The classification of hyperspectral images with a paucity of labeled samples is a challenging task. This paper describes the use of a superpose probability matrix and weight matrix of an L1 graph, thereby forming a strong discriminating DL1 graph. Combining the local information of the space with the global information of the spectrum through the superposition of a KNN graph and a DL1 graph, a graph-based framework is built that combines the spatial and spectral information. This framework of a DL1KNN graph can reflect the more sophisticated structure of hyperspectral image data. Experimental results show that the improvement in classification accuracy is significant when the percentage of labeled samples is 5% through the use of the label propagation of the graph to achieve semi-supervised classification for improving the automatic classification accuracy of hyperspectral data with a small number of samples.
国家自然科学基金(61461002)
宁夏自然科学基金(NZ15105)
北方民族大学校级科研项目(JSKY06)
北方民族大学研究生创新项目(YCX1657)
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Figure 1
(a) Pseudo color image and (b) four kinds of vegetation of the sub scene of AVIRIS Indiana Pines
Figure 2
The overall classification accuracy comparison chart
Figure 3
Classification accuracies of sub scene of Indiana Pines, the percentage of labeled samples is 5%, $k$=5. (a) L1 graph; (b) DL1 graph; (c) L1KNN graph; (d) DL1KNN graph
Figure 4
Classification accuracies of sub scene of Indiana Pines, the percentage of labeled samples is 25%, $k$=5. (a) L1 graph; (b) DL1 graph; (c) L1KNN graph; (d) DL1KNN graph
Figure 5
Confusion matrix of sub scene of Indiana Pines, the percentage of labeled samples is 25%, $k$=5. class1: Corn-notill, class2: Grass-trees, class3: Soybean-notill, class4: Soybean-mintill. (a) L1 graph; (b) DL1 graph; (c) L1KNN graph; (d) DL1KNN graph
Figure 6
(Color online) Overall accuracy and Kappa factor of Indiana Pines sub scene when percentage of labeled samples is 25%, $k=5$
Figure 7
(Color online) Accuracy per class of Indiana Pines sub scene when percentage of labeled samples is 25%, $k=5$
Figure 8
(Color online) Omission of Indiana Pines sub scene when percentage of labeled samples is 25%, $k=5$
Figure 9
(Color online) The curve graph of classification accuracy (%) with varying scale coefficient of graph under different percentages of labeled samples
| Indiana Pines (%) | L1图 | DL1图 | L1KNN图 | DL1KNN图 | |||||||||||
| $k=5$ | $k=8$ | $k=10$ | Average | $k=5$ | $k=8$ | $k=10$ | Average | ||||||||
| 5 | 0.792 | 0.891 | 0.883 | 0.818 | 0.876 | 0.906 | |||||||||
| 10 | 0.887 | 0.909 | 0.873 | 0.881 | 0.910 | 0.880 | |||||||||
| 15 | 0.932 | 0.904 | 0.898 | 0.913 | 0.909 | 0.918 | |||||||||
| 20 | 0.931 | 0.924 | 0.918 | 0.931 | 0.923 | 0.928 | |||||||||
| 25 | 0.939 | 0.916 | 0.923 | 0.948 | 0.920 | 0.923 | |||||||||
输入高光谱图像, 其中$l$个标记样本$X_l=[x_1,x_2,\ldots,x_l]$, $u$个无标记样本$X_u=[x_{l+1},x_{l+2},\ldots,x_{l+u}]$, 初始的标记矩阵$Y_l\in~\mathbb{R}^{l~\times~c}$; |
预处理样本: 归一化样本$x_i=x_i/\Vert~{x_i}~\Vert_2$, 去掉样本$x_i$得到预处理样本$X=[x_1,x_2,\ldots,x_{i-1},x_{i+1},\ldots,x_n]$; |
通过式(2)得到L1范数图权值矩阵$W_{{\rm~L}1}=\{W_{ij}\}_{n\times~n}$; |
通过式(4)和(5)得到类概率矩阵$\{P_{ij}\}_{n\times~n}$; |
根据式(6)获得DL1图的权值矩阵$W_{(\rm~DL1)}$; |
通过式(7)得到K近邻矩阵$K=\{K_{ij}\}_{n~\times~n}$; |
通过式(8)将DL1图和KNN图叠加得到叠加矩阵$W_3$, 根据实验设置$\beta$的值为0.2; |
输出叠加图$G_3=(X,W_3~)$. |
| $\beta$ (%) | 0 | 0.1 | 0.2 | 0.25 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1 | 10 | 100 |
| 5 | 74.4 | 84.4 | 85.5 | 84.9 | 85.3 | 85.2 | 83.2 | 82.4 | 82.8 | 83.2 | 84.4 | 83.0 | 80.5 | |
| 10 | 87.3 | 86.3 | 88.4 | 87.0 | 86.6 | 84.9 | 83.0 | 82.7 | 82.6 | 82.4 | 82.5 | 84.9 | 84.2 | |
| 15 | 86.8 | 88.8 | 88.8 | 88.0 | 88.9 | 86.8 | 85.1 | 84.1 | 84.2 | 83.5 | 83.8 | 81.9 | 83.3 | |
| 20 | 87.1 | 90.6 | 90.6 | 90.9 | 89.7 | 89.5 | 88.1 | 87.2 | 87.9 | 87.6 | 87.9 | 90.6 | 91.7 | |
| 25 | 88.0 | 89.0 | 93.0 | 90.0 | 88.0 | 89.0 | 88.5 | 88.7 | 87.0 | 87.5 | 86.7 | 92.3 | 89.3 |
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