Hyperspectral Image Classification Based on Two-Stage Subspace Projection
Abstract
:1. Introduction
- (1)
- The discrimination information is utilized to compute the samples’ kernel distances from a k-nearest neighborhood in the subspace, so the local structure of the original HSI data can be captured adaptively.
- (2)
- The proposed TwoSP framework is an effective way for supervised HSI classification by combining the existing KPCA and the proposed DLPP methods, which not only extracts the nonlinear feature, but also exploits the discrimination information to preserve both global and local structures of the original HSI data. In an optimal low-dimensional subspace, the classification boundary can be found for the HSI data.
2. Kernel Principal Component Analysis
3. Discrimination-Information-Based Locality Preserving Projection
4. The Proposed Framework
Algorithm 1: The Proposed Framework for HSI classification. |
First-Stage Subspace Projection:
Second-Stage Subspace Projection:
Classification: fordo
end Result: Obtain the class estimation for all the test samples, i.e., . |
5. Experimental Results
5.1. Experimental Setting
5.2. Performance on Hyperspectral Image Datasets
5.3. Discussion on Computational Cost
5.4. Performance of Reduced Dimensionality
5.5. Analysis of Classifier
5.6. Analysis of Parameters
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Indian Pines | KSC | ||||||
---|---|---|---|---|---|---|---|
Class No. | Land Cover | Training | Test | Class No. | Land Cover | Training | Test |
1 | Alfalfa | 3 | 43 | 1 | Scurb | 39 | 722 |
2 | Corn-notill | 72 | 1356 | 2 | Willow-swamp | 13 | 230 |
3 | Corn-mintill | 42 | 788 | 3 | Cabbage-palm-hammock | 13 | 243 |
4 | Corn | 12 | 225 | 4 | Cabbage-palm/oak-hammock | 13 | 239 |
5 | Grass-pasture | 25 | 458 | 5 | Slash-pine | 9 | 152 |
6 | Grass-tree | 37 | 693 | 6 | Oak/broadleaf-hammock | 12 | 217 |
7 | Grass-pasture-mowed | 2 | 26 | 7 | Hardwood-swamp | 6 | 99 |
8 | Hay-windrowed | 24 | 454 | 8 | Graminoid-marsh | 22 | 409 |
9 | Oats | 1 | 19 | 9 | Spartina-marsh | 26 | 494 |
10 | Soybeans-notill | 49 | 923 | 10 | Cattail-marsh | 21 | 383 |
