric Interactions, chapter 0, pages 123-142, Springer.
    • Handle: RePEc:spr:sprchp:978-981-97-8269-7_5
    DOI: 10.1007/978-981-97-8269-7_5
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