Unsupervised Feature Extraction and Band Subset Selection techniques based on Relative Entropy Criteria for Hyperspectral data Analysis

Feature extraction, implemented as a linear projection from a higher dimensional space to a lower dimensional subspace, is a very important issue in hyperspectral data analysis. This reduction must be done in a manner that minimizes the redundancy, maintaining the information content. This paper proposes methods for feature extraction and band subset selection based on Relative Entropy Criteria. The main objective of the feature extraction and band selection methods implemented is to reduce the dimensionality of the data maintaining the capability of discriminating objects of interest from the cluttered background. These methods accomplish the described goal by maximizing the difference between the data distribution of the lower dimensional subspace and the standard Gaussian distribution. The difference between the low dimensional space and the Gaussian distribution is measured using relative entropy, also known as information divergence. A Projection Pursuit unsupervised algorithm based on an optimization algorithm of the relative entropy is presented. An unsupervised version for selecting bands in hyperspectral data will be presented as well. The relative entropy criterion will measure the information divergence between the probability density function of the feature subset and the Gaussian probability density function. This augments the separability of the unknown clusters in the lower dimensional space. One advantage of these methods is that there is no use of labeled samples. These methods were tested using simulated data as well as remotely sensed data.