Kernel-Based Constrained Energy Minimization for Hyperspectral Mixed Pixel Classification

One fundamental task of hyperspectral imaging is spectral unmixing. In this case, the conventional pure pixel-based hyperspectral image classification (HSIC) may not work effectively for mixed pixels. This article presents a kernel-based approach to hyperspectral mixed pixel classification (HMPC) which includes two nonlinear mixed pixel classifiers, kernel constrained energy minimization (KCEM) and kernel linearly constrained minimum variance (KLCMV) to replace the widely used pure pixel-based support vector machine (SVM) classifier. Interestingly, what the binary-class and multiclass SVM classifiers are to pure pixel-based HSIC can be similarly derived for what a single-class KCEM detector and a multiclass KLCMV detector are to HMPC. In particular, the commonly used discrete classification map-based hard classification measures, average accuracy (AA) and overall accuracy (OA) for performance evaluation can be further generalized to real-valued mixed class abundance fractional map-based soft classification measures via 3-D receiver operating characteristic (3-D ROC) analysis-derived detection measures. Extensive experiments are conducted to demonstrate the utility of HMPC where KCEM/KLCMV not only significantly improve the classification performance of CEM/LCMV-based classifiers but also outperform many existing spectral-spatial classification methods.