Supervised Functional Data Discriminant Analysis for Hyperspectral Image Classification

This article proposes a functional data discriminant analysis (FDDA) method for hyperspectral image (HSI) classification. This method analyzes and processes the HSI data from a functional point of view, which is a novel perspective in HSI processing. The classical methods achieve dimensionality reduction by directly eliminating the redundancy of the HSI data. However, the proposed method extracts the functional features by utilizing the redundancy of the HSI data. Functional features can effectively reveal inherent characteristics of the HSI data with the change in the wavelengths. Based on this, a regularized weighted fitting model is first built for converting a spectral vector into a spectral curve. Second, an FDDA method defined in the function field is presented for extracting the functional features of the spectral curves. Finally, a novel spectral–spatial framework is designed for classification tasks of HSI data sets. Experimental results in three commonly used HSI data sets indicate that the proposed method is effective and leads to promising classification results compared with some benchmarking methods. More importantly, the work tries to diversify and develop the existing theory and methods of HSI classification from discrete (vector) data learning methods to continuous (functional) data learning methods.