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Measurement of Similarity between Latent Variables
Takahiro MURAKAMI Toshihisa TANAKA Yoshihisa ISHIDA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E92A
No.3
pp.824831 Publication Date: 2009/03/01 Online ISSN: 17451337
DOI: 10.1587/transfun.E92.A.824 Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Latest Advances in Fundamental Theories of Signal Processing) Category: Keyword: similarity, FIR filter, MSE, eigenvalue problem, correlation coefficient,
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Summary:
A method for measuring similarity between two variables is presented. Our approach considers the case where available observations are arbitrarily filtered versions of the variables. In order to measure the similarity between the original variables from the observations, we propose an errorminimizing filter (EMF). The EMF is designed so that an error between outputs of the EMF is minimized. In this paper, the EMF is constructed by a finite impulse response (FIR) filter, and the error between the outputs is evaluated by the mean square error (EMF). We show that minimization of the MSE results in an eigenvalue problem, and the optimal solution is given in a closed form. We also reveal that the minimal MSE by the EMF is efficient in the measurement of the similarity from the viewpoint of a correlation coefficient between the originals.


