A Novel Hybrid Learning System Using Modified Breaking Ties Algorithm and Multinomial Logistic Regression for Classification and Segmentation of Hyperspectral Images
Abstract
:1. Introduction
- First, the main feature is that spectral information lies in the third dimension against each pixel entry in a data cube, and it can be extracted for the exploitation of linear separability of the classes. Numerous methods have been developed for extraction, such as independent component analysis [16], linear spectral unmixing [17,18], and maximum noise fraction [19].
2. Materials and Methods
2.1. Datasets
2.2. Multinomial Logistic Regression (MLR)
2.3. Regression Estimator Using MAP
2.4. EMAPs with Spatial Information
2.5. Approach of Generalized Composite Kernels
2.6. Isotropic Multi-Level Logistic (MLL) Prior
2.7. Performance Measures
3. Results and Discussion
3.1. Experimental Setup
3.2. Comparison with Existing Techniques
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Class No. | Class Name | #Samples | Classification Accuracy over Different AL Methods | |||||
---|---|---|---|---|---|---|---|---|
Train | Test | Random Selection | Maximum Entropy | Mutual Information | Breaking Ties | Modified Breaking Ties | ||
1 | Alfalfa | 5 | 50 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
2 | Corn-no till | 5 | 1429 | 99.90 | 100.00 | 100.00 | 100.00 | 100.00 |
3 | Corn-min till | 5 | 829 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
4 | Corn | 5 | 229 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
5 | Grass-pasture | 5 | 492 | 93.54 | 90.38 | 82.06 | 90.37 | 97.87 |
6 | Grass-tree | 5 | 742 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
7 | Grass-pasture-mowed | 5 | 21 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
8 | Hay-windrowed | 5 | 484 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
9 | Oats | 5 | 15 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
10 | Soyabeans-no till | 5 | 961 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
11 | Soyabeans-min till | 5 | 2463 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
12 | Soyabeans-clean till | 5 | 609 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
13 | Wheat | 5 | 207 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
14 | Woods | 5 | 1289 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
15 | Building-grass-trees-drives | 5 | 375 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
16 | Stone-steel towers | 5 | 90 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
Overall Accuracy | 99.92 | 99.39 | 98.13 | 99.27 | 99.93 | |||
Average Accuracy | 99.59 | 99.39 | 98.87 | 99.39 | 99.86 | |||
Kappa Statistics | 98.99 | 99.77 | 97.38 | 98.96 | 99.84 |
Class No. | Class Name | Segmentation Accuracy over Different AL Methods | ||||
---|---|---|---|---|---|---|
Random Selection | Maximum Entropy | Mutual Information | Breaking Ties | Modified Breaking Ties | ||
1 | Alfalfa | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
2 | Corn-no till | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
3 | Corn-min till | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
4 | Corn | 99.84 | 100.00 | 99.56 | 100.00 | 100.00 |
5 | Grass-pasture | 94.16 | 92.50 | 84.50 | 93.46 | 99.63 |
6 | Grass-tree | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
7 | Grass-pasture-mowed | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
8 | Hay-windrowed | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
9 | Oats | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
10 | Soyabeans-no till | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
11 | Soyabeans-min till | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
12 | Soyabeans-clean till | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
13 | Wheat | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
14 | Woods | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
15 | Building-grass-trees-drives | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
16 | Stone-steel towers | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
Overall Accuracy | 99.44 | 99.23 | 98.50 | 99.59 | 99.98 | |
Average Accuracy | 99.62 | 99.51 | 99.00 | 99.59 | 99.98 | |
Kappa Statistics | 99.21 | 98.93 | 97.19 | 99.43 | 99.98 |
