Abstract
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.
Highlights
The past few years have witnessed the availability of images with very high spectral resolution through the development of Hyperspectral Imaging (HSI) sensors [1]
We investigate the effect of our proposed method on the classification accuracy, computational complexity, and contiguous memory requirement for all five datasets described in the previous section
We applied our proposed FLDA to reduce the dimensionality of the five datasets and used the outputs to train the Support Vector Machine (SVM) classifier, comparing with the conventional Linear Discriminant Analysis (LDA), and other methods including 2D LDA, Generalized Discriminant Analysis (GDA), Nonparametric Weighted Feature Extraction (NWFE), Kernel PCA (KPCA), and F-Principal Component Analysis (PCA). 1) Classification Accuracy for the Botswana Dataset
Summary
The past few years have witnessed the availability of images with very high spectral resolution through the development of Hyperspectral Imaging (HSI) sensors [1]. The dimensions of HSI data are often reduced through feature extraction techniques before they are presented to the models for classification [18] Applying these techniques to transform the hyperspectral data into a lower dimensional space is capable of increasing the classification accuracy and reducing the computational complexity and memory requirement. The number of extracted features is no longer given as c-1 but the product of the number of columns in the converted matrices (folded pixels) and the rank of the between-class variance matrix This gives room for the selection of many more discriminant features thereby making the proposed approach more flexible than the conventional LDA, leading to more informative features (capturing local structure of the data thanks to the folded samples), and targeting higher classification accuracy than LDA, 2D LDA and the original feature space.
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