Cluster Analysis and Discriminant Analysis for Determining Post-Earthquake Road Recovery Patterns †
Abstract
:1. Introduction
2. Materials and Methods
2.1. Vehicle Tracking Map
2.2. System
2.2.1. Hardware
2.2.2. Software
2.3. Data Processing
- (1)
- The vehicle tracking maps constructed from the G-BOOK telematics data were provided in the Google Maps KMZ format. For our analysis, we first converted the KMZ files into SHP files (i.e., shape files), which are compatible with ArcGIS using the “ogr2ogr” function [22] on the Linux operating system [23].The data coordinates were converted from the terrestrial latitude and longitude into the x and y coordinates in a rectangular coordinate system.
- (2)
- After merging the daily data into weekly data and removing duplicates, we were able to calculate the exact available road distance for a given week.
- (3)
- Next, we calculated the proportion of the cumulative distance up to the specified date and considered the cumulative distance up to 30 September 2011, to be 100%.
2.4. Cluster Analysis
2.5. Discriminant Analysis for Validation of the Cluster Analysis Results
2.5.1. Canonical Discriminant Analysis
2.5.2. Canonical Discriminant Function Determination
3. Results
3.1. The Cluster Analysis Results
3.2. Validated Results of Discriminant Analysis on Classification
3.2.1. Standardized Canonical Discriminant Function
3.2.2. Unstandardized Canonical Discriminant
0.356 × X8 − 0.190 × X9 − 0.001 × X10 − 14.3
0.171 × X8 + 0.169 × X9 + 0.119 × X10 − 1.76
4. Discussion
4.1. Data Collection on Factors Affecting Road Recovery
4.1.1. Geographic Location and Topography
- The 2011 Digital Road Map data in the SHP file only provide the latitude and longitude and are generally saved as x and y attributes in the geometry. We used the “add z value” function of GIS to add the digital elevation model (DEM) data [29] to the z values of the road data.
- The road data are stored in intervals in the SHP file’s properties. We calculated the average of the z values (i.e., the average elevation) of the roads in intervals and saved them together in the attribute table.
- We calculated the distance of roads with an average elevation of less than 50 m, 50 to 100 m, 100 to 200 m, 200 to 500 m, and more than 500 m for each municipality and then calculated the percentage of road length at each elevation compared to the total road length of the municipality.
4.1.2. Population Density
4.1.3. Damage
4.1.4. Road Importance
4.1.5. Road Density
4.1.6. Snow
4.2. Pearson Correlation Analysis