11 | Soybeans-mintill | 123 | 2332 | 11 | Salt-marsh | 21 | 398 |
12 | Soybeans-clean | 30 | 563 | 12 | Mud-flats | 26 | 477 |
13 | Wheat | 11 | 194 | 13 | Water | 47 | 880 |
14 | Woods | 64 | 1201 | ||||
15 | Bldg-grass-tree-drives | 20 | 366 | ||||
16 | Stone-steel-towers | 5 | 88 | ||||
Total | 520 | 9729 | Total | 268 | 4943 |
Class No. | RAW (200) | PCA (17) | ICA (17) | LDA (11) | KDA (16) | KPCA (40) | DLPP (14) | TwoSP (20) |
---|---|---|---|---|---|---|---|---|
1 | 40.0 ± 12.6 | 42.3 ± 20.6 | 41.4 ± 22.2 | 42.8 ± 17.8 | 45.1 ± 11.2 | 43.3 ± 23.5 | 49.3 ± 15.7 | 31.6 ± 12.2 |
2 | 48.1 ± 1.2 | 49.3 ± 2.0 | 38.9 ± 4.1 | 57.0 ± 2.1 | 68.1 ± 3.6 | 39.5 ± 3.3 | 59.8 ± 3.1 | 67.0 ± 1.7 |
3 | 44.2 ± 2.4 | 44.0 ± 2.3 | 29.0 ± 3.2 | 42.6 ± 6.6 | 59.4 ± 3.4 | 29.9 ± 4.4 | 48.6 ± 5.4 | 56.1 ± 3.2 |
4 | 30.2 ± 6.3 | 28.2 ± 6.9 | 29.4 ± 5.6 | 27.9 ± 3.2 | 39.3 ± 5.0 | 29.9 ± 5.8 | 31.8 ± 5.3 | 40.1 ± 4.8 |
5 | 76.3 ± 5.1 | 75.9 ± 3.6 | 44.4 ± 3.2 | 83.6 ± 5.5 | 82.6 ± 2.9 | 47.8 ± 4.1 | 83.4 ± 3.3 | 84.1 ± 4.4 |
6 | 92.2 ± 1.9 | 92.4 ± 2.2 | 78.0 ± 4.5 | 91.2 ± 2.1 | 92.0 ± 2.5 | 78.8 ± 4.1 | 90.1 ± 2.5 | 92.3 ± 1.7 |
7 | 80.0 ± 10.0 | 79.2 ± 10.4 | 55.4 ± 15.5 | 76.2 ± 14.7 | 73.1 ± 12.5 | 59.2 ± 15.0 | 85.4 ± 9.2 | 82.3 ± 6.4 |
8 | 94.5 ± 2.3 | 94.9 ± 2.5 | 87.5 ± 2.9 | 96.0 ± 1.4 | 84.7 ± 1.8 | 87.1 ± 1.0 | 93.7 ± 2.8 | 89.3 ± 5.8 |
9 | 14.7 ± 10.8 | 14.7 ± 10.8 | 1.1 ± 2.4 | 12.6 ± 9.6 | 6.3 ± 6.9 | 2.1 ± 4.7 | 24.2 ± 13.2 | 30.5 ± 9.4 |
10 | 61.3 ± 6.5 | 62.2 ± 6.7 | 50.3 ± 6.1 | 46.8 ± 3.8 | 61.2 ± 3.0 | 51.3 ± 5.1 | 57.4 ± 2.9 | 69.1 ± 1.4 |
11 | 67.4 ± 3.4 | 67.4 ± 2.1 | 56.4 ± 2.4 | 64.8 ± 1.7 | 75.9 ± 2.8 | 57.6 ± 2.3 | 63.1 ± 1.1 | 74.8 ± 2.0 |
12 | 35.0 ± 2.6 | 34.6 ± 3.7 | 29.5 ± 1.9 | 46.8 ± 3.9 | 59.3 ± 8.0 | 29.6 ± 1.9 | 48.4 ± 4.9 | 56.0 ± 6.3 |
13 | 93.3 ± 1.5 | 93.2 ± 1.7 | 77.9 ± 6.7 | 92.6 ± 3.7 | 97.4 ± 1.0 | 78.6 ± 6.6 | 93.7 ± 5.0 | 96.4 ± 1.3 |
14 | 90.3 ± 2.9 | 89.3 ± 3.8 | 81.1 ± 3.0 | 93.4 ± 1.6 | 94.2 ± 1.1 | 81.6 ± 2.8 | 94.0 ± 2.0 | 95.2 ± 2.1 |
15 | 27.2 ± 2.0 | 27.3 ± 2.3 | 20.3 ± 3.2 | 44.6 ± 8.1 | 44.2 ± 3.3 | 20.9 ± 3.6 | 44.5 ± 7.7 | 46.7 ± 6.1 |
