Unsupervised Hyperspectral Band Selection via Multimodal Evolutionary Algorithm and Subspace Decomposition
Abstract
:1. Introduction
- To increase the diversity of obtained solutions, the multimodal evolutionary algorithm is first applied to hyperspectral band selection. It converges the candidate solutions towards different directions. Therefore, it can seek out multiple optimal (global or local) band subsets, in which each of them can express the original HSI information well.
- In consideration of the ordered property of spectral bands, a boundary encoding strategy and modified evaluation criterion for subspace decomposition is proposed. Different from seeking the spectral bands directly, the target of boundary encoding strategy is to find the optimal division modes of band space. Additionally, a modified evaluation criterion, endeavoring to increase the difference between neighbor subspaces rather than all clusters, is employed to evaluate the divided subspaces. Therefore, the selected bands from each subspace are scattered and lower correlative.
- Although a single band subset can express original hyperspectral information, the generalization ability might be poor. In order to alleviate this problem, an integrated utilization strategy is employed to utilize the acquired diverse band subsets.
2. Related Work
2.1. Greedy-Based Methods
2.2. Ranking-Based Methods
2.3. Clustering-Based Methods
2.4. EA-Based Methods
3. Unsupervised Band Selection Based on Multimodal Evolutionary Algorithm and Subspace Decomposition (MEA-SD)
3.1. Boundary Encoding Strategy
3.2. Fitness Evaluation Criterion
3.3. Multimodal Optimization Framework
Algorithm 1 Procedure of FERDE. |
|
3.4. Integrated Utilization Strategy
- Calculate information entropy of all bands according to Equation (7).
- Sort the obtained solution set P according the fitness values, and select the top k different individuals, denote as X.
- For each individual in X, the corresponding band subset is composed of the bands with the maximum entropy in each subspace.
- According to k band subsets, operate corresponding pattern recognition tasks (classification or regression), respectively.
- Implement integration operation and output the final prediction results.
3.5. Computational Complexity
4. Experiments on Remote Sensing Datasets
4.1. Description of Remote Sensing Datasets
4.2. Experimental Setup
4.3. Experimental Results
4.3.1. Parameter Analysis
4.3.2. Comparison of Experimental Results
4.3.3. Comparison of Execution Time
5. Experiments on Mulberry Fruit Dataset
