*5.2. Salinas*

A second set of AVIRIS data used for experiments was the Salinas scene shown in Figure 2a, which was captured by the AVIRIS sensor over Salinas Valley, California, with a spatial resolution of 3.7 m per pixel and spectral resolution of 10 nm. It has a size of 512 × 217 × 224. Figure 2b,c show the color composite of the Salinas image along with the corresponding ground truth class labels.

**Figure 2.** Ground truth of Salinas scene with 16 classes. (**a**) Band 126, (**b**) color ground-truth image, (**c**) class labels.

## *5.3. ROSIS Data*

The last hyperspectral image data used for experiments was the University of Pavia image shown in Figure 3, which is an urban area surrounding the University of Pavia, Italy. It was recorded using the ROSIS-03 satellite sensor. It is of size 610 × 340 × 115 with a spatial resolution of 1.3 m per pixel and spectral coverage ranging from 0.43 to 0.86 μm with spectral resolution of 4 nm (the 12 most noisy channels were removed before experiments). Nine classes of interest, plus a background (BKG) class (class 0), were considered for this image.

**Figure 3.** Ground truth of University of Pavia scene with nine classes. (**a**) Band 95, (**b**) color ground truth image, (**c**) class labels.

In the following experiments, four types of BS methods were tested for a comparative study and analysis.


As noted in the introduction and in Section 3, although PSO, FA, and MTSP are also SMMBS methods, they are not compared in this paper for the following reasons. One is that their design rationale is completely different from that of LCMV-BSS. Secondly, the initial candidate sets from which their search algorithms find an optimal band subset are random and are also too small. So, their results are not representative and also are not reproducible. Thirdly, the details of their used parameters were not specified and provided in their papers. Therefore, it is very difficult to implement their algorithms for fair comparisons.

Table 1 tabulates the number *n*BS of selected bands estimated for three scenes using Harsanyi-Farrand-Chang (HFC) method/noise whitened HFC (NWHFC method developed for VD in [69,74,75] where *n*BS was determined to be *n*BS = 18 for Purdue's data, 21 for Salinas and 14 for University of Pavia with a false alarm probability of 10−4.


**Table 1.** *n*BS estimated by HySime and HFC/NWHFC.

Table 2 lists the bands selected by seven BS methods—uniform BS (UBS), minimum estimated abundance covariance (MEAC), multigraph determinantal point process (MDPP), dominant set extraction BS (DSEBS), SQ LCMV-BSS-1, SQ LCMV-BSS-2, and SC LCMV-BSS—for the three scenes; *n*BS = 18 for Purdue's Indian Pines, *n*BS = 21 for Salinas, and *n*BS = 14 for University of Pavia.

> **Table 2.** Bands selected by UBS, SQ LCMV-BSS-1, SQ LCMV-BSS-2, SC LCMV-BSS.


In order to perform HSIC, choosing an appropriate classifier is crucial. Recently, Yu et al. [76] developed a new classifier, called the iterative multiclass constrained background suppression classifier (IMCBSC), and further demonstrated that IMCBSC performed well in both overal accuarcy rate (POA) and precision rate (PR) Since IMCBSC was also derived from LCMV and implemented by LCMV in an iterative manner, the iterative linearly constrained minimum variance (ILCMV) is used in this paper instead of IMCBSC to reflect its idea arising from LCMV and its iterative nature in algorithm implementation. Most importantly, ILCMV was adopted for two main reasons. One is because of the work in [76], which showed that ILCMV could perform at least comparably in POA but significantly better than the work in [12]. The other is that ILCMV is indeed derived from the LCMV criterion specified by (2). So, it is natural to use ILCMV to perform classification.

Two remarks on the implementation of ILCMV are noteworthy.


Figure 4c–i, Figures 5c–i and 6c–i show classification maps produced by ILCMV, using bands selected in Table 2 by seven BS methods—UBS, MEAC, MDPP, DSEBS, SQ LCMV-BSS-1, SQ LCMV-BSS-2, and SC LCMV-BSS, respectively—where the ground truth map and classification map produced by the full bands are also included in (a) and (b), respectively, for comparison.

**Figure 4.** Classification maps produced by iterative LCMV (ILCMV) for Purdue's data using bands selected in Table 2. (**a**) Ground truth, (**b**) Full bands, (**c**) UBS, (**d**) MEAC, (**e**) MDPP, (**f**) DSEBS, (**g**) SQ LCMV-BSS-1, (**h**) SQ LCMV-BSS-2, (**i**) SC LCMV-BSS.

**Figure 5.** Classification maps produced by ILCMV for Salinas using bands selected in Table 2. (**a**) Ground truth, (**b**) Full bands, (**c**) UBS, (**d**) MEAC, (**e**) MDPP, (**f**) DSEBS, (**g**) SQ LCMV-BSS-1, (**h**) SQ LCMV-BSS-2, (**i**) SC LCMV-BSS.

**Figure 6.** Classification maps produced by ILCMV for Pavia using bands selected in Table 2. (**a**) Ground truth, (**b**) Full bands, (**c**) UBS, (**d**) MEAC, (**e**) MDPP, (**f**) DSEBS, (**g**) SQ LCMV-BSS-1, (**h**) SQ LCMV-BSS-2, (**i**) SC LCMV-BSS.

