High-precision hyperspectral image classification when the number of samples is small is the focus of research in the field of hyperspectrum. At present, there are few studies on the effect of different training set samples on classification accuracy. To determine the effect of different training set samples on the classification accuracy of a hyperspectral image, the hyperspectral image of an Indian Pines farm is used as the data source. In this work, we study the classification accuracy results of support vector machine (SVM) and back propagation (BP) neural network when the training set samples are 1, 2, 5, 10, and 20%. Simulation results show that the overall accuracy (OA), average accuracy (AA), and Kappa coefficients of SVM and BP increase continuously with the number of samples in the training set. Under different numbers of training set samples, the classification accuracy of BP is greater than that of SVM. When the number of samples in the training set is 20%, the recognition accuracy of the BP classification method for seven features (Grass-pasture, Grass-trees, Hay-windrowed, Oats, Wheat, Woods, and Stone-Steel-Towers) is higher than 90%, and the recognition accuracy of Hay-windrowed features is 93.97%.

The fractional derivative has the advantages in terms of memory and globality, and it can overcome the shortcomings of the traditional integer differential algorithm. Moreover, the absorption characteristics of available phosphorus in soil in visible near-infrared bands are unclear, and the prediction model has a low precision. In this paper, we propose a novel method to improve the accuracy of the prediction model for available phosphorus content, which is based on the fractional derivative and stepwise multiple linear regression (SMLR). First, the relationship between the soil spectrum and the available phosphorus content under different fractional orders was studied. Secondly, spectrum dimensionality reduction based on sensitive bands was performed. Finally, the SMLR model was adopted to quantitatively predict the available phosphorus content, and the precision of different fractional order models was discussed. Simulation results revealed that the fractional derivative can describe the small differences in spectral data and increase the correlation between the soil spectrum and the available phosphorus content. The 1.4th-order model is the optimum fractional model. Thus, these results indicate that the fractional derivative could improve the accuracy of the estimation model for available phosphorus content.