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A nonparametric density model for classification in a high dimensional space

When the dimensionality of the feature space increases and takes beyond a certain point, the classification performance of a parametric classifier begins to deteriorate. This is because the number of parameters of the classifier depends on the dimensionality and gets too large in a high dimensional space. To obtain the density value at the point of interest without deriving the parameters, we propose a nonparametric Gaussian density model, where the sum of the log-density values at two points is described, without any parameter, by a function of the distance between the two points. The density value at the point of interest is estimated from the distance between the point and each of the training sample points using this model. We will empirically show that the density values estimated by the nonparametric model are more accurate than those by the parametric model in a high dimensional space. In a character recognition experiment, our nonparametric classifier achieved higher classification accuracy in comparison with the parametric classifier.