Shallow water bathymetry based on a back propagation neural network and ensemble learning using multispectral satellite imagery
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Abstract: The back propagation (BP) neural network method is widely used in bathymetry based on multispectral satellite imagery. However, the classical BP neural network method faces a potential problem because it easily falls into a local minimum, leading to model training failure. This study confirmed that the local minimum problem of the BP neural network method exists in the bathymetry field and cannot be ignored. Furthermore, to solve the local minimum problem of the BP neural network method, a bathymetry method based on a BP neural network and ensemble learning (BPEL) is proposed. First, the remote sensing imagery and training sample were used as input datasets, and the BP method was used as the base learner to produce multiple water depth inversion results. Then, a new ensemble strategy, namely the minimum outlying degree method, was proposed and used to integrate the water depth inversion results. Finally, an ensemble bathymetric map was acquired. Anda Reef, northeastern Jiuzhang Atoll, and Pingtan coastal zone were selected as test cases to validate the proposed method. Compared with the BP neural network method, the root-mean-square error and the average relative error of the BPEL method can reduce by 0.65–2.84 m and 16%–46% in the three test cases at most. The results showed that the proposed BPEL method could solve the local minimum problem of the BP neural network method and obtain highly robust and accurate bathymetric maps.
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Figure 1. Procedures of bathymetry method based on a back propagation (BP) neural network and ensemble learning.
Figure 3. Study areas and data for the Anda Reef (a), northeastern Jiuzhang Atoll (b), and Pingtan coastal zone (c).
Figure 4. Root-mean-square errors (RMSEs) of 100 repeated experiments of the back propagation (BP) and BP neural network and ensemble learning (BPEL) methods for the Anda Reef (a) northeastern Jiuzhang Atoll (b) and Pingtan coastal zone (c).
Figure 5. Bathymetric maps of the three worst results for the back propagation (BP) and BP neural network and ensemble learning (BPEL) methods in the Anda Reef. a–c. Bathymetric maps of the 85th, 31st, and 91st repeated experiments for the BP method. d–f. Bathymetric maps of the 50th, 70th, and 96th repeated experiments for the BPEL method.
Figure 6. Scatterplots (estimated depth versus measured depth) of the three worst results for the back propagation (BP) and BP neural network and ensemble learning (BPEL) methods in the Anda Reef. a–c. Scatterplots of the 85th, 31st, and 91st repeated experiments for the BP method. d–f. Scatterplots of the 50th, 70th, and 96th repeated experiments for the BPEL method.
Figure 7. Bathymetric maps of the three worst results for the back propagation (BP) and BP neural network and ensemble learning (BPEL) methods in the northeastern Jiuzhang Atoll. a–c. Bathymetric maps of the 57th, 72nd, and 91st repeated experiments for the BP method. d–f. Bathymetric maps of the 96th, 58th, and 8th repeated experiments for the BPEL method.
Figure 8. Scatterplots (estimated depth versus measured depth) of the three worst results for the back propagation (BP) and BP neural network and ensemble learning (BPEL) methods in the northeastern Jiuzhang Atoll. a–c. Scatterplots of the 57th, 72nd, and 91st repeated experiments for the BP method. d–f. Scatterplots of the 96th, 58th, and 8th repeated experiments for the BPEL method.
Figure 9. Bathymetric maps of the three worst results for the back propagation (BP) and BP neural network and ensemble learning (BPEL) methods in the Pingtan coastal zone. a–c. Bathymetric maps of the 41st, 39th, and 45th repeated experiments for the BP method. d–f. Bathymetric maps of the 43rd, 74th, and 59th repeated experiments for the BPEL method.
Figure 10. Scatterplots (estimated depth versus measured depth) of the three worst results for the back propagation (BP) and BP neural network and ensemble learning (BPEL) methods in the Pingtan coastal zone. a–c. Scatterplots of the 41st, 39th, and 45th repeated experiments for the BP method. d–f. Scatterplots of the 43rd, 74th, and 59th repeated experiments for the BPEL method.
Figure 11. Effects of the number of training samples on the accuracy of back propagation (BP) and BP neural network and ensemble learning (BPEL) methods. RMSE of bathymetric inversion experiments in the Anda Reef (a), northeastern Jiuzhang Atoll (b), and Pingtan coastal zone (c). Error bars are the standard deviation of the RMSE values.
Figure 12. Effects of the number of base learners on the accuracy of BP neural network and ensemble learning (BPEL) methods. RMSE of bathymetric inversion experiments in the Anda Reef (a), northeastern Jiuzhang Atoll (b), and Pingtan coastal zone (c). Error bars are the standard deviation of the RMSE values. The blue point and line in L=1 are the RMSE and error bar of the back propagation (BP) methods.
Table 1. Comparison of inversion accuracies (RMSEs) of the three worst results of the back propagation (BP) and BP neural network and ensemble learning (BPEL) methods
Study area Water
depth/mN BP BPEL Worst result Second worst result Third worst result Worst result Second worst result Third worst result Anda Reef 0–5 180 1.87 2.17 2.32 1.59 1.58 1.66 5–10 386 2.99 1.96 1.33 0.92 0.93 0.88 10–15 324 1.39 1.56 1.65 0.85 0.95 0.89 15–20 125 5.41 3.56 3.76 1.35 1.20 1.31 Overall 1 025 2.91 2.22 2.13 1.15 1.14 1.14 Northeastern
Jiuzhang Atoll0–5 150 5.07 2.73 10.09 0.84 0.77 0.85 5–10 145 5.84 7.88 2.05 1.73 1.51 1.62 10–15 73 7.54 7.79 4.02 3.26 2.98 3.42 15–20 285 3.14 3.08 4.38 2.96 2.52 3.03 20–25 187 2.98 2.67 4.4 2.27 2.04 2.62 25–30 181 8.01 7.32 3.49 3.28 3.91 2.48 Overall 1 021 5.39 5.35 5.33 2.55 2.53 2.53 Pingtan
coastal zone0–1 104 0.47 0.56 0.26 0.25 0.23 0.21 1–2 135 1.44 0.47 0.29 0.20 0.22 0.15 2–3 181 0.92 0.82 0.27 0.26 0.21 0.24 3–4 256 0.37 0.69 0.39 0.27 0.31 0.35 4–5 209 1.27 0.83 1.13 0.41 0.41 0.36 Overall 885 0.96 0.81 0.76 0.31 0.31 0.30 Note: N represents the number of test samples. 
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