6. Discussion
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Dataset | Size | Samples | Classes | Bands |
---|---|---|---|---|
Indian Pines | 145 × 145 | 10,249 | 16 | 200 |
Pavia University | 610 × 340 | 42,776 | 9 | 103 |
Salinas | 512 × 217 | 54,129 | 16 | 204 |
Dataset | k | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
---|---|---|---|---|---|---|---|---|---|---|
Indian Pines | 1 | 69.36 | 77.99 | 79.18 | 79.51 | 80.94 | 79.97 | 81.22 | 80.70 | 81.36 |
3 | 70.72 | 79.23 | 81.17 | 81.60 | 81.43 | 82.09 | 83.31 | 82.72 | 82.66 | |
5 | 71.37 | 79.89 | 81.51 | 81.91 | 83.20 | 83.01 | 83.56 | 82.98 | 82.79 | |
Pavia University | 1 | 85.91 | 86.78 | 87.31 | 91.55 | 91.41 | 91.78 | 91.98 | 92.69 | 92.08 |
3 | 84.79 | 87.38 | 87.85 | 92.09 | 92.59 | 92.65 | 92.47 | 93.28 | 93.32 | |
5 | 84.92 | 87.27 | 88.70 | 92.54 | 92.85 | 93.18 | 92.92 | 93.33 | 93.56 | |
Salinas | 1 | 88.66 | 91.54 | 91.91 | 92.51 | 93.30 | 92.92 | 93.15 | 92.74 | 92.92 |
3 | 89.06 | 91.84 | 92.67 | 92.80 | 93.51 | 93.37 | 93.28 | 93.09 | 92.81 | |
5 | 89.30 | 91.59 | 92.91 | 92.90 | 93.30 | 93.62 | 93.59 | 93.51 | 93.47 |
Dataset | Selected Bands |
---|---|
18, 29, 42, 117, 131, 160 | |
Indian Pines | 18, 29, 42, 75, 117, 131 |
29, 42, 54, 89, 117, 160 | |
21, 36, 47, 63, 78, 91 | |
Pavia University | 11, 21, 40, 63, 78, 91 |
21, 36, 49, 63, 77, 91 | |
15, 34, 45, 57, 120, 164 | |
Salinas | 34, 45, 57, 79, 120, 164 |
15, 34, 45, 93, 120, 164 |
Dataset | Selected Bands |
---|---|
5, 8, 17, 21, 38, 42, 60, 69, 71, 117, 131, 134, 160, 166, 174, 191 | |
Indian Pines | 17, 29, 42, 69, 71, 75, 97, 99, 117, 130, 136, 159, 160, 176, 183, 191 |
18, 21, 28, 29, 42, 54, 70, 89, 117, 130, 132, 154, 160, 166, 182, 190 | |
2, 4, 13, 18, 21, 24, 39, 45, 48, 57, 63, 64, 74, 83, 91, 96 | |
Pavia University | 2, 15, 18, 21, 23, 34, 40, 49, 55, 59, 63, 67, 71, 78, 83, 91 |
4, 13, 21, 31, 36, 38, 41, 47, 57, 58, 63, 65, 76, 87, 91, 103 | |
8, 15, 21, 45, 52, 72, 88, 93, 94, 120, 125, 135, 158, 164, 187, 191 | |
Salinas | 24, 28, 34, 45, 52, 64, 72, 78, 125, 135, 138, 158, 164, 172, 179, 187 |
1, 9, 15, 27, 34, 45, 60, 71, 72, 117, 120, 125, 131, 158, 164, 180 |
Classes | E-FDPC | WaLuDi | TOF | MIMR-CSA | ISD-ABC | MEA-SD (ours) | MEA-SD-IUS (ours) |
---|---|---|---|---|---|---|---|
1. Alfalfa | 78.05 ± 7.54 | 14.63 ± 17.10 | 65.85 ± 3.93 | 84.37 ± 9.5 | 56.10 ± 2.09 | 85.37 ± 3.55 | 80.49 ± 2.72 |
2. Corn-notill | 61.13 ± 4.26 | 63.35 ± 2.05 | 66.21 ± 1.16 | 65.86 ± 3.0 | 62.88 ± 1.28 | 74.01 ± 2.01 | 73.46 ± 1.76 |
