Feature Extraction Of Hyperspectral Images Based On Functional Data Analysis

Hyperspectral images(HSIs)contain considerable different reflections of electromagnetic waves from visible light to far-infrared.This characteristic allows various ground objects to be discriminated based on HSIs with abundant information.However,because of the limited labeled samples and numerous spectral bands,it would be difficult to analyze and classify the hyperspectral pixels by traditional remote sensing technology.Therefore,Dimensionality Reduction(DR),a pre-processing procedure which tries to preserve the discriminating spectral information while reducing the dimensions of the spectral,plays a vital role in HSIs data analysis and classification.Since there is high correlation information between the adjacent bands in HSIs,this thesis mainly focuses on the following aspects on the basis of Functional Data Analysis.(1)Traditional feature extraction methods treat the observed high-dimensional spectral features as discrete vector-valued data rather than continuous curves/functional data,which neglect the high correlation information between the adjacent bands.To solve this problem,we propose unsupervised Functional Locality Preserving Projection(FLPP),which regards the observed bands of each pixel as a continuous functional data and discovers the high correlation in functional data.Compared to Functional Principal Analysis(FPCA),FLPP is insensitive to noise and outliers.Experimental results show that FLPP can effectively reduce the redundancy in spectral features,and thus improve the classification accuracy.(2)The limited labeled samples with high-dimensional features is one of the key factors that affects the classification effect of HSIs.For this problem,we propose supervised Functional Locality Preserving Projection(SFLPP).SFLPP redefines the intrinsic graph based on the intraclass instances and the penalty graph based on the interclass instances,which characterizes the intraclass compactness and enforces the interclass separability of the projected low-dimensional data.Experimental results illustrate that the proposed SFLPP is capable of extracting more discriminating features when encountering small sample size problem.(3)The generation of functional data is essentially a stochastic process.Gaussian Process(GP),as a ubiquitous and important stochastic process,completes model learning and prediction with Bayesian theorem.The hyperparameters of kernels in GP can be learned automatically by gradients based optimization algorithms,thus avoiding the overfitting problem.Inspired by the benefits of GP,we propose Gaussian Process Graph based Discriminate Analysis(GPGDA),which can avoid manually parameters tuning compared to FLPP and SFLPP.GPGDA treats each spectrum as a sample function in stochastic process and makes full use of the covariance function in GP to construct the similarity graph of the sample functions.Experimental results on three HSIs data sets demonstrate that the proposed GPGDA can effectively improve the classification accuracy without time-consuming model parameters tuning.