Correlation Integral Decomposition for Classification

Authors:
Marcel Jiřina;Marcel Jiřina, Jr.
Affiliations:
Institute of Computer Science AS CR, Pod vodarenskou vezi 2, Liben, Czech Republic;Faculty of Biomedical Engineering, Czech Technical University in Prague, Kladno, Czech Republic 272 01
Venue:
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part II
Year:
2008

Citing 4
Cited 0

Intrinsic Dimension Estimation of Data: An Approach Based on Grassberger–Procaccia's Algorithm

Neural Processing Letters
Iterative Bayes

Theoretical Computer Science
Pattern Classification (2nd Edition)

Pattern Classification (2nd Edition)
Learning Weighted Metrics to Minimize Nearest-Neighbor Classification Error

IEEE Transactions on Pattern Analysis and Machine Intelligence

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.