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A New Algorithm to Solve Parafac-Model

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Abstract

PARAFAC is a three mode factor analytic method developed by R.A. Harshman and is useful for data analysis. The fundamental idea says

$${x_{ijk}} \approx \sum\limits_s^S {a_{is}}{b_{js}}{c_{ks}}$$

where xijk is given by measurement for i=1, 2…,I, j=1, 2,…, J, k = 1, 2,…, K; aisbjs, and cks are unknown solutions for the s-th factor, s=1, 2,…, S. However the computer program of PARAFAC developed by Harshman seems to require great skill to understand how to handle it and select the optimal solution through many steps. Here a new fool-proof algorithm not to require any skill is presented.

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Author information

Authors and Affiliations

  1. The Institute of Statistical Mathematics, 4-6-7, Minami-azabu, Minato-ku, Tokyo, 106, Japan

    Chikio Hayashi & Fumi Hayashi

Authors
  1. Chikio Hayashi
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  2. Fumi Hayashi
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Additional information

This paper has been developed through discussions with J.B. Kruskal in Tokyo, 1980.

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Hayashi, C., Hayashi, F. A New Algorithm to Solve Parafac-Model. Behaviormetrika 9, 49–60 (1982). https://doi.org/10.2333/bhmk.9.11_49

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  • DOI: https://doi.org/10.2333/bhmk.9.11_49

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