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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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.3 pp.824-831

- Publication Date
- 2009/03/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E92.A.824

- Type of Manuscript
- Special Section PAPER (Special Section on Latest Advances in Fundamental Theories of Signal Processing)

- Category

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Takahiro MURAKAMI, Toshihisa TANAKA, Yoshihisa ISHIDA, "Measurement of Similarity between Latent Variables" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 3, pp. 824-831, March 2009, doi: 10.1587/transfun.E92.A.824.

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.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.824/_p

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@ARTICLE{e92-a_3_824,

author={Takahiro MURAKAMI, Toshihisa TANAKA, Yoshihisa ISHIDA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Measurement of Similarity between Latent Variables},

year={2009},

volume={E92-A},

number={3},

pages={824-831},

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.},

keywords={},

doi={10.1587/transfun.E92.A.824},

ISSN={1745-1337},

month={March},}

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TY - JOUR

TI - Measurement of Similarity between Latent Variables

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 824

EP - 831

AU - Takahiro MURAKAMI

AU - Toshihisa TANAKA

AU - Yoshihisa ISHIDA

PY - 2009

DO - 10.1587/transfun.E92.A.824

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E92-A

IS - 3

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - March 2009

AB - 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.

ER -