Unsupervised linear feature-extraction methods and their effects in the classification of high-dimensional data

This paper presents an analysis and a comparison of different linear unsupervised feature-extraction methods applied to hyperdimensional data and their impact on classification. The dimensionality reduction methods studied are under the category of unsupervised linear transformations: principal component analysis, projection pursuit (PP), and band subset selection. Special attention is paid to an optimized version of the PP introduced in this paper: optimized information divergence PP, which is the maximization of the information divergence between the probability density function of the projected data and the Gaussian distribution. This paper is particularly relevant with current and the next generation of hyperspectral sensors that acquire more information in a higher number of spectral channels or bands when compared to multispectral data. The process to uncover these high-dimensional data patterns is not a simple one. Challenges such as the Hughes phenomenon and the curse of dimensionality have an impact in high-dimensional data analysis. Unsupervised feature extraction, implemented as a linear projection from a higher dimensional space to a lower dimensional subspace, is a relevant process necessary for hyperspectral data analysis due to its capacity to overcome some difficulties of high-dimensional data. An objective of unsupervised feature extraction in hyperspectral data analysis is to reduce the dimensionality of the data maintaining its capability to discriminate data patterns of interest from unknown cluttered background that may be present in the data set. This paper presents a study of the impact these mechanisms have in the classification process. The impact is studied for supervised classification even on the conditions of a small number of training samples and unsupervised classification where unknown structures are to be uncovered and detected.