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Cluster | Municipality | Mar.—3 w | Mar.—4 w | Apr.—1 w | Apr.—2 w | Apr.—3 w | Apr.—4 w | May | Jun. | Jul. | Aug. | Sep. |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | Hirono-machi | 38 | 69 | 71 | 88 | 92 | 93 | 97 | 98 | 99 | 100 | 100 |
1 | Minamisoma-shi | 34 | 71 | 83 | 89 | 93 | 93 | 95 | 97 | 98 | 99 | 100 |
1 | Shinchi-machi | 44 | 64 | 77 | 86 | 88 | 94 | 97 | 98 | 98 | 99 | 100 |
1 | Kunimi-machi | 33 | 71 | 79 | 88 | 89 | 89 | 98 | 98 | 98 | 98 | 100 |
1 | Tamura-shi | 43 | 71 | 80 | 87 | 91 | 94 | 96 | 96 | 98 | 99 | 100 |
1 | Aizubange-machi | 41 | 69 | 81 | 85 | 89 | 92 | 96 | 97 | 97 | 100 | 100 |
1 | Nishiaizu-machi | 39 | 67 | 81 | 88 | 88 | 88 | 99 | 100 | 100 | 100 | 100 |
2 | Iitate-mura | 55 | 63 | 67 | 76 | 82 | 86 | 93 | 93 | 100 | 100 | 100 |
2 | Kawamata-machi | 56 | 71 | 71 | 76 | 85 | 90 | 95 | 96 | 98 | 100 | 100 |
2 | Tenei-mura | 49 | 63 | 72 | 76 | 80 | 85 | 97 | 97 | 98 | 99 | 100 |
2 | Furudono-machi | 57 | 58 | 59 | 73 | 86 | 93 | 93 | 93 | 99 | 100 | 100 |
2 | Samegawa-mura | 72 | 72 | 73 | 76 | 78 | 95 | 98 | 98 | 98 | 100 | 100 |
2 | Inawashiro-machi | 52 | 68 | 71 | 72 | 77 | 85 | 95 | 97 | 98 | 100 | 100 |
2 | Yugawa-mura | 59 | 68 | 69 | 78 | 78 | 83 | 89 | 96 | 96 | 98 | 100 |
3 | Katsurao-mura | 60 | 74 | 96 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
3 | Kawauchi-mura | 40 | 95 | 98 | 98 | 99 | 99 | 99 | 99 | 100 | 100 | 100 |
3 | Kori-machi | 57 | 86 | 93 | 95 | 96 | 96 | 100 | 100 | 100 | 100 | 100 |
3 | Kagamiishi-machi | 57 | 85 | 89 | 95 | 98 | 98 | 98 | 98 | 99 | 100 | 100 |
3 | Motomiya-shi | 69 | 87 | 93 | 95 | 97 | 98 | 99 | 99 | 100 | 100 | 100 |
3 | Ono-machi | 51 | 88 | 95 | 95 | 97 | 97 | 98 | 98 | 98 | 98 | 100 |
3 | Hirata-mura | 57 | 82 | 90 | 95 | 96 | 96 | 97 | 97 | 100 | 100 | 100 |
3 | Nakajima-mura | 58 | 81 | 88 | 92 | 97 | 97 | 97 | 97 | 98 | 98 | 100 |
3 | Tamakawa-mura | 52 | 78 | 85 | 93 | 98 | 100 | 100 | 100 | 100 | 100 | 100 |
3 | Yabuki-machi | 63 | 90 | 91 | 94 | 96 | 98 | 98 | 100 | 100 | 100 | 100 |
4 | Soma-shi | 54 | 77 | 84 | 86 | 92 | 95 | 96 | 96 | 96 | 99 | 100 |
4 | Date-shi | 55 | 71 | 81 | 88 | 93 | 95 | 96 | 97 | 98 | 100 | 100 |
4 | Nihonmatsu-shi | 59 | 75 | 80 | 84 | 87 | 91 | 94 | 95 | 97 | 99 | 100 |
4 | Otama-mura | 46 | 75 | 84 | 89 | 91 | 93 | 94 | 94 | 94 | 100 | 100 |
4 | Hanawa-machi | 60 | 65 | 75 | 85 | 87 | 88 | 88 | 88 | 88 | 88 | 100 |
4 | Ishikawa-machi | 57 | 69 | 89 | 92 | 93 | 97 | 97 | 97 | 100 | 100 | 100 |
4 | Izumizaki-mura | 55 | 78 | 87 | 89 | 91 | 95 | 96 | 97 | 99 | 100 | 100 |
4 | Nishigo-mura | 53 | 71 | 82 | 91 | 92 | 99 | 100 | 100 | 100 | 100 | 100 |
