Abstract
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.
