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Providing the kernel function of the local tangent space alignment (LTSA) algorithm, the generalisation of both LTSA and supervised LTSA (SLTSA) is achieved. Moreover, using the generalised SLTSA (GSLTSA), a simplified classification algorithm is proposed for hyperspectral image data. Experimental results demonstrate, that the generalisation method has good performance, and the GSLTSA is capable of exploiting the nonlinear properties of hyperspectral data to benefit the classification.