Correlation dimension is usually used to study features of fractals and data generating processes. For estimation of value of correlation dimension in a particular case often a polynomial approximation of correlation integral is used and then the linear regression for logarithms of variables is applied. In this paper we show that correlation integral can be decomposed into functions each related to particular point of data space. For these functions one can use similar polynomial approximations as for the correlation integral. Essential difference is that value of exponent, which would correspond to correlation dimension, differs in accordance to position of point in question. Moreover we show that multiplicative constant represents probability density estimation at that point. This finding is used for construction of a classifier. Tests with some data sets from Machine Learning Repository shows that this classifier can be very effective.
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