Sr. No. | References | Classification Accuracy | Segmentation Accuracy | ||||
---|---|---|---|---|---|---|---|
OA | AA | Kappa | OA | AA | Kappa | ||
1 | Li et al. [28] | 19.08 | 11.64 | 6.66 | 14.37 | 17.73 | 12.34 |
2 | Li et al. [30] | 38.32 | 48.30 | 40.04 | 42.05 | 62.41 | 39.04 |
3 | Li et al. [31] | 55.55 | 64.32 | 50.04 | 62.49 | 70.92 | 57.75 |
4 | Li et al. [32] | 48.32 | 64.38 | 44.19 | 82.84 | 88.32 | 78.19 |
5 | Proposed (HLS) | 99.93 | 99.86 | 99.84 | 99.98 | 99.98 | 99.98 |
Class No. | Class Name | # Samples | Classification Accuracy over Different AL Methods | |||||
---|---|---|---|---|---|---|---|---|
Train | Test | Random Selection | Maximum Entropy | Mutual Information | Breaking Ties | Modified Breaking Ties | ||
1 | Asphalt | 5 | 7174 | 98.28 | 97.81 | 96.52 | 99.13 | 99.01 |
2 | Bare Soil | 5 | 19,184 | 99.88 | 99.99 | 100 | 99.98 | 99.98 |
3 | Bitumen | 5 | 2486 | 96.68 | 95.63 | 93.04 | 98.27 | 98.05 |
4 | Bricks | 5 | 3583 | 99.96 | 99.99 | 100.00 | 100.00 | 100.00 |
5 | Gravel | 5 | 1605 | 99.99 | 100.00 | 100.00 | 100.00 | 99.99 |
6 | Meadows | 5 | 5556 | 83.60 | 88.87 | 96.05 | 89.92 | 90.03 |
7 | Metal Sheets | 5 | 1700 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
8 | Shadows | 5 | 4191 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
9 | Trees | 5 | 1173 | 99.98 | 99.98 | 99.65 | 99.48 | 99.99 |
Overall Accuracy | 99.09 | 99.33 | 99.25 | 99.37 | 99.14 | |||
Average Accuracy | 97.59 | 98.03 | 98.36 | 98.53 | 98.56 | |||
Kappa Statistics | 98.23 | 98.72 | 98.93 | 99.09 | 99.01 |
Class No. | Class Name | Segmentation Accuracy over Different AL Methods | ||||
---|---|---|---|---|---|---|
Random Selection | Maximum Entropy | Mutual Information | Breaking Ties | Modified Breaking Ties | ||
1 | Asphalt | 98.97 | 98.95 | 98.48 | 99.75 | 99.64 |
2 | Bare Soil | 99.75 | 99.92 | 99.88 | 99.87 | 99.85 |
3 | Bitumen | 98.19 | 97.98 | 97.09 | 99.62 | 99.44 |
4 | Bricks | 99.99 | 100.00 | 100.00 | 100.00 | 100.00 |
5 | Gravel | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
6 | Meadows | 86.74 | 92.95 | 97.26 | 94.72 | 94.90 |
7 | Metal sheets | 100.00 | 99.99 | 99.99 | 99.99 | 99.84 |
8 | Shadows | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
9 | Trees | 100.00 | 100.00 | 100.00 | 100.00 | 99.99 |
Overall Accuracy | 99.34 | 99.59 | 99.55 | 99.69 | 99.42 | |
Average Accuracy | 98.18 | 98.87 | 99.19 | 99.33 | 99.29 | |
Kappa Statistics | 98.45 | 99.21 | 99.32 | 99.48 | 99.28 |
Sr. No. | References | Classification Accuracy | Segmentation Accuracy | ||||
---|---|---|---|---|---|---|---|
OA | AA | Kappa | OA | AA | Kappa | ||
1 | Li et al. [28] | 2.15 | 3.08 | 0.80 | 3.15 | 5.89 | 1.21 |
2 | Li et al. [30] | 12.84 | 67.87 | 9.54 | 14.30 | 77.50 | 10.42 |
3 | Li et al. [31] | 42.91 | 62.01 | 18.24 | 48.83 | 66.13 | 22.99 |
4 | Li et al. [32] | 43.02 | 31.73 | 8.18 | 40.14 | 38.81 | 10.78 |
5 | Proposed HLS | 99.14 | 98.56 | 99.01 | 99.42 | 99.29 | 99.28 |
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Shah, S.T.H.; Qureshi, S.A.; Rehman, A.u.; Shah, S.A.H.; Amjad, A.; Mir, A.A.; Alqahtani, A.; Bradley, D.A.; Khandaker, M.U.; Faruque, M.R.I.; et al. A Novel Hybrid Learning System Using Modified Breaking Ties Algorithm and Multinomial Logistic Regression for Classification and Segmentation of Hyperspectral Images. Appl. Sci. 2021, 11, 7614. https://doi.org/10.3390/app11167614
Shah STH, Qureshi SA, Rehman Au, Shah SAH, Amjad A, Mir AA, Alqahtani A, Bradley DA, Khandaker MU, Faruque MRI, et al. A Novel Hybrid Learning System Using Modified Breaking Ties Algorithm and Multinomial Logistic Regression for Classification and Segmentation of Hyperspectral Images. Applied Sciences. 2021; 11(16):7614. https://doi.org/10.3390/app11167614
Chicago/Turabian StyleShah, Syed Taimoor Hussain, Shahzad Ahmad Qureshi, Aziz ul Rehman, Syed Adil Hussain Shah, Arslan Amjad, Adil Aslam Mir, Amal Alqahtani, David A. Bradley, Mayeen Uddin Khandaker, Mohammad Rashed Iqbal Faruque, and et al. 2021. "A Novel Hybrid Learning System Using Modified Breaking Ties Algorithm and Multinomial Logistic Regression for Classification and Segmentation of Hyperspectral Images" Applied Sciences 11, no. 16: 7614. https://doi.org/10.3390/app11167614