Hyperspectral remote image sensing is a rapidly developing integrated technology used widely in numerous areas. The rich spectral information from hyperspectral images aids in recognition and classification of many types of objects, but the high dimensionality of these images leads to information redundancy. In this paper, we used sensitivity analysis for dimension reduction. However, another challenge is that hyperspectral images identify objects as either a "different body with the same spectrum" or "same body with a different spectrum." Therefore, it is difficult to maintain the correct correspondence between ground objects and samples, which hinders classification of the images. This issue can be addressed using multi-instance learning for classification. In our proposed method, we combined neural network sensitivity analysis with a multi-instance learning algorithm based on a support vector machine to achieve dimension reduction and accurate classification for hyperspectral images. Experimental results demonstrated that our method provided strong overall classification effectiveness when compared with prior methods.