3. Corn-mintill | 64.79 ± 3.87 | 57.56 ± 3.83 | 64.66 ± 0.69 | 62.45 ± 2.8 | 63.59 ± 1.24 | 63.99 ± 0.90 | 68.61 ± 0.87 |
4. Corn | 48.83 ± 6.45 | 23.94 ± 3.25 | 63.38 ± 0.80 | 73.24 ± 4.1 | 72.77 ± 2.38 | 76.06 ± 1.82 | 77.00 ± 1.13 |
5. Grass-pasture | 87.59 ± 1.71 | 83.91 ± 1.63 | 88.51 ± 0.16 | 86.51 ± 1.5 | 90.80 ± 0.61 | 92.13 ± 0.24 | 90.80 ± 0.17 |
6. Grass-trees | 87.20 ± 0.66 | 88.45 ± 1.94 | 87.85 ± 0.17 | 89.30 ± 0.8 | 88.58 ± 0.52 | 91.02 ± 0.48 | 92.54 ± 0.35 |
7. Grass-pasture-mowed | 76.14 ± 1.81 | 48.90 ± 1.81 | 72.49 ± 2.05 | 84.60 ± 2.7 | 76.05 ± 3.91 | 88.41 ± 1.33 | 88.99 ± 0.76 |
8. Hay-windrowed | 91.86 ± 0.72 | 97.67 ± 0.92 | 91.40 ± 0.08 | 94.98 ± 0.7 | 92.79 ± 0.49 | 95.12 ± 0.74 | 95.58 ± 0.58 |
9. Oats | 51.14 ± 6.23 | 38.89 ± 15.09 | 48.60 ± 3.26 | 62.67 ± 8.3 | 38.89 ± 4.22 | 65.35 ± 3.59 | 74.40 ± 2.23 |
10. Soybean-notill | 74.29 ± 2.40 | 73.24 ± 3.17 | 72.11 ± 1.46 | 76.91 ± 3.2 | 74.40 ± 1.18 | 78.39 ± 0.90 | 79.43 ± 0.53 |
11. Soybean-mintill | 75.02 ± 0.74 | 72.19 ± 2.08 | 75.18 ± 0.42 | 78.05 ± 1.2 | 81.63 ± 0.57 | 82.26 ± 0.81 | 82.81 ± 0.71 |
12. Soybean-clean | 56.93 ± 2.59 | 42.23 ± 4.28 | 57.68 ± 1.71 | 74.29 ± 2.9 | 79.21 ± 1.80 | 76.03 ± 1.56 | 73.78 ± 1.44 |
13. Wheat | 96.22 ± 0.70 | 88.11 ± 2.76 | 95.68 ± 0.08 | 92.97 ± 0.2 | 97.84 ± 0.43 | 94.59 ± 0.18 | 94.62 ± 0.13 |
14. Woods | 85.61 ± 0.92 | 87.69 ± 1.10 | 90.68 ± 0.67 | 92.54 ± 0.9 | 93.94 ± 0.67 | 95.00 ± 0.81 | 96.05 ± 0.47 |
15. Buildings-grass-trees | 44.67 ± 2.28 | 23.34 ± 2.87 | 36.60 ± 1.79 | 36.31 ± 3.3 | 47.84 ± 2.88 | 44.96 ± 4.33 | 41.79 ± 3.67 |
16. Stone-steel-towers | 85.71 ± 3.45 | 75.24 ± 5.57 | 80.29 ± 0.41 | 81.48 ± 1.6 | 85.95 ± 1.13 | 89.29 ± 1.84 | 90.48 ± 1.21 |
OA | 73.44 ± 0.48 | 69.96 ± 0.71 | 74.61 ± 0.35 | 77.21 ± 0.69 | 78.37 ± 0.67 | 80.94 ± 0.72 | 81.43 ± 0.54 |
AA | 72.82 ± 2.90 | 61.21 ± 4.34 | 72.32 ± 1.18 | 77.03 ± 2.92 | 75.20 ± 1.59 | 80.75 ± 1.57 | 81.30 ± 1.17 |
Classes | E-FDPC | WaLuDi | TOF | MIMR-CSA | ISD-ABC | MEA-SD (ours) | MEA-SD-IUS (ours) |
---|---|---|---|---|---|---|---|
1. Asphalt | 89.53 ± 0.28 | 89.65 ± 0.30 | 91.15 ± 0.14 | 90.80 ± 0.20 | 89.18 ± 0.21 | 92.85 ± 0.23 | 92.85 ± 0.23 |
2. Meadows | 95.25 ± 0.15 | 95.85 ± 0.18 | 96.18 ± 0.20 | 95.31 ± 0.14 | 95.98 ± 0.22 | 96.11 ± 0.17 | 97.38 ± 0.12 |
3. Gravel | 66.79 ± 1.39 | 63.68 ± 2.36 | 65.43 ± 1.16 | 68.13 ± 1.68 | 69.75 ± 0.89 | 74.11 ± 0.73 | 74.38 ± 0.40 |
4. Trees | 89.51 ± 0.86 | 87.93 ± 1.51 | 87.35 ± 0.33 | 88.87 ± 1.85 | 89.65 ± 0.36 | 90.65 ± 0.80 | 91.88 ± 0.27 |
