Discovering the Representative Subset with Low Redundancy for Hyperspectral Feature Selection
Abstract
:1. Introduction
2. Related Works
- (1)
- When compared with the the LCMV-based methods; although both the LCMV-based methods and the MRMR method evaluate the representativeness of bands, their explicit selection criteria are totally different. The LCMV-based methods measure one band’s representativeness relative to the whole dataset by using a finite impulse response (FIR) filter [10]. The MRMR method evaluates the representativeness of a band subset relative to the remaining bands by using OP. Moreover, LCMV cannot consider redundancy among selected bands [10,19], but the MRMR method can achieve it.
- (2)
- When compared with the existing OP-based methods like OPBS, OSP-BSVD and VGBS; although both these similar methods and the MRMR method use OP to measure the relationship among bands, their objectives are totally different. For the OPBS, OSP-BSVD and VGBS methods, OP is used to evaluate the redundancy or the dissimilarity between a candidate band and the currently selected bands [19,20,21]; while for the MRMR method, OP is used to measure the representativeness of a band subset relative to the remaining unselected bands. The existing OP-based mainly consider the redundancy among selected bands but do not pay sufficient attention on the selected bands’ representativeness [19], in contrast, the MRMR method can well consider both the redundancy and the representativeness of the selected band subset.
- (3)
- Finally, all the LCMV, OPBS, OSP-BSVD and VGBS methods are point-wise band selection methods, namely, the desired bands are obtained individually [10,19,20,21]; whereas the MRMR method is a group-wise method, in which the desired bands are obtained simultaneously. Because the selected bands actually works together in the applications like pixel classification, the effect of the selected bands should be considered jointly. The group-wise methods are usually more effective than the point-wise methods, since the group searching strategy is more suitable for evaluating the joint effect of multiple bands.
3. The Proposed Method
3.1. Background of OP
3.2. MRMR Selection Criterion
3.3. Subset Searching Strategy
3.4. Practical Considerations
3.4.1. Adaptive Determination of
3.4.2. Accelerating Tricks of Computing
3.4.3. The Number of Selected Bands
Algorithm 1: The MRMR Algorithm |
Input: Observations , the number of selected bands n. |
Initialize: m, , and . |
Step1: Compute the Gram matrix , then use it to compute subsets’ representativeness (using (20)) in the following processes. |
Step2: Compute the correlation coefficient matrix of D, then use it to compute subsets’s redundancy (using (8)) in the following processes. |
Step3: Establish the initial set of the antibody population, i.e., . |
Step4: |
while the stop criterion is not met do |
1: Copy the antibodies according to their affinities. |
2: According to the clone selection strategy, randomly select some bands from each copied antibody and replace them with other candidate bands. |
3: Select the m antibodies that have the highest affinities to construct the new antibody population. |
end while |
Step5: The antibody that has the largest affinity is regarded as the final selected band subset. |
Output:n selected bands. |
4. Experiments
4.1. Indian Pine Dataset
4.1.1. Classification Results
4.1.2. Band Correlation Comparison
4.1.3. Computing Time Comparison
4.2. Pavia University Image
4.2.1. Classification Results
4.2.2. Band Correlation Comparison
4.2.3. Computing Time Comparison
4.3. Salinas Dataset
4.3.1. Classification Results
4.3.2. Band Correlation Comparison
4.3.3. Computing Time Comparison
4.4. Summary
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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SVM | KNN | |||
---|---|---|---|---|
OA (100%) | AA (100%) | OA (100%) | AA (100%) | |
1.MVPCA | 67.74 | 67.99 | 59.95 | 61.19 |
2.LCMVBCC | 64.39 | 63.82 | 54.25 | 54.90 |
3.LCMVBCM | 70.48 | 72.02 | 62.60 | 63.52 |
4.ECA | 77.45 | 76.99 | 70.62 | 69.41 |
5.OPBS | 75.90 | 76.15 | 68.70 | 67.86 |
6.MRMR | 81.32 | 82.70 | 72.94 | 72.86 |
Band Correlation (ACC) | Computing Time (s) | |
---|---|---|
1.MVPCA | 0.5950 | 0.2825 |
2.LCMVBCC | 0.9816 | 3.0452 |
3.LCMVBCM | 0.9882 | 2.5048 |
4.ECA | 0.2988 | 1.6770 |
5.OPBS | 0.1815 | 0.6376 |
6.MRMR | 0.2179 | 1.7101 |
SVM | KNN | |||
---|---|---|---|---|
OA (100%) | AA (100%) | OA (100%) | AA (100%) | |
1.MVPCA | 70.96 | 62.83 | 63.87 | 59.09 |
2.LCMVBCC | 69.08 | 64.36 | 60.69 | 62.52 |
3.LCMVBCM | 77.19 | 70.20 | 68.27 | 68.27 |
4.ECA | 83.89 | 79.96 | 76.62 | 72.65 |
5.OPBS | 86.58 | 83.62 | 80.87 | 78.38 |
6.MRMR | 90.15 | 87.78 | 83.76 | 82.57 |
Band Correlation (ACC) | Computing Time (s) | |
---|---|---|
1.MVPCA | 0.9981 | 1.1549 |
2.LCMVBCC | 0.9880 | 5.7662 |
3.LCMVBCM | 0.9934 | 4.3998 |
4.ECA | 0.6223 | 15.2934 |
5.OPBS | 0.5267 | 2.5998 |
6.MRMR | 0.5788 | 2.3671 |
SVM | KNN | |||
---|---|---|---|---|
OA (100%) | AA (100%) | OA (100%) | AA (100%) | |
1.MVPCA | 84.75 | 87.78 | 80.16 | 83.56 |
2.LCMVBCC | 88.06 | 90.91 | 84.08 | 86.57 |
3.LCMVBCM | 86.36 | 87.02 | 82.65 | 85.44 |
4.ECA | 92.16 | 95.67 | 88.58 | 92.87 |
5.OPBS | 91.72 | 95.34 | 84.54 | 88.77 |
6.MRMR | 93.02 | 96.31 | 88.83 | 93.13 |
Band Correlation (ACC) | Computing Time (s) | |
---|---|---|
1.MVPCA | 0.9976 | 1.1549 |
2.LCMVBCC | 0.6282 | 5.7662 |
3.LCMVBCM | 0.7001 | 4.3998 |
4.ECA | 0.4509 | 15.2934 |
5.OPBS | 0.3728 | 2.5998 |
6.MRMR | 0.3039 | 2.3671 |
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Zhang, W.; Li, X.; Zhao, L. Discovering the Representative Subset with Low Redundancy for Hyperspectral Feature Selection. Remote Sens. 2019, 11, 1341. https://doi.org/10.3390/rs11111341
Zhang W, Li X, Zhao L. Discovering the Representative Subset with Low Redundancy for Hyperspectral Feature Selection. Remote Sensing. 2019; 11(11):1341. https://doi.org/10.3390/rs11111341
Chicago/Turabian StyleZhang, Wenqiang, Xiaorun Li, and Liaoying Zhao. 2019. "Discovering the Representative Subset with Low Redundancy for Hyperspectral Feature Selection" Remote Sensing 11, no. 11: 1341. https://doi.org/10.3390/rs11111341