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• A precise crop classification method of UAV hyperspectral imagery is proposed. • KTSSCC can retain the spectral and spatial information while improving the linear separability. • The KTSSOMP algorithm adaptively learns the sparse coding coefficients of KTSSCC. • There are very few parameters in our proposed KTSSCC model. Precise crop classification plays a significant role in the agriculture field. An appropriate data source for precise crop classification is high spatial resolutions hyperspectral imagery (H2 imagery) acquired by unmanned aerial vehicle (UAV). However, for imagery with many different classes of crops, crop classification of UAV H2 imagery is a huge challenge. The significant spectral diversity, spatial heterogeneity and nonlinear data structure of UAV H2 imagery results in poor spectral discriminability. To improve the discriminability, a kernel tensor slice sparse coding-based classifier (KTSSCC) is proposed for precise crop classification of UAV H2 imagery in this research. The kernel tensor representation mechanism in KTSSCC can reduce the nonlinear separation while well preserving the spectral characteristics and spatial constraints of land-covers, and thus the discriminability is greatly improved. Furthermore, this paper puts forward the kernel tensor slice sparse orthogonal matching pursuit (KTSSOMP) algorithm to optimize kernel tensor slice sparse coding in the spectral space, which greatly reduces the computation cost. Moreover, there are very few parameters to be tuned in our proposed model. We assess the performance of KTSSCC on two real UAV hyperspectral imagery datasets, and find that, based on visual and quantitative results, it provides satisfactory crop classification results and outperforms the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]