Locality-Preserving Dimensionality Reduction and Classification for Hyperspectral Image Analysis

Hyperspectral imagery typically provides a wealth of information captured in a wide range of the electromagnetic spectrum for each pixel in the image; however, when used in statistical pattern-classification tasks, the resulting high-dimensional feature spaces often tend to result in ill-conditioned formulations. Popular dimensionality-reduction techniques such as principal component analysis, linear discriminant analysis, and their variants typically assume a Gaussian distribution. The quadratic maximum-likelihood classifier commonly employed for hyperspectral analysis also assumes single-Gaussian class-conditional distributions. Departing from this single-Gaussian assumption, a classification paradigm designed to exploit the rich statistical structure of the data is proposed. The proposed framework employs local Fisher´s discriminant analysis to reduce the dimensionality of the data while preserving its multimodal structure, while a subsequent Gaussian mixture model or support vector machine provides effective classification of the reduced-dimension multimodal data. Experimental results on several different multiple-class hyperspectral-classification tasks demonstrate that the proposed approach significantly outperforms several traditional alternatives.