The classification effect of hyperspectral remote sensing images is greatly affected by the problem of dimensionality. Feature extraction, as a common dimension reduction method, can make up for the deficiency of the classification of hyperspectral remote sensing images. However, different feature extraction methods and classification methods adapt to different conditions and lack comprehensive comparative analysis. Therefore, principal component analysis (PCA), linear discriminant analysis (LDA), and locality preserving projections (LPP) were selected to reduce the dimensionality of hyperspectral remote sensing images, and subsequently, support vector machine (SVM), random forest (RF), and the k-nearest neighbor (KNN) were used to classify the output images, respectively. In the experiment, two hyperspectral remote sensing data groups were used to evaluate the nine combination methods. The experimental results show that the classification effect of the combination method when applying principal component analysis and support vector machine is better than the other eight combination methods.