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.

Training sample selection is a great challenge for hyperspectral image classification (HSIC), specifically when only a very limited number of labeled data samples are available for training. Two recently developed concepts for training sample selection are of particular interest. One is active learning (AL), which augments labeled training samples by including unlabeled data samples as new training samples. The other is iterative training sampling (ITS), which expands data cubes by including additional spatial classification information into the training samples. This article combines AL and ITS simultaneously to derive a joint ITS–AL spectral–spatial (SS) classification approach, to be called ITS augmentation by AL spectral–spatial classification, referred to as ITSA-AL-SS, which can improve SS classification using either AL or ITS alone. The novel idea of ITSA-AL-SS is to take advantage of ITS to expand data cubes by incorporating additional spatial classification information iteratively into the AL-augmented unlabeled data samples to update the current training samples iteration by iteration in one-shot operation. As expected, ITSA-AL-SS is benefited from both ITS and AL to not only further improve classification accuracy but also reduce classification inconsistency.

Hyperspectral image classification (HSIC) has generated considerable interests over the past years. However, one of challenging issues arising in HSIC is inconsistent classification which is mainly caused by random training sampling (RTS) of selecting training data. This is because a different set of training samples may produce a different classification result. A general approach to addressing this problem is so-called K-fold method which implements RTS K times and takes the average of overall accuracy (OA) with respect to standard deviation (SD) to describe a confidence level of classification performance. To deal with this issue this paper develops an iterative random training sampling (IRTS) method as an alternative to the K-fold method to reduce the uncertainty caused by RTS. Its idea is to add the spatial filter-ed classification maps to the current being processed image cube via feedback loops to augment image cubes iteratively. Then, the training samples will be re-selected randomly from the new augmented image cubes iteration-by-iteration. As a result, the training samples selected from each iteration will be updated by new added spatial information captured by spatial filters implemented at the iteration. The experimental results clearly demonstrate that IRTS successfully improves classification accuracy as well as reduce inconsistency in results.

Band clustering has been widely used for hyperspectral band selection (BS). However, selecting an appropriate band to represent a band cluster is a key issue. Density peak clustering (DPC) provides an effective means for this purpose, referred to as DPC-based BS (DPC-BS). It uses two indicators, cluster density and cluster distance, to rank all bands for BS. This paper reinterprets cluster density and cluster distance as band local density (BLD) and band distance (BD) and also introduces a new concept called band prominence value (BPV) as a third indicator. Combining BLD and BD with BPV derives new band prioritization criteria for BS, which can extend the currently used DPC-BS to a new DPC-BS method referred to as band density prominence clustering (BDPC). By taking advantage of the three key indicators of BDPC, i.e., cut-off band distance b_c, k nearest neighboring-band local density, and BPV, two versions of BDPC can be derived called b_c-BDPC and k-BDPC, both of which are quite different from existing DPC-based BS methods in three aspects. One is that the parameter b_c of b_c-BDPC and the parameter k of k-BDPC can be automatically determined by the number of clusters and virtual dimensionality (VD), respectively. Another is that instead of using Euclidean distance, a spectral discrimination measure is used to calculate BD as well as inter-band correlation. The most important and significant aspect is a novel idea that combines BPV with BLD and BD to derive new band prioritization criteria for BS. Extensive experiments demonstrate that BDPC generally performs better than DPC-BS as well as many current state-of-the art BS methods.

Constrained energy minimization (CEM) has been extended to several generalized versions, iterative CEM (ICEM), Nystrom method-based kernel CEM (NKCEM), and iterative training sampling-based NKCEM (ITS-NKCEM) for hyperspectral image classification (HSIC). Since CEM is a subpixel target detector that specifies a target signature to detect its target abundance fractions present in data samples, this article takes the advantage of CEM’s ability in subpixel detection to consider NKCEM as a nonlinear mixed pixel classifier for hyperspectral mixed pixel classification (HMPC). Recently, a new concept of band sampling (BSam) was proposed by utilizing random signal sampling derived from compressive sensing (CS) to show its performance better than band selection (BSel) for HSIC. Thus, incorporating BSam into NKCEM and ITS-NKCEM yields two new versions for HPMC, called band sampling NKCEM (BSam-NKCEM) and band sampling ITS-NKCEM (BSam-ITS-NKCEM). Interestingly, despite that BSam-ITS-NKCEM uses sampled bands as well as training samples, extensive experiments demonstrate that it can perform better than all other CEM and KCEM versions using full bands and ground truth. Specifically, it also shows that BSam-ITS-NKCEM can do better than spectral–spatial HSIC techniques using BSel.