*Remote Sens.* **2017**,

 *9*, 884

In the unsupervised manner, the dimension of the signal subspace was firstly estimated as nine using the HySime algorithm. Then, according to the proposed method, a spectral library was established from the spectral variability of each class, regardless of the ground truth map. In order to evaluate the spectral similarity of the endmembers obtained with the spectrum of each class from the ground truth map, the average spectra of the two sets was compared with the spectral information divergence (SID) [39] similarity measure. The results obtained are provided in Table 5. The lower the value of SID, the more similar the two spectra will be. According to the results, the corn class was split into three sub-classes. However, the spectrum of the other classes was estimated properly.

The estimated fractional abundances using the 61 selected bands by the proposed ISI-PS algorithm (Table 4) and the FCLS method are illustrated in Figure 18. As can been seen, the corn class was split into three sub-classes, as in Figure 18a,h,i. The fractional abundances of the bare soil and the wheat classes (i.e., Figure 18c,d, respectively) were partially overlaid, which was due the harvesting of wheat and the appearance of the background soil of the farms. It is worth mentioning that this issue had mostly occurred in farms with a lesser vegetation density due to the type of irrigation and fertilization. This could be obviously understood by the comparison of the obtained results and Figure 7.

**Figure 18.** The estimated fractions using the selected bands by the ISI-PS method in an unsupervised manner for: (**a**) Corn; (**b**) Alfalfa; (**c**) Bare soil; (**d**) Wheat; (**e**) Native grass; (**f**) Tomato; (**g**) Weather station; (**h**) Corn; and (**i**) Corn.


**Table 5.** Similarity values among the extracted endmembers and the reference spectral signatures of each endmembers by spectral information divergence (SID).

> Bold number is the minimum SID in each column.

All of the pre-mentioned process for the LTRAS dataset was performed on the Salinas and Indiana Indian Pines datasets as well (Table 4).

In this table, in order to evaluate the accuracy of the proposed method when no in situ data were available, the results have been provided for the supervised and the unsupervised manners. In the unsupervised approach, the endmember sets were extracted from the image without any prior knowledge. In this regard, using the position of the pure pixels obtained, a fractional map with a 100 percent abundance was first generated for each endmember to compute the threshold value. Then, the fractional abundances of the endmembers were estimated using the extracted endmembers and the different bands obtained from different threshold values. Finally, the threshold value that led to the minimum RMSE of the estimation of the fractional abundances of endmembers was selected as the optimal threshold value.

In order to compare the results obtained from the supervised and the unsupervised approaches, the estimated fractional maps using the FCLS method over the Salinas dataset are illustrated in Figures 19 and 20. As can be seen, the results of the unsupervised approach were compatible with the supervised approach, and the proposed method was able to separate the similar spectral classes. However, due to the similar spectral behaviors in the endmember extraction step, the two classes grapes\_untrained and vineyard\_untrained were considered as unique classes.

In this section, a comparison is made between the computational times of different methods and is reported in Table 6. All of the methods were executed on a PC with an i7 5820k CPU and 32 GB of RAM.


**Table 6.** Computational times of unmixing using full bands and reduced bands from different band selection methods.

As can be seen, ISI-PS showed disadvantages from the computational time point of view. This was mainly due to the exhaustive search, which was applied to locate an optimum value for threshold *T* (see Section 3.4). We had chosen a rather vast domain of T for the sake of a richer evaluation. However, the processing time of ISI-PS can be highly improved by a more exact estimation of the search domain for *T*. In addition, more advanced search strategies—instead of the exhaustive search applied herein—can be of grea<sup>t</sup> help to mitigate the computational costs of ISI-PS, which is suggested for further study.