5. Painted metal sheets | 99.42 ± 0.25 | 99.39 ± 0.45 | 99.34 ± 0.30 | 99.47 ± 0.33 | 98.59 ± 0.17 | 99.60 ± 0.12 | 99.51 ± 0.13 |
6. Bare soil | 73.67 ± 1.48 | 65.36 ± 3.52 | 59.36 ± 1.74 | 67.69 ± 2.2 | 70.70 ± 0.39 | 80.20 ± 0.36 | 82.48 ± 0.35 |
7. Bitumen | 75.52 ± 0.18 | 74.02 ± 0.69 | 75.86 ± 0.11 | 80.86 ± 0.10 | 71.17 ± 0.25 | 81.95 ± 0.41 | 83.54 ± 0.30 |
8. Self-blocking bricks | 88.77 ± 0.29 | 88.53 ± 0.31 | 86.63 ± 0.21 | 87.96 ± 0.55 | 88.16 ± 0.11 | 89.20 ± 0.24 | 91.52 ± 0.21 |
9. Shadows | 96.53 ± 0.20 | 99.65 ± 0.18 | 97.65 ± 0.16 | 99.53 ± 0.23 | 98.77 ± 0.18 | 99.55 ± 0.25 | 99.65 ± 0.15 |
OA | 89.01 ± 0.16 | 88.05 ± 0.34 | 87.60 ± 0.16 | 88.71 ± 0.30 | 88.91 ± 0.23 | 91.41 ± 0.17 | 92.59 ± 0.16 |
AA | 85.40 ± 0.56 | 83.82 ± 1.06 | 83.13 ± 0.48 | 85.71 ± 0.81 | 84.98 ± 0.31 | 88.95 ± 0.37 | 89.97 ± 0.24 |
Classes | E-FDPC | WaLuDi | TOF | MIMR-CSA | ISD-ABC | MEA-SD (ours) | MEA-SD-IUS (ours) |
---|---|---|---|---|---|---|---|
1. Brocoli_greenweeds_1 | 98.67 ± 0.22 | 98.06 ± 0.14 | 97.43 ± 0.07 | 98.45 ± 0.24 | 98.56 ± 0.18 | 98.78 ± 0.15 | 99.45 ± 0.08 |
2. Brocoli_greenweeds_2 | 99.73 ± 0.19 | 99.46 ± 0.12 | 99.78 ± 0.06 | 99.69 ± 0.22 | 99.91 ± 0.07 | 99.97 ± 0.02 | 99.94 ± 0.02 |
3. Fallow | 98.71 ± 0.14 | 98.59 ± 0.17 | 97.98 ± 0.13 | 97.47 ± 0.08 | 98.99 ± 0.24 | 98.59 ± 0.25 | 99.33 ± 0.09 |
4. Fallow_rough_plow | 99.44 ± 0.34 | 99.68 ± 0.23 | 99.68 ± 0.19 | 99.60 ± 0.11 | 99.52 ± 0.35 | 99.52 ± 0.19 | 99.44 ± 0.16 |
5. Fallow_smooth | 98.76 ± 0.18 | 97.76 ± 0.25 | 98.76 ± 0.10 | 97.97 ± 0.32 | 98.55 ± 0.22 | 98.55 ± 0.18 | 98.71 ± 0.09 |
6. Stubble | 99.75 ± 0.12 | 99.64 ± 0.08 | 99.78 ± 0.05 | 99.80 ± 0.11 | 99.83 ± 0.13 | 99.83 ± 0.09 | 99.83 ± 0.12 |
7. Celery | 99.38 ± 0.27 | 99.47 ± 0.14 | 99.47 ± 0.09 | 99.25 ± 0.22 | 99.50 ± 0.13 | 99.63 ± 0.19 | 99.60 ± 0.16 |
8. Grapes_untrained | 84.86 ± 0.20 | 80.39 ± 0.18 | 84.52 ± 0.12 | 85.28 ± 0.14 | 86.18 ± 0.09 | 88.40 ± 0.15 | 88.91 ± 0.14 |
9. Soil_vinyard_develop | 98.68 ± 0.13 | 98.98 ± 0.06 | 98.92 ± 0.14 | 99.80 ± 0.07 | 99.73 ± 0.20 | 99.91 ± 0.05 | 99.93 ± 0.05 |
10. Corn_senesced_green | 95.59 ± 0.31 | 90.20 ± 0.11 | 93.12 ± 0.08 | 94.64 ± 0.21 | 95.02 ± 0.18 | 95.83 ± 0.12 | 96.00 ± 0.13 |
11. Lettuce_romaine_4wk | 95.42 ± 0.25 | 93.76 ± 0.23 | 95.53 ± 0.15 | 95.84 ± 0.39 | 92.92 ± 0.27 | 98.96 ± 0.14 | 99.06 ± 0.11 |
12. Lettuce_romaine_5wk | 99.83 ± 0.06 | 99.88 ± 0.09 | 99.83 ± 0.05 | 99.83 ± 0.07 | 98.87 ± 0.19 | 99.84 ± 0.05 | 99.88 ± 0.03 |
13. Lettuce_romaine_6wk | 98.67 ± 0.17 | 98.42 ± 0.13 | 98.91 ± 0.20 | 98.55 ± 0.21 | 99.03 ± 0.16 | 99.52 ± 0.25 | 99.39 ± 0.23 |