16 | 86.4 ± 3.0 | 86.4 ± 3.1 | 89.1 ± 4.9 | 79.8 ± 8.3 | 76.6 ± 9.9 | 80.9 ± 5.6 | 82.1 ± 6.0 | 86.4 ± 3.2 |
AA | 61.3 ± 1.4 | 61.3 ± 2.0 | 50.6 ± 1.9 | 62.4 ± 2.7 | 66.2 ± 1.5 | 51.1 ± 2.1 | 65.6 ± 0.8 | 68.6 ± 0.9 |
OA | 64.8 ± 1.0 | 64.9 ± 0.8 | 53.6 ± 1.0 | 65.8 ± 1.7 | 73.4 ± 0.9 | 54.4 ± 0.7 | 67.5 ± 0.9 | 73.9 ± 1.2 |
KC | 59.7 ± 1.1 | 59.8 ± 0.8 | 47.1 ± 1.1 | 60.8 ± 2.1 | 61.0 ± 18.4 | 48.0 ± 0.7 | 62.9 ± 1.0 | 70.1 ± 1.4 |
Class No. | RAW (176) | PCA (23) | ICA (8) | LDA (10) | KDA (10) | KPCA (87) | DLPP (41) | TwoSP (22) |
---|---|---|---|---|---|---|---|---|
1 | 87.7 ± 3.2 | 87.6 ± 3.2 | 60.9 ± 3.7 | 86.1 ± 4.2 | 66.9 ± 3.4 | 65.9 ± 5.7 | 82.4 ± 1.8 | 90.6 ± 2.3 |
2 | 75.7 ± 13.3 | 75.7 ± 13.2 | 50.9 ± 13.4 | 86.4 ± 1.9 | 58.2 ± 14.3 | 49.7 ± 12.7 | 87.8 ± 2.4 | 77.4 ± 2.0 |
3 | 66.7 ± 3.7 | 66.8 ± 3.8 | 26.2 ± 3.1 | 53.4 ± 7.1 | 27.7 ± 5.1 | 28.0 ± 4.6 | 55.3 ± 7.7 | 77.4 ± 3.5 |
4 | 50.0 ± 3.3 | 49.9 ± 3.0 | 24.4 ± 2.5 | 39.9 ± 4.5 | 26.0 ± 4.8 | 23.3 ± 3.7 | 39.3 ± 5.1 | 64.0 ± 4.2 |
5 | 45.8 ± 13.1 | 45.4 ± 12.9 | 29.3 ± 8.7 | 50.4 ± 4.7 | 33.6 ± 12.7 | 27.9 ± 11.2 | 51.3 ± 1.9 | 73.0 ± 1.8 |
6 | 34.2 ± 5.2 | 34.5 ± 5.1 | 23.8 ± 0.4 | 50.6 ± 8.2 | 22.8 ± 3.5 | 23.7 ± 5.5 | 52.9 ± 8.8 | 59.0 ± 7.5 |
7 | 64.0 ± 11.2 | 63.0 ± 10.3 | 23.0 ± 6.4 | 53.7 ± 13.0 | 23.6 ± 11.1 | 24.7 ± 7.4 | 47.3 ± 9.2 | 78.8 ± 9.5 |
8 | 69.4 ± 6.8 | 69.0 ± 7.4 | 42.4 ± 6.8 | 78.4 ± 4.4 | 46.0 ± 7.3 | 44.7 ± 7.7 | 77.7 ± 3.8 | 83.1 ± 3.5 |
9 | 88.5 ± 4.0 | 88.5 ± 4.0 | 67.4 ± 6.3 | 82.3 ± 3.2 | 67.7 ± 7.8 | 68.2 ± 5.7 | 80.7 ± 2.3 | 93.5 ± 2.6 |
10 | 81.1 ± 2.4 | 81.2 ± 2.5 | 50.2 ± 8.8 | 94.8 ± 0.8 | 61.9 ± 5.5 | 54.6 ± 6.0 | 91.6 ± 1.6 | 82.5 ± 1.7 |
11 | 92.8 ± 1.6 | 92.8 ± 1.6 | 88.3 ± 1.7 | 87.6 ± 2.6 | 94.4 ± 1.6 | 88.2 ± 3.6 | 87.5 ± 3.1 | 85.2 ± 3.0 |
12 | 78.3 ± 4.7 | 78.2 ± 4.6 | 62.9 ± 9.1 | 89.1 ± 2.6 | 68.1 ± 6.1 | 64.1 ± 5.3 | 88.3 ± 4.1 | 80.9 ± 4.2 |
13 | 98.4 ± 0.9 | 98.4 ± 0.9 | 98.0 ± 1.0 | 99.6 ± 0.4 | 98.1 ± 0.7 | 98.2 ± 0.9 | 98.5 ± 0.9 | 98.5 ± 0.9 |
AA | 71.7 ± 1.8 | 71.6 ± 1.8 | 49.8 ± 1.7 | 73.3 ± 1.1 | 53.5 ± 1.9 | 50.9 ± 1.7 | 72.4 ± 1.3 | 80.3 ± 0.9 |
OA | 79.6 ± 0.6 | 79.5 ± 0.6 | 60.9 ± 1.6 | 81.4 ± 0.6 | 64.6 ± 0.9 | 62.4 ± 1.0 | 80.3 ± 0.6 | 85.0 ± 0.6 |
