Measurement of Similarity between Latent Variables

Takahiro MURAKAMI  Toshihisa TANAKA  Yoshihisa ISHIDA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.3   pp.824-831
Publication Date: 2009/03/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.824
Print ISSN: 0916-8508
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 error-minimizing 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.