14. Lettuce_romaine_7wk | 94.70 ± 0.21 | 92.63 ± 0.26 | 95.95 ± 0.12 | 94.81 ± 0.09 | 93.67 ± 0.23 | 97.40 ± 0.27 | 96.68 ± 0.20 |
15. Vinyard_untrained | 67.59 ± 0.19 | 65.37 ± 0.15 | 67.97 ± 0.08 | 66.54 ± 0.14 | 69.59 ± 0.17 | 72.53 ± 0.20 | 72.86 ± 0.16 |
16. Vinyard_vertical | 97.79 ± 0.26 | 96.25 ± 0.18 | 98.59 ± 0.10 | 98.71 ± 0.21 | 99.08 ± 0.16 | 99.04 ± 0.22 | 99.14 ± 0.19 |
OA | 91.53 ± 0.16 | 89.79 ± 0.21 | 91.38 ± 0.08 | 91.49 ± 0.23 | 92.13 ± 0.15 | 93.30 ± 0.19 | 93.51 ± 0.13 |
AA | 95.07 ± 0.20 | 93.78 ± 0.16 | 94.99 ± 0.11 | 94.96 ± 0.18 | 95.21 ± 0.19 | 96.38 ± 0.16 | 96.49 ± 0.12 |
Data Set | E-FDPC | WaLuDi | TOF | MIMR-CSA | ISD-ABC | MEA-SD (ours) |
---|---|---|---|---|---|---|
Indian Pines | 0.202 | 2.238 | 0.694 | 4.084 | 3.253 | 3.392 |
Pavia University | 0.217 | 1.449 | 0.712 | 2.750 | 1.898 | 1.791 |
Salinas | 0.635 | 2.730 | 2.127 | 4.553 | 5.823 | 3.542 |
The Number of Bands | Selected Bands |
---|---|
15, 30, 86, 110, 114, 128, 164, 173, 235, 243, 255, 269 | |
12 | 15, 30, 40, 77, 133, 164, 170, 223, 235, 242, 249, 272 |
13, 15, 30, 53, 63, 68, 86, 128, 147, 164, 241, 273 | |
13, 15, 30, 77, 83, 89, 108, 127, 128, 135, 142, 164, 194, 203, 235, 239, 255, 266 | |
18 | 2, 30, 72, 110, 127, 128, 135, 144, 148, 170, 194, 198, 235, 241, 251, 258, 267, 279 |
2, 15, 30, 63, 76, 93, 110, 128, 142, 146, 164, 172, 229, 235, 245, 250, 270, 277 |
Anthocyanin | Flavonoid | |||
---|---|---|---|---|
MSE () | MSE () | |||
E-FDPC | 3.46 ± 0.18 | 0.85 | 7.23 ± 0.82 | 0.86 |
WaLuDi | 3.61 ± 0.41 | 0.85 | 7.86 ± 1.10 | 0.84 |
TOF | 3.27 ± 0.17 | 0.86 | 6.86 ± 0.36 | 0.86 |
MIMR-CSA | 3.14 ± 0.09 | 0.87 | 5.96 ± 0.68 | 0.88 |
ISD-ABC | 3.28 ± 0.13 | 0.86 | 6.13 ± 0.79 | 0.88 |
MEA-SD | 3.13 ± 0.08 | 0.87 | 5.56 ± 0.57 | 0.89 |
MEA-SD-IUS | 3.06 ± 0.05 | 0.87 | 5.37 ± 0.44 | 0.89 |
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Wei, Y.; Hu, H.; Xu, H.; Mao, X. Unsupervised Hyperspectral Band Selection via Multimodal Evolutionary Algorithm and Subspace Decomposition. Sensors 2023, 23, 2129. https://doi.org/10.3390/s23042129
Wei Y, Hu H, Xu H, Mao X. Unsupervised Hyperspectral Band Selection via Multimodal Evolutionary Algorithm and Subspace Decomposition. Sensors. 2023; 23(4):2129. https://doi.org/10.3390/s23042129
Chicago/Turabian StyleWei, Yunpeng, Huiqiang Hu, Huaxing Xu, and Xiaobo Mao. 2023. "Unsupervised Hyperspectral Band Selection via Multimodal Evolutionary Algorithm and Subspace Decomposition" Sensors 23, no. 4: 2129. https://doi.org/10.3390/s23042129