# An Entropy-Based Tool to Help the Interpretation of Common-Factor Spaces in Factor Analysis

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Center for Educational Outreach and Admissions, Kyoto University, Yoshida-machi, Sakyoku, Kyoto 660-8501, Japan

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Department of Statistics and Quantitative Methods, University of Milano Bicocca, 20126 Milano, Italy

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Department of Mathematical Sciences, Osaka Prefecture University, Osaka 599-8532, Japan

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Department of Applied Mathematics, Tokyo University of Science, Kagurazaka, Shinzyukuku, Tokyo 162-0825, Japan

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Author to whom correspondence should be addressed.

Received: 27 December 2020 / Revised: 18 January 2021 / Accepted: 19 January 2021 / Published: 24 January 2021

(This article belongs to the Section Information Theory, Probability and Statistics)

This paper proposes a method for deriving interpretable common factors based on canonical correlation analysis applied to the vectors of common factors and manifest variables in the factor analysis model. First, an entropy-based method for measuring factor contributions is reviewed. Second, the entropy-based contribution measure of the common-factor vector is decomposed into those of canonical common factors, and it is also shown that the importance order of factors is that of their canonical correlation coefficients. Third, the method is applied to derive interpretable common factors. Numerical examples are provided to demonstrate the usefulness of the present approach.