Apparently, it is difficult to see any appreciable difference among all the classification results in Figures 4–6 by visual inspection. In this case, to better evaluate each BS method, conducting a quantitative analysis is necessary. It has been shown in [23,76] that using overall accuracy (OA), POA may not be sufficient to evaluate the effectiveness of classification performance. To address this issue, two additional measures, called precision rate, PR, and detection rate, PD (also known as recall rate), developed in [23,76] were introduced for HSIC where PR and PD have been widely used in pattern recognition such as medical imaging, handwritten character recognition, and biometric recognition. The definitions and details of POA, PR, and PD can be found in [23,76].

Tables 3–5 show PD, POA, and PR calculated by the ILCMV classification results in Figures 4–6 using the bands selected in Table 2 for Purdue's data, Salinas, and University of Pavia, respectively, where the best results with highest rates are shown in boldface. Here, we would like to point out a crucial fact used in the experiments, as noted in the second remark described above, where the PD, POA, and PR were calculated by including the background (BKG) for classification because LCMV is particularly designed to take care of the BKG issue in classification, as shown in [76]. This is quite different from many reports which calculate POA excluding BKG from classification, such as [12].

Since PD varies with each class, it is difficult to evaluate the overall classification performance. So, our analysis is conducted based on POA and PR. As we can see from the tables, SQ LCMV-BSS-2 and SC LCMV-BSS outperformed all the other five BS methods in terms of POA and PR for Salinas and University of Pavia scenes, but were slightly worse than MDPP in POA and DSEBS in PR. Interestingly, both MDPP and DSEBS produced the best results in terms of POA and PR respectively for the Purdue data. As also noted in Tables 3–5, the POA and PR using full bands were generally not as good as those produced by most of the test BS methods, but also worse than that produced by UBS. These experiments showed that hyperspectral image classification can benefit greatly from the judicious selection of bands with appropriately determined *n*BS.


**Table 3.** PD, POA, and PR calculated from the classification results in Figure 4 for Purdue's data.

**Table 4.** PD, POA, and PR calculated from the classification results in Figure 5 for Salinas.


**Table 5.** PD, POA, and PR calculated from the classification results in Figure 6 for University of Pavia.


Table 6 tabulates the computing times in seconds for each of six BS methods in a computer environment with a 1.6 GHz Intel Core i5 with OS X EI Capitan and 4 GB 1600 MHz DDR3; the software used to run experiments was Matlab\_R2014b. Obviously, the best time was achieved by DSEBS, followed by SC LCMV-BSS and SQ LCMV-BSS. The worst time was achieved by MDPP for the Purdue data and MEAC for Salinas and University of Pavia.


**Table 6.** Computing time in seconds required by six test BS methods: MEAC, MDPP, DSEBS, SQ LCMV-BSS-1, SQ LCMV-BSS-2, SC LCMV-BSS.

As noted above, a classifier can also have a significant impact on BS, especially when BKG is included for consideration. A recent work [12] developed four edge preserving filtering (EPF)-based techniques—EPF-B-c, EPF-G-c, EPF-B-g, and EPF-G-g for HSIC—and also conducted a comprehensive comparative analysis to show that their methods indeed performed better than most recently developed spectral–spatial techniques. Therefore, in what follows, we conducted experiments to evaluate the performance of ILCMV in comparison with these four EPF-based techniques with BKG particularly included for classification. To see this, we also implemented these four EPF-based techniques with "B" and "G" used to specify bilateral filter and guided filter, respectively, and "g" and "c" indicate that the first principal component and color composite of the three principal components are used as reference images [12].

Tables 7–15 tabulate the results in terms of POA and PR rates produced by the four EFP-based methods and ILCMV, all of which included BKG for classification and also used the bands selected in Table 2 to implement the three image scenes. Data for the Purdue image is shown in Tables 7–9 using bands selected by SQ LCMV-BSS-1, SQ LCMV-BSS-2, and SC LCMV-BSS; data for Salinas is shown in Tables 10–12 using bands selected by SQ LCMV-BSS-1, SQ LCMV-BSS-2, and SC LCMV-BSS; and data for University of Pavia is shown in Tables 13–15 using bands selected by SQ LCMV-BSS-1, SQ LCMV-BSS-2, and SC LCMV-BSS. In addition, their computing times in seconds are included in the tables for comparison.


**Table 7.** POA and PR calculated by the classification results using the bands selected by SQ LCMV-BSS-1 for the Purdue data.


**Table 8.** POA and PR calculated by the classification results using full bands and the bands selected by SQ LCMV-BSS-2 for the Purdue data.

PR 45.52 44.93 44.89 44.34 97.61 39.72 39.61 39.00 37.85 97.80 Time(s) 194.14 199.37 194.13 200.36 25.37 31.16 37.93 32.56 36.51 41.58












**Table 15.** POA and PR calculated by the classification results using full bands and the bands selected by SC LCMV-BSS in Table 2 for University of Pavia.


Several interesting findings can be derived from the results in Tables 7–15.

