**6. Conclusions**

This paper developed an SMMBS method, called LCMV-BSS, which selects multiple bands as a band subset using LCMV to linearly constrain class signature vectors as a criterion to select an optimal band subset. It is completely different from existing BS methods, with the following contributions: (i) It is a BSS method particularly developed for HSIC; (ii) It is quite different from single band-constrained methods in [26] and multiple-band constrained methods in [68], by constraining multiple class signature vectors instead of multiple bands; (iii) It develops three numerical search algorithms to find optimal band subsets which are different from the graph-based approaches [40,43] used by other SMMBS methods; (iv) It is very simple to implement via (7) with no parameters needing to be tuned; (v) Most importantly, it shows that HSIC can be improved by BS provided that the number *n*BS of selected bands and the set of *n*BS bands are properly selected.

**Acknowledgments:** The work of C.Y. is supported by National Nature Science Foundation of Liaoning Province (20170540095). The work of M.S. is supported by National Nature Science Foundation of China (61601077) and State Key Laboratory of Integrated Services Networks. The work of C.-I.C. is supported by the Fundamental Research Funds for Central Universities under Grant 3132016331. The authors would like to thank Xiaoqiang Lu for helping run the MDPP method with the same parameters used in [43] and the authors of ref. [40] for providing their software to run DSEBS.

**Author Contributions:** C.Y. and M.S. conceived and designed the experiments; C.Y. performed the experiments; C.Y. and C.-I.C. analyzed the data; C.Y. and M.S. contributed reagents/materials/analysis tools; C.-I.C. wrote the paper.

**Conflicts of Interest:** All authors have declared no conflict of interest.
