DISCRIMINANT ANALYSIS OF MULTI-DIMENSIONAL INTERVAL DATA AND ITS APPLICATION TO CHEMICAL SENSING

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Abstract
A conventional discriminant problem is to determine a discriminant function, which maps a point in a multi-dimensional feature space to a point in a one-dimensional decision space, using a set of labeled (known classification) samples. In many cases, attribute values of each sample are not constant but fluctuating with time. In this paper, we represent the fluctuating attribute values of each sample by an interval vector in the feature space, and propose a discriminant method for a set of interval vectors. The proposed method is based on a linear interval model which maps an interval vector in the feature space to an interval in the decision space. A mathematical programming problem is formulated to determine the coefficients of this model. We also propose a set of discriminant rules to discriminate unknown samples. The proposed method is applied to a smell sensing problem.