# Classification of Hyperspectral Images Based on Supervised Sparse Embedded Preserving Projection
## 4 Experimental Results and Analysis
### Indian Pines Dataset  
The Indian Pines dataset [18] was used in the first experiment. The image had \(145\times 145\) pixels and its spatial resolution was \(20\) m. The image had a total of \(220\) spectral bands, of which \(20\) bands were more affected by water absorption and were removed before the experiment [19]. The remaining \(200\) bands were used for experiments. The wavelength range was between \(0.4\) and \(2.5\) um. In the entire HSI image, there was a total of \(10249\) pixels with label information. There were \(16\) sample ground truth classes, of which \(10\%\) were used as training samples and the rest were used for testing. Table 1 lists the classes and the number of their training samples. In the Indian Pines HSI dataset experiment, the dimensions of different dimensionality reduction algorithms were uniformly set to 30 dimensions. Then, the nearest neighbor classifier (1-NN) was used for classification, that is, \(K\) was set to 1. The SPGL1 algorithm was used to solve the sparse reconstruction coefficients. In order to obtain better performance, the sparse reconstruction error value \(\zeta\) was set to 0.9. Figure 1 showed a comparison of the classification results of the Indian Pines. Figure 1a showed the false color image of Indian pines, Figure 1b showed the ground truth, Figure 1c showed the sparsity preserving projection (SPP), Figure 1d showed the principal component analysis (PCA), Figure 1e showed the sparse discriminant embedding, and Figure 1f showed the supervised sparse embedding preserving projection (SSEPP). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**\#** & **Class** & **Samples** & **Color (R,G,B)** \\ \hline C1 & Alfalfa & 46 & 255,254,137 \\ C2 & Corn-notill & 1428 & \\ C3 & Corn-min & 830 & 255,891 \\ C4 & Corn & 237 & 5,255,133 \\ C5 & Grass/pasture & 483 & 255,251 \\ C6 & Grass/trees & 730 & \\ C7 & Grass/pasture-mowed & 28 & 3,171,255 \\ C8 & Hay-windowed & 478 & 12,255,7 \\ C9 & Oats & 20 & 172,175,84 \\ C10 & Soybean-notill & 972 & 160,78158 \\ C11 & Soybean-min & 2455 & 101,173,255 \\ C12 & Soybean-clean & 593 & 60,911,12 \\ C13 & Wheat & 205 & 104,192,63 \\ C14 & Woods & 1265 & 169,696 \\ C15 & Bldg-Grass-Trees-Drives & 386 & 119,255,172 \\ C16 & Stone-Steel towers & 93 & 254,255,3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Information about the Indian Pines dataset. Figure 1: (**a**) False color image of Indian Pines; (**b**) ground truth; (**c**) sparsity preserving projection (SPP); (**d**) principal component analysis (PCA); (**e**) sparse discriminant embedding (SDE); and (**f**) supervised sparse embedding preserving projection (SSEPP). Figure 1 showed that the SSEPP algorithm is better than the SPP, PCA, and SDE comparison algorithms. SSEPP had the least misclassification and leakage, and was the closest to the ground truth image of the Indian Pines. The SPP algorithm had the worst classification result because SPP is an unsupervised algorithm. SSEPP and SDE are both supervised algorithms, which means that they can introduce sample label information to enhance their discrimination ability, thus improving the classification accuracy. In addition, compared to the SDE algorithm, according to the similarity of the samples, SSEPP constructed a similarity matrix that assigned different weights to samples of the same class; it therefore enhanced the natural discrimination ability of sparse representation. In order to improve classification accuracy of the Indian Pines dataset, it also constructed multi-objective optimization based on the original objective function that minimized both the sparse reconstruction error and same class sample spacing. As shown in Table 2 and Figure 2, the difference in feature dimensions directly led to different levels of classification accuracy of hyperspectral remote sensing images. With the increase in feature dimensions, the overall accuracy showed an upward trend, and when dimensions reached about 30, the trend was stable.