Greedy modular eigenspaces and positive Boolean function for supervised hyperspectral image classification

This paper presents a new supervised classification technique for hyperspectral imagery, which consists of two algorithms, referred to as the greedy modular eigenspace (GME) and the positive Boolean function (PBF). The GME makes use of the data correlation matrix to reorder spectral bands from which a group of feature eigenspaces can be generated to reduce dimensionality. It can be implemented as a feature extractor to generate a particular feature eigenspace for each of the material classes present in hyperspectral data. The residual reconstruction errors (RREs) are then calculated by projecting the samples into different individual GME-generated modular eigenspaces. The PBF is a stack filter built by using the binary RRE as classifier parameters for supervised training. It implements the minimum classification error (MCE) as a criterion so as to improve classification performance. Experimental results demonstrate that the proposed GME feature extractor suits the nonlinear PBF-based multiclass classifier well for classification preprocessing. Compared to the conventional principal components analysis (PCA), it not only significantly increases the accuracy of image classification but also dramatically improves the eigendecomposition computational complexity.