Summary
The correlation dimension is usually used to study features of fractals and data generating processes. For estimating the value of the correlation dimension in a particular case, a polynomial approximation of correlation integral is often used and then linear regression for logarithms of variables is applied. In this Chapter, 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 such as 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 to construct a classifier. Tests with some data sets from the Machine Learning Repository show that this classifier can be very effective.
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Jiřina, M., Jiřina, M. (2009). Classification by the Use of Decomposition of Correlation Integral. In: Abraham, A., Hassanien, AE., Snášel, V. (eds) Foundations of Computational Intelligence Volume 5. Studies in Computational Intelligence, vol 205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01536-6_2
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