Integration of Information Theory, K-Means Cluster Analysis and the Logistic Regression Model for Landslide Susceptibility Mapping in the Three Gorges Area, China
Abstract
:1. Introduction
2. Methodology
2.1. Study Area
2.1.1. General Characteristics and Geological Setting
2.1.2. Slope Failures and Causative Factors
- √
- A Landsat-8 OLI image obtained on 14 April 2015, with the path/row number of 125/38. To perform feature extraction, we have performed a series of operations on this multispectral image. This process includes radiometric correction to avoid radiometric errors or distortions over the whole image, geometric correction to avoid geometric distortion due to Earth’s rotation and other imaging conditions from the image and atmospheric correction to remove the effects of the atmosphere on the reflectance values of the image. Meanwhile, Bands 4 and 5 of the image are used for computing the normalized difference vegetable index (NDVI), whereas Bands 3 and 6 of the image are used for computing the normalized difference water index (NDWI).
- √
- The 1:50,000-scale geological maps provided by Hubei Geological Bureau for the exaction of geological factors, including lithology and distance to fault.
- √
- ASTER GDEM Version 2 (V2) data, representing the surface in raster format, for the extraction of geomorphological and hydrological factors, including elevation, distance to rivers, the terrain roughness index (TRI), the terrain position index (TPI), slope gradient, catchment area, catchment slope, terrain curvature, the topographic wetness index (TWI), terrain surface convexity, terrain surface texture, slope aspect and slope form.
2.2. The Proposed Framework
2.2.1. Information Coefficient Based on Shannon’s Entropy Index
2.2.2. Certainty Factor
2.2.3. K-means Clustering Analysis
2.2.4. Multicollinearity Analysis
2.2.5. Logistic Regression
2.3. Objective Evaluation Measures
3. Results
3.1. The Construction of the Proposed Framework
3.1.1. Choosing the Number of Classes for Each Causative Factor
3.1.2. Selecting Causative Factors for Each Grid Cell
3.1.3. Clustering Grid Cells into Different Groups
3.1.4. Multicollinearity Analysis of the Selected Causative Factors
3.2. Validation and Comparison
4. Discussion
4.1. Impact of K
4.2. The Suitability for Urban Development
- near the county of Badong, southwest south and southeast of this county.
- near the county of Xietan, west, northwest, north, northeast and east of this county.
- near the county of Shazhenxi, northwest, north, northeast and south of this county.
- near the county of Guizhou, north, northeast, east and southeast of this county.
- near the county of Guojiaba, south and southeast of this county.
- near the county of Xiangxi, north, northeast and east of this county.
- near the county of Quyuan, northwest, north, northeast, east and southeast of this county.
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Causative Factor | Information Coefficient | ||||
---|---|---|---|---|---|
2 Classes | 3 Classes | 4 Classes | 5 Classes | 6 Classes | |
Elevation | 0.8655 | 0.3912 | 0.4209 | NC | NC |
Distance to river | 0.8040 | 0.4542 | 0.3068 | 0.2743 | NC |
NDVI | 0.2898 | 0.1578 | 0.1223 | 0.1172 | 0.1053 |
NDWI | 0.2776 | 0.1439 | 0.1486 | 0.1428 | 0.1175 |
TRI | 0.2343 | 0.2270 | 0.2472 | 0.2398 | NC |
