A dimension reduction framework for HSI classification using fuzzy and kernel NFLE transformation

In this paper, a general nearest feature line (NFL) embedding (NFLE) transformation called fuzzy-kernel NFLE (FKNFLE) is proposed for hyperspectral image (HSI) classification in which kernelization and fuzzification are simultaneously considered. Though NFLE has successfully demonstrated its discriminative capability, the non-linear manifold structure cannot be structured more efficiently by linear scatters using the linear NFLE method. According to the proposed scheme, samples were projected into a kernel space and assigned larger weights based on that of their neighbors. The within-class and between-class scatters were calculated using the fuzzy weights, and the best transformation was obtained by maximizing the Fisher criterion in the kernel space. In that way, the kernelized manifold learning preserved the local manifold structure in a Hilbert space as well as the locality of the manifold structure in the reduced low-dimensional space. The proposed method was compared with various state-of-the-art methods to evaluate the performance using three benchmark data sets. Based on the experimental results: the proposed FKNFLE outperformed the other, more conventional methods.