KC | 77.3 ± 0.6 | 77.2 ± 0.6 | 56.5 ± 1.8 | 79.3 ± 0.7 | 60.6 ± 1.0 | 58.1 ± 1.1 | 78.1 ± 0.7 | 83.3 ± 0.8 |
Methods | Indian Pines | KSC | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
PCA | ICA | LDA | KDA | KPCA | DLPP | TwoSP | PCA | ICA | LDA | KDA | KPCA | DLPP | TwoSP | |
RAW | −0.3 | 20.8 | −1.9 | −1.3 | 20.2 | −4.9 | −18.7 | 0.9 | 26.6 | −3.0 | 24.3 | 26.9 | −1.3 | −9.4 |
PCA | - | 21.5 | −1.7 | −1.2 | 20.9 | −4.7 | −18.1 | - | 26.5 | −3.1 | 24.2 | 26.8 | −1.2 | −9.5 |
ICA | - | - | −19.3 | −19.1 | −1.5 | −22.1 | −33.7 | - | - | −24.5 | −4.7 | −1.0 | −21.7 | −25.4 |
LDA | - | - | - | 0.7 | 18.6 | −3.6 | −15.5 | - | - | - | 21.9 | 24.3 | 5.5 | −7.1 |
KDA | - | - | - | - | 18.5 | −3.9 | −17.4 | - | - | - | - | 4.2 | −18.8 | −23.1 |
KPCA | - | - | - | - | - | −21.4 | −33.2 | - | - | - | - | - | −21.5 | −25.1 |
DLPP | - | - | - | - | - | - | −12.8 | - | - | - | - | - | - | −10.2 |
Methods | Indian Pines | KSC | ||||||
---|---|---|---|---|---|---|---|---|
T1 | T2 | T3 | T4 | T1 | T2 | T3 | T4 | |
RAW | - | 1.67 | 35.48 | 2.84 | - | 0.42 | 20.63 | 2.88 |
PCA | 0.68 | 0.70 | 21.48 | 0.92 | 0.28 | 0.19 | 12.81 | 0.67 |
ICA | 11.69 | 0.66 | 21.36 | 3.19 | 5.41 | 0.17 | 8.44 | 0.52 |
LDA | 0.20 | 0.62 | 17.64 | 0.63 | 0.08 | 0.18 | 7.58 | 0.31 |
KDA | 1.05 | 0.69 | 19.42 | 0.80 | 0.35 | 0.16 | 7.64 | 0.30 |
KPCA | 423.63 | 0.83 | 26.03 | 1.60 | 89.23 | 0.31 | 16.70 | 0.66 |
DLPP | 0.61 | 0.67 | 18.48 | 0.53 | 0.17 | 0.22 | 10.20 | 0.41 |
TwoSP | 428.25 | 0.68 | 21.28 | 0.83 | 89.38 | 0.19 | 12.00 | 0.41 |
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Li, X.; Zhang, L.; You, J. Hyperspectral Image Classification Based on Two-Stage Subspace Projection. Remote Sens. 2018, 10, 1565. https://doi.org/10.3390/rs10101565
Li X, Zhang L, You J. Hyperspectral Image Classification Based on Two-Stage Subspace Projection. Remote Sensing. 2018; 10(10):1565. https://doi.org/10.3390/rs10101565
Chicago/Turabian StyleLi, Xiaoyan, Lefei Zhang, and Jane You. 2018. "Hyperspectral Image Classification Based on Two-Stage Subspace Projection" Remote Sensing 10, no. 10: 1565. https://doi.org/10.3390/rs10101565