TPI | 0.0011 | 0.0715 | 0.0889 | 0.1021 | 0.1089 |
Slope gradient | 0.1144 | 0.1229 | 0.1140 | 0.1123 | 0.1180 |
Distance to fault | 0.0193 | 0.0037 | 0.0048 | 0.0322 | 0.0181 |
Catchment area | 0.0531 | 0.0386 | 0.0294 | 0.0315 | 0.0360 |
Catchment slope | 0.1175 | 0.1350 | 0.1230 | 0.1279 | 0.1258 |
Terrain curvature | 0.0080 | 0.0384 | 0.0640 | 0.0808 | 0.0933 |
TWI | 0.0858 | 0.1798 | 0.1690 | 0.1424 | 0.1539 |
Terrain surface convexity | 0.0582 | 0.0847 | 0.0933 | 0.0781 | 0.0729 |
Terrain surface texture | 0.3848 | 0.3495 | 0.3139 | 0.3040 | 0.2940 |
Category | Value Range | Description | Stability |
---|---|---|---|
1 | Basically no landslides occurred | stable | |
2 | Landslides are less likely to occur | relatively stable | |
3 | Uncertain whether landslides will occur | uncertain | |
4 | Landslides are more likely to occur | unstable | |
5 | The possibility of landslides is great | extremely unstable |
Causative Factor | Classes | Percentage of Landslide | Percentage of Class | CF |
---|---|---|---|---|
Elevation | 80~700 | 99.00 | 65.50 | 0.3599 |
>700~2000 | 1.00 | 34.50 | −0.9728 | |
Distance to river | <2000 | 96.80 | 48.57 | 0.5300 |
2000~6900 | 3.20 | 51.43 | −0.9412 | |
NDVI | −0.7186~0.4140 | 16.24 | 4.46 | 0.7713 |
>0.4140~0.9190 | 83.76 | 95.54 | −0.1301 | |
NDWI | −0.8879~0.4503 | 88.29 | 96.79 | 0.0929 |
>0.4503~0.8025 | 11.71 | 3.21 | 0.7718 | |
Catchment area | 900~18,590 | 96.13 | 91.52 | −0.0624 |
>18,590~412,609 | 3.87 | 8.48 | 0.4134 | |
Terrain surface texture | 4.4474~28.4901 | 82.07 | 45.10 | 0.4792 |
>28.4901~61.9701 | 17.93 | 54.90 | −0.6869 | |
Slope gradient | <20 | 48.77 | 35.17 | 0.2967 |
20~35 | 44.61 | 44.25 | 0.0086 | |
>35~75 | 6.62 | 20.58 | −0.6920 | |
Lithology | mudstone, shale and Quaternary deposits | 3.94 | 22.48 | −0.8660 |
sandstones and thinly bedded limestones | 51.82 | 26.97 | 0.5153 | |
limestones and massive sandstones | 44.24 | 50.55 | −0.1257 | |
TWI | 0.8704~3.4408 | 23.12 | 51.64 | −0.5676 |
>3.4408~6.2721 | 76.49 | 47.49 | 0.4033 | |
>6.2721~10.4071 | 0.39 | 0.87 | −0.5626 | |
Catchment slope | <0.3224 | 36.43 | 28.02 | 0.2457 |
0.3224~0.4946 | 56.68 | 47.52 | 0.1719 | |
>0.4946~1.1306 | 6.89 | 24.46 | −0.7308 | |
TRI | <8.8293 | 58.80 | 39.26 | 0.3535 |
8.8293~15.0834 | 35.76 | 41.89 | −0.1542 | |
>15.0834~26.1201 | 5.26 | 16.50 | −0.6947 | |
>26.1201~94.1794 | 0.18 | 2.35 | −0.9277 | |
Terrain surface convexity | >13.9169~42.4579 | 12.13 | 5.10 | 0.6168 |
>42.4579~48.8004 | 31.42 | 25.02 | 0.2167 | |
>48.8004~53.7838 | 41.06 | 43.07 | −0.0495 | |
>53.7838~71.9051 | 15.39 | 26.81 | −0.4412 | |
Distance to fault | <1200 | 24.54 | 28.50 | −0.1464 |
1200~2400 | 22.32 | 27.37 | −0.1940 | |
>2400~3600 | 29.61 | 22.88 | 0.2418 | |
>3600~5400 | 20.84 | 16.01 | 0.2463 | |
>5400~8700 | 2.69 | 5.24 | −0.5011 | |
TPI | −90.8220~−18.5199 | 0.52 | 2.13 | −0.7665 |
>−18.5199~−8.4604 | 6.04 | 10.30 | −0.4283 | |
>−8.4604~−2.7133 | 26.97 | 22.60 | 0.1724 | |
>−2.7133~4.1138 | 48.00 | 35.04 | 0.2873 | |
>4.1138~12.2871 | 17.17 | 23.56 | −0.2835 | |
>12.2871~70.1288 | 1.30 | 6.37 | −0.8060 | |
Terrain curvature | −2.1060~−0.4418 | 0.21 | 1.07 | −0.8173 |
>−0.4418~−0.1991 | 3.83 | 7.44 | −0.5006 | |
>−0.1991~−0.0604 | 20.45 | 20.08 | 0.0194 | |
>−0.0604~0.0782 | 56.76 | 45.41 | 0.2128 | |
>0.0782~0.2863 | 17.65 | 22.28 | −0.2178 | |
