Correlation Dimension-Based Classifier *

Correlation dimension is used for complexity estimation of fractals or any other data generating processes. Basic idea was introduced in the well known paper by Grassberger and Procaccia and there are papers dealing with the correlation dimension estimation. Some experiments that use the correlation dimension for classification has been published too. In this paper we introduce an innovative approach that utilizes the correlation dimension (CD) both for probability density estimate of data and consequently for classification. It will be shown that just a classifier utilizing CD exhibits significantly better behavior (classification accuracy) then other kinds of classifiers. The idea of correlation dimension classifier directly follows the principle of classifier, which uses the distribution mapping exponent (DME). The basic difference between these two approaches is that DME is a local feature depending on the position of the query point and on the number of points of the learning set while CD is not. It will be shown that CD-based classifier outperforms DME classifier and many classifiers published on Machine Learning Repository pages. One of basic steps in the CD-based classifier is correlation dimension estimation from limited number of data. There are methods and heuristics used for CD estimation. Even this heuristics are rather good they are time-consuming and often give underestimated results. Therefore, we suggest a new "hyperbolic " approximation of the correlation integral for the correlation dimension estimation and show that this approximation gives better results