Nonparametric Fuzzy Feature Extraction for Hyperspectral Image Classification

Feature extraction plays an essential role in high-dimensional data classification. Linear discriminant analysis (LDA) is one of the most well-known methods for reducing data dimensionality in various fields. However, there are three inherent limitations when applying LDA to extract features. First, the number of features that can be extracted by LDA is the number of classes minus one at most. Second, it cannot perform well for non-normally distributed data. Third, it suffers from the singularity problem when handling the small sample size (SSS) problem. Nonparametric feature extraction algorithms such as nonparametric discriminant analysis (NDA) and nonparametric weighted feature extraction (NWFE) are developed to overcome the limitations of LDA and preserve better data structure in the reduced feature space for classification. In this study, we propose a novel nonparametric feature extraction method, called nonparametric fuzzy feature extraction (NFFE) method, to which some properties revealed from the fuzzification procedure of the fuzzy K-nearest neighbor algorithm are introduced. The performance of NFFE is investigated on two remotely sensed hyperspectral images with different training sample sizes, including the so-called ill-posed and poorly posed classification cases. The experimental results demonstrate that 1NN and SVM classifiers with NFFE features achieve better classification results than with features extracted from some existing methods.