Title: Reducing dimensionality of hyperspectral data with diffusion maps and clustering with k-means and Fuzzy ART

Authors: Louis Du Plessis; Rui Xu; Steven Damelin; Michael Sears; Donald C. Wunsch II

Addresses: School of Computational and Applied Mathematics, University of the Witwatersrand, South Africa. ' Machine Learning Laboratory, GE Global Research, Niskayuna, NY 12309, USA. ' The Unit for Advances in Mathematics and its Applications, Department of Mathematical Sciences, Georgia Southern University, GA 30460, USA; School of Computational and Applied Mathematics, University of the Witwatersrand, South Africa. ' School of Computer Science, University of the Witwatersrand, South Africa. ' Department of Electrical and Computer Engineering, Missouri University of Science & Technology, Rolla, MO 65409, USA

Abstract: It is very difficult to analyse large amounts of hyperspectral data. Here we present a method based on reducing the dimensionality of the data and clustering the result in moving toward classification of the data. Dimensionality reduction is done with diffusion maps, which interpret the eigenfunctions of Markov matrices as a system of coordinates on the original dataset in order to obtain an efficient representation of data geometric descriptions. Clustering is done using k-means and a neural network clustering theory, Fuzzy ART (FA). The process is done on a subset of core data from AngloGold Ashanti, and compared to results obtained by AngloGold Ashanti|s proprietary method. Experimental results show that the proposed methods are promising in addressing the complicated hyperspectral data and identifying the minerals in core samples.

Keywords: hyperspectral data; diffusion maps; clustering; dimensionality reduction; k-means; fuzzy ART; mineral classi?cation; neural networks; Markov systems; mineral identification; minerals; core samples.

DOI: 10.1504/IJSCC.2011.042430

International Journal of Systems, Control and Communications, 2011 Vol.3 No.3, pp.232 - 251

Published online: 11 Sep 2011 *

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