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

Authors:
Francesco Camastra;Alessandro Vinciarelli
Affiliations:
Elsag spa, Via G. Puccini 2, 16154 Genova, Italy. E-mail: francesco.camastra@elsag.it;IDIAP – Institut Dalle Molle d'Intelligence Artificielle Perceptive, Rue du Simplon 4, CP592 – 1920 Martigny, Switzerland. E-mail: alessandro.vinciarelli@idiap.ch
Venue:
Neural Processing Letters
Year:
2001

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Abstract

In this paper the problem of estimating the intrinsic dimension of a data set is investigated. An approach based on the Grassberger–Procaccia's algorithm has been studied. Since this algorithm does not yield accurate measures in high-dimensional data sets, an empirical procedure has been developed. Grassberger–Procaccia's algorithm was tested on two different benchmarks and was compared to a TRN-based method.