Author Affiliations
1 College of Missile Engineering, Rocket Force University of Engineering, Xi′an, Shaanxi 710025, China2 Key Laboratory of Spectral Imaging Technology, Xian Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi′an, Shaanxi 710119, Chinashow less
Fig. 1. Diagrams of manifold difference. (a) LLE algorithm; (b) GLE algorithm
Fig. 2. Dimensionality reduction frame of tensor manifold
Fig. 3. Indian Pines hyperspectral data. (a) Pseudo-color image; (b) ground-truth map
Fig. 4. PaviaU hyperspectral data. (a) Pseudo-color image; (b) ground-truth map
Fig. 5. Influence of sparse parameters λ on classification performance (Indian Pines data)
Fig. 6. Dimensionality reduction performance of Indian Pines data obtained with different algorithms. (a) Ground-truth map; (b) PCA algorithm; (c) MNF algorithm; (d) LLE algorithm; (e) LE algorithm; (f) LPP algorithm; (g) RP algorithm; (h) proposed algorithm
Fig. 7. Dimensionality reduction performance of PaviaU data obtained with different algorithms. (a) Ground-truth map; (b) PCA algorithm; (c) MNF algorithm; (d) LLE algorithm; (e) LE algorithm; (f) LPP algorithm; (g) RP algorithm; (h) proposed algorithm
Fig. 8. Projection results obtained with different dimensionality reduction algorithms (Indian Pines data). (a) Original data (band 1 & 2); (b) PCA algorithm; (c) MNF algorithm; (d) LLE algorithm; (e) LE algorithm; (f) LPP algorithm; (g) RP algorithm; (h) proposed algorithm
Fig. 9. Classification accuracy of different algorithms obtained at different embedding dimensions. (a) Indian Pines data; (b) PaviaU data
Dataset | SVM classification | PCA | MNF | LLE | LE | LPP | RP | LETM |
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Indian Pines (M=30) | OCA /% | 76.69 | 83.74 | 71.44 | 68.88 | 79.09 | 81.16 | 85.10 | ACA /% | 69.26 | 79.74 | 70.08 | 63.52 | 75.48 | 77.95 | 81.96 | PaviaU(M=20) | OCA /% | 92.46 | 93.09 | 85.67 | 82.58 | 93.56 | 90.56 | 95.55 | ACA /% | 89.04 | 91.94 | 82.15 | 75.98 | 90.55 | 86.98 | 93.93 |
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Table 1. Classification accuracy of different dimensionality reduction algorithms
Algorithm | Time complexity |
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PCA | O(N2D) | MNF | O(2N2D) | LLE | O[NDlb k·lb D+NDk3+DN2+N3] | LE | O[NDlb k·lb D+NDk3+MD2] | LPP | O[NDlb k·lb D+NDk3+2DMN+kMD2] | RP | O(DMN) | LETM | O(t4N4+t2N2D2+2t3N3+2t2N2D+kMD2) |
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Table 2. Time complexity of different algorithms
Data | Reduced dimensionality | Computation times /s |
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PCA | NMF | LLE | LE | LPP | RP | LETM |
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Indian Pines | 10 | 0.273 | 0.386 | 44.912 | 13.520 | 13.065 | 0.079 | 42.367 | 30 | 0.274 | 0.391 | 45.774 | 13.733 | 13.177 | 0.079 | 42.803 | 50 | 0.277 | 0.403 | 46.265 | 14.210 | 13.313 | 0.090 | 43.116 | PaviaU | 10 | 0.763 | 1.039 | 3633.611 | 2187.667 | 2454.708 | 0.239 | 304.150 | 30 | 0.807 | 1.068 | 3672.186 | 2193.203 | 2454.845 | 0.294 | 307.489 | 50 | 0.811 | 1.085 | 3714.503 | 2199.186 | 2454.896 | 0.401 | 310.316 |
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Table 3. Computation time of different algorithms