Feature extraction with modified Fisher's linear discriminant analysis

Abstract

Hyperspectral remotely sensed imagery is rapidly developed recently. It collects radiance from the ground with hundreds of channels which results in hundreds of co-registered images. How to process this huge amount of data is a great challenge. Feature extraction methods are designed to remove redundant and remain useful information in the hyperspectral images. Many feature extraction approaches have been developed in the past, including the well known Principal Component Analysis (PCA) and Fisher's Linear Discriminant Analysis (LDA). The PCA is designed to search for directions with maximum variances. It compress most of the signal in the first a few principal components, but the experimental result shows that the extracted features by PCA does not perform well for target classification. On the other hand, Fisher's LDA is designed target classification, which maximize the between class distance while minimize the within class distance, but it can only find number of features which equal to the number of classes minus one. This will become a problem for subpixel target classification. Under this circumstance, this paper presents a modified Fisher's LDA which can extract features more than number of classes. The experiments are conducted to compare the classification results of PCA, Fisher's LDA and proposed method.