**4. Conclusions**

In this paper, we proposed a hierarchical feature extraction method for HSI classification. The proposed method is inspired by the promising performance of multiple features fusion. We hold the opinion that further utilization for the multiple features will contribute to the classification accuracy, and this idea is similar to that of deep learning methods. Therefore, instead of data dimension reduction or direct ensembling, in H2F, we propose a hierarchical feature extraction strategy based on hashing, which attempts to explore the deep distinctive information among the original HSI data. Spectral as well as local and global spatial features are firstly extracted, and these low-level features are further represented in a very sparse manner.

We compare H2F with some ensemble based or deep learning based methods in the experimental part. Although the advantages are not apparent, a paired t-test has confirmed that our improvements are statistically significant. In particular, the idea of extracting hierarchical information from basic features may work as an inspiration for the further research.

In our future works, we will focus on improving the computational efficiency of the hierarchical feature extraction process. Meanwhile, the relationships among different features should also be investigated.

**Acknowledgments:** The authors would like to thank Telops Inc. (Que´bec, Canada) for acquiring and providing the data used in this study, the IEEE GRSS Image Analysis and Data Fusion Technical Committee and Michal Shimoni (Signal and Image Centre, Royal Military Academy, Belgium) for organizing the 2014 Data Fusion Contest, the Centre de Recherche Public Gabriel Lippmann (CRPGL, Luxembourg) and Martin Schlerf (CRPGL) for their contribution of the Hyper-Cam LWIR sensor, and Michaela De Martino (University of Genoa, Italy) for her contribution to data preparation. The work was supported by the National Natural Science Foundation of China under the Grant 61671037, and the Beijing Natural Science Foundation under the Grant 4152031, and the Excellence Foundation of BUAA for PhD Students under Grant 2017057.

**Author Contributions:** Bin Pan and Zhenwei Shi designed the algorithm; Xia Xu designed and performed the experiments; Yi Yang contributed to the English expression of this paper; Bin Pan wrote the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
