Performance comparison of initialization representations for functional data analysis based hyperspectral image classification

In functional data analysis (FDA) based hyperspectral image (HSI) classification, the optimizing initialization representations of high dimension spectral vectors for individual pixels in the HSI is crucial for obtaining the high-precision classification results. In FDA, basis functions are commonly used to represent a given function as its initialization representations in terms of root mean square error (RMSE) scheme. Unfortunately, RMSE based basis function fittings for initialization representations of HSI spectral vector seems not be optimal from HSI classification perspective. As a result, this study compares five types of basis functions to obtain the optimal initialization representations from a classification perspective and explores their essential characteristics. The research results suggest that the basis functions can in nature express low-frequency and high-frequency features, where the low-frequency features are more clustering properties and these features are more useful for HSI classification. The Gaussian function, in particular, attenuates high-frequency features while amplifying low-frequency features, promoting intra-class aggregatability and inter-class separability. Thus, despite yielding relatively higher RMSE compared to the classical FDA approach, it achieves better classification accuracy. Consequently, RMSE should not be the sole criterion for evaluating the optimal initialization representations in HSI classification. Additionally, this study introduces regularized basis weighted local least squares penalty (RBWLP) strategy that better handles non-stationary HSI data, contributing to the further extension of FDA methods in the context of HSI.