Correlation Integral Decomposition for Classification

In this paper we show that the correlation integral can be decomposed into functions each related to a particular point of data space. For these functions, one can use similar polynomial approximations as used in the correlation integral. The essential difference is that the value of the exponent, which would correspond to the correlation dimension, differs in accordance to the position of the point in question. Moreover, we show that the multiplicative constant represents the probability density estimation at that point. This finding is used for the construction of a classifier. Tests with some data sets from the Machine Learning Repository show that this classifier can be very effective. ∗ Artificial neural networks ICANN 2008 (V. K rková, R. Neruda, J. Koutník, eds.) Held 18th International Conference Prague, Czech Republic, Sept. 2008, Proceedings Part II, Lecture Notes in Computer Science LNCS 5164, pp. 62-71.