>0.2863~2.3318 | 1.10 | 3.72 | −0.7184 | |
Slope aspect | Flat | 0.26 | 0.57 | −0.5560 |
North | 23.54 | 14.83 | 0.3936 | |
North–East | 15.95 | 12.57 | 0.2249 | |
East | 9.67 | 11.86 | −0.1940 | |
South–East | 7.27 | 10.62 | −0.3292 | |
South | 13.52 | 12.47 | 0.0826 | |
South-West | 6.43 | 10.86 | −0.4234 | |
West | 9.46 | 14.52 | −0.3620 | |
North–West | 13.90 | 11.70 | 0.1690 | |
Slope form | V/V | 29.74 | 28.71 | 0.0367 |
GE/V | 2.70 | 1.63 | 0.4238 | |
X/V | 10.60 | 11.15 | −0.0522 | |
V/GR | 4.05 | 3.54 | 0.1340 | |
GE/GR | 1.30 | 0.58 | 0.5896 | |
X/GR | 3.27 | 3.05 | 0.0728 | |
V/X | 13.05 | 13.84 | −0.0605 | |
GE/X | 3.72 | 2.37 | 0.3867 | |
X/X | 31.57 | 35.13 | −0.1100 |
Causative Factor/Intercept | No Clustering | |||||||
---|---|---|---|---|---|---|---|---|
Cluster 1 | Cluster 2 | Cluster 3 | ||||||
Intercept | −8.125 | −8.783 | −17.097 | 1.415 | ||||
SE | RC | SE | RC | SE | RC | SE | RC | |
Elevation | √ | 1.838 | ||||||
Distance to river | √ | 2.801 | √ | 4.473 | ||||
NDVI | √ | −0.597 | √ | 0.709 | ||||
NDWI | √ | 0.276 | ||||||
Catchment area | √ | −0.156 | ||||||
Terrain surface texture | √ | 1.295 | √ | 0.906 | √ | 0.908 | ||
Slope gradient | √ | 0.255 | √ | 5.476 | √ | 4.256 | ||
Lithology | √ | −1.191 | ||||||
TWI | √ | 0.671 | √ | 4.470 | √ | −13.190 | ||
Catchment slope | √ | 0.400 | √ | 3.643 | ||||
TRI | √ | 1.340 | √ | 3.859 | ||||
Terrain surface convexity | √ | 0.836 | √ | 13.433 | ||||
Distance to fault | √ | 0.286 | ||||||
TPT | √ | 0.573 | √ | 1.819 | ||||
Terrain curvature | √ | −0.648 | √ | −1.322 | √ | −0.346 | ||
Slope aspect | √ | −0.297 | √ | −0.898 | ||||
Slope form | √ | 0.012 | √ | −0.184 |
Causative Factor | Cluster 1 | Cluster 2 | Cluster 3 |
---|---|---|---|
TOL/VIF | |||
Elevation | |||
Distance to river | 0.940/1.064 | ||
NDVI | 0.944/1.059 | ||
NDWI | |||
Catchment area | |||
Terrain surface texture | 0.977/1.023 | 0.944/1.060 | |
Slope gradient | 0.648/1.543 | 0.402/2.489 | |
Lithology | |||
TWI | 0.741/1.350 | 0.408/2.451 | |
Catchment slope | 0.612/1.634 | ||
TRI | 0.401/2.494 | ||
Terrain surface convexity | 0.538/1.860 | ||
Distance to fault | |||
TPI | 0.775/1.291 | ||
Terrain curvature | 0.812/1.231 | 0.907/1.102 | |
Slope aspect | 0.961/1.041 | ||
Slope form | 0.999/1.001 |
Methods | Overall Accuracy |
---|---|
LR | 80.26% |
SVM | 83.74% |
DT | 84.13% |
LR_K3 | 85.32% |
Causative Factor/Intercept | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Cluster 1 | Cluster 2 | Cluster 1 | Cluster 2 | Cluster 3 | Cluster 4 | |||||||
Intercept | −3.600 | −0.508 | −17.628 | −30.784 | −50.719 | −12.063 | ||||||
SE | RC | SE | RC | SE | RC | SE | RC | SE | RC | SE | RC | |
Elevation | √ | 3.321 | √ | 4.392 | √ | 20.754 | ||||||
Distance to river | √ | 4.473 | √ | 7.241 | √ | 13.396 | √ | 3.392 | ||||
NDVI | √ | 0.709 | ||||||||||
NDWI | √ | 3.447 | ||||||||||
Catchment area | ||||||||||||
Terrain surface texture | √ | 0.906 | √ | 0.908 | √ | 17.378 | √ | 2.841 | ||||
Slope gradient | √ | 5.476 | ||||||||||
Lithology | √ | 1.350 | √ | 3.513 | ||||||||
TWI | √ | 4.470 | √ | 14.754 | √ | −3.863 | √ | 0.400 | ||||
Catchment slope | √ | 3.643 | √ | 3.990 | ||||||||
TRI | ||||||||||||
Terrain surface convexity | √ | 7.693 | √ | 31.940 | ||||||||
Distance to fault | ||||||||||||
TPT | √ | 1.819 | √ | 3.560 | √ | −2.669 | √ | 0.778 | ||||
