Folded LDA: extending the linear discriminant analysis algorithm for feature extraction and data reduction in hyperspectral remote sensing

The rich spectral information provided by hyperspectral imaging (HSI) has made this technology very useful in the classification of remotely sensed data. However, classification of hyperspectral data is typically affected by noise and the Hughes phenomenon due to the presence of hundreds of spectral bands and correlation among them, with usually a limited number of samples for training. Linear Discriminant Analysis (LDA) is a well-known technique that has been widely used for supervised dimensionality reduction of hyperspectral data. However, the use of LDA in hyperspectral remote sensing is limited due to 1) its poor performance on small training datasets and 2) the limited number of features that can be selected i.e. c-1 where c is the number of classes in the data. To solve these problems, this work presents a Folded LDA (F-LDA) for dimensionality reduction of remotely sensed HSI data in Small Sample Size (SSS) scenarios. The proposed approach allows many more discriminant features to be selected in comparison to the conventional LDA since the selection is no longer bound by the limiting factor, leading to significantly higher accuracy in the classification of pixels under SSS restrictions. The proposed approach is evaluated on five different datasets, where the experimental results demonstrate the superiority of the F-LDA to the conventional LDA in terms of not only higher classification accuracy but also reduced computational complexity, and reduced contiguous memory requirements.