Institute of Mathematics for Industry

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Predicting Precision Matrices for Color Matching Problem


Hold Date 2019-02-05 16:00~2019-02-05 17:00

Place Seminar Room W1-D-710, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Takayoshi NAKAMOTO (Mazda Motor Corpotation)

Abstract:
In this paper, as data, ellipsoids in a color coordinate called CIE-Lab system are given for 19 colors. Each ellipsoid is the region whose all points are visually recognized as the same color at the center in the coordinate system. Our aim here is to predict the shape of an ellipsoid whose center is given by a new color. We proposed two prediction meth-ods of positive definite matrices detemining ellipsoids. The first one is a nonparametric method with Gaussian kernel. The prediction is provided as a weighted sum of positive definite matrices corresponding to 19 ellipsoids in the training data. The second one is to use a matrix-valued regression model to a logarithm of positive definite matrices where explanatory variables are three elements of color centers. The best result was obtained by the nonparametric methods with three bandwidth parameters. The log normal regression shows weaker perfor-mance, but the model estimation is easily carried out.