Terrain curvature | √ | −1.322 | √ | −1.286 | ||||||||
Slope aspect | √ | −0.898 | √ | −1.151 | ||||||||
Slope form | √ | −0.184 | √ | −0.519 |
Causative Factor | (TOL/VIF) | (TOL/VIF) | ||||
---|---|---|---|---|---|---|
Cluster 1 | Cluster 2 | Cluster 1 | Cluster 2 | Cluster 3 | Cluster 4 | |
Elevation | 0.569/1.756 | 0.861/1.162 | 0.464/2.154 | |||
Distance to river | 0.934/1.070 | 0.563/1.777 | 0.406/2.462 | 0.985/1.016 | ||
NDVI | ||||||
NDWI | 0.915/1.093 | 0.969/1.032 | ||||
Catchment area | ||||||
Terrain surface texture | 0.975/1.026 | 0.670/1.493 | 0.946/1.057 | |||
Slope gradient | ||||||
Lithology | 0.977/1.023 | 0.852/1.173 | 0.864/1.157 | |||
TWI | 0.789/1.268 | 0.949/1.054 | 0.774/1.291 | 0.627/1.594 | ||
Catchment slope | 0.806/1.240 | 0.632/1.581 | ||||
TRI | ||||||
Terrain surface convexity | 0.958/1.043 | 0.780/1.282 | ||||
Distance to fault | ||||||
TPI | 0.975/1.026 | 0.931/1.074 | 0.912/1.097 | 0.638/1.567 | ||
Terrain curvature | 0.908/1.101 | 0.998/1.002 | ||||
Slope aspect | 0.997/1.003 | 0.879/1.138 | ||||
Slope form | 0.685/1.460 |
Clusters | Statistics | ||||
---|---|---|---|---|---|
−2ln Likelihood | −2ln L0 | Goodness of Fit | Pseudo R2 | ||
No clustering | 68,666.849 | 36,819.425 | 69,332.399 | 0.463 | |
Cluster 1 | 15,559.511 | 8542.172 | 215.389 | 0.451 | |
Cluster 2 | 27,105.308 | 10,245.806 | 2833.666 | 0.622 | |
Cluster 1 | 21,731.018 | 1738.480 | 1887.318 | 0.920 | |
Cluster 2 | 62,526.249 | 46,769.634 | 3962.812 | 0.252 | |
Cluster 3 | 12,830.029 | 3412.788 | 2805.024 | 0.734 | |
Cluster 1 | 24,014.293 | 17,722.546 | 1954.458 | 0.262 | |
Cluster 2 | 16,054.908 | 5025.186 | 19,513.817 | 0.687 | |
Cluster 3 | 10,818.555 | 2704.639 | 2940.536 | 0.750 | |
Cluster 4 | 11,601.296 | 7865.679 | 34,575.656 | 0.322 |
Methods | Overall Accuracy |
---|---|
LR_K2 | 81.85% |
LR_K3 | 85.32% |
LR_K4 | 91.76% |
Factors | Potential Rating | Weights Wi | ||||
---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | ||
Elevation (m) | >1000 | >750–1000 | >500–750 | 250–500 | <250 | 0.080 |
Distance to river (m) | >4000 | >3000–4000 | >2000–3000 | 1000–2000 | <1000 | 0.078 |
Distance to main towns (m) | >4000 | >3000–4000 | >2000–3000 | 1000–2000 | <1000 | 0.212 |
Landslide susceptibility map | Very high | High | Medium | Low | 0.320 | |
Slope gradient (°) | >25 | >15–25 | >10–15 | 5–10 | <5 | 0.246 |
Slope aspect | N | NE, NW | E, W | SE, SW | S, Flat | 0.064 |
© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Wang, Q.; Wang, Y.; Niu, R.; Peng, L. Integration of Information Theory, K-Means Cluster Analysis and the Logistic Regression Model for Landslide Susceptibility Mapping in the Three Gorges Area, China. Remote Sens. 2017, 9, 938. https://doi.org/10.3390/rs9090938
Wang Q, Wang Y, Niu R, Peng L. Integration of Information Theory, K-Means Cluster Analysis and the Logistic Regression Model for Landslide Susceptibility Mapping in the Three Gorges Area, China. Remote Sensing. 2017; 9(9):938. https://doi.org/10.3390/rs9090938
Chicago/Turabian StyleWang, Qian, Yi Wang, Ruiqing Niu, and Ling Peng. 2017. "Integration of Information Theory, K-Means Cluster Analysis and the Logistic Regression Model for Landslide Susceptibility Mapping in the Three Gorges Area, China" Remote Sensing 9, no. 9: 938. https://doi.org/10.3390/rs9090938