4 | Aizuwakamatsu-shi | 55 | 69 | 80 | 83 | 86 | 92 | 95 | 97 | 98 | 100 | 100 |
4 | Kitakata-shi | 55 | 61 | 74 | 86 | 91 | 92 | 94 | 95 | 97 | 98 | 100 |
5 | Iwaki-shi | 60 | 81 | 88 | 90 | 93 | 95 | 97 | 98 | 99 | 99 | 100 |
5 | Fukushima-shi | 66 | 80 | 85 | 88 | 90 | 95 | 96 | 98 | 99 | 99 | 100 |
5 | Koriyama-shi | 66 | 84 | 89 | 91 | 94 | 96 | 97 | 98 | 99 | 99 | 100 |
5 | Miharu-machi | 60 | 80 | 83 | 85 | 90 | 97 | 99 | 99 | 100 | 100 | 100 |
5 | Sukagawa-shi | 64 | 80 | 85 | 90 | 92 | 95 | 97 | 97 | 98 | 100 | 100 |
5 | Asakawa-machi | 67 | 76 | 79 | 86 | 95 | 98 | 99 | 99 | 99 | 99 | 100 |
5 | Shirakawa-shi | 67 | 80 | 86 | 89 | 92 | 92 | 97 | 98 | 99 | 99 | 100 |
5 | Tanagura-machi | 82 | 86 | 89 | 94 | 98 | 98 | 99 | 99 | 100 | 100 | 100 |
5 | Yamatsuri-machi | 81 | 83 | 90 | 93 | 93 | 93 | 93 | 100 | 100 | 100 | 100 |
6 | Aizumisato-machi | 39 | 51 | 71 | 75 | 81 | 93 | 93 | 96 | 98 | 99 | 100 |
6 | Mishima-machi | 16 | 54 | 80 | 80 | 82 | 82 | 84 | 98 | 98 | 98 | 100 |
6 | Yanaizu-machi | 29 | 50 | 87 | 92 | 92 | 94 | 98 | 100 | 100 | 100 | 100 |
7 | Bandai-machi | 28 | 52 | 56 | 59 | 59 | 70 | 95 | 97 | 98 | 98 | 100 |
7 | Kaneyama-machi | 0 | 13 | 61 | 61 | 64 | 64 | 65 | 97 | 100 | 100 | 100 |
7 | Kitashiobara-mura | 39 | 44 | 48 | 54 | 71 | 82 | 97 | 98 | 98 | 98 | 100 |
7 | Showa-mura | 0 | 33 | 46 | 47 | 70 | 73 | 95 | 95 | 95 | 95 | 100 |
7 | Hinoemata-mura | 0 | 0 | 0 | 0 | 0 | 31 | 61 | 100 | 100 | 100 | 100 |
7 | Minamiaizu-machi | 32 | 47 | 59 | 64 | 64 | 77 | 84 | 88 | 99 | 99 | 100 |
7 | Shimogo-machi | 41 | 57 | 59 | 62 | 75 | 85 | 93 | 94 | 99 | 99 | 100 |
7 | Tadami-machi | 4 | 4 | 27 | 38 | 53 | 55 | 78 | 90 | 94 | 95 | 100 |
Function | Eigenvalue | % of Variance | Cumulative % | Canonical Correlation |
---|---|---|---|---|
1 | 8.366 a | 65.6 | 65.6 | 0.945 |
2 | 2.648 a | 20.8 | 86.3 | 0.852 |
3 | 1.002 a | 7.9 | 94.2 | 0.707 |
4 | 0.630 a | 4.9 | 99.1 | 0.622 |
5 | 0.074 a | 0.6 | 99.7 | 0.262 |
6 | 0.042 a | 0.3 | 100.0 | 0.202 |
Test of Function(s) | Wilks’ Lambda | Chi-Square | df | Sig. |
---|---|---|---|---|
1 | 0.008 | 214.775 | 60 | 0.000 |
2 | 0.075 | 115.227 | 45 | 0.000 |
3 | 0.274 | 57.634 | 32 | 0.004 |
4 | 0.548 | 26.743 | 21 | 0.180 |
5 | 0.894 | 5.010 | 12 | 0.958 |
6 | 0.959 | 1.851 | 5 | 0.869 |
Cluster | Mar.—3 w | Mar.—4 w | Apr.—1 w | Apr.—2 w | Apr.—3 w | Apr.—4 w | May | Jun. | Jul. | Aug. | Sep. |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 39 | 69 | 79 | 87 | 90 | 92 | 97 | 98 | 98 | 99 | 100 |
2 | 57 | 66 | 69 | 75 | 81 | 88 | 94 | 96 | 98 | 100 | 100 |
3 | 56 | 85 | 92 | 95 | 97 | 98 | 99 | 99 | 99 | 100 | 100 |
4 | 55 | 71 | 82 | 87 | 90 | 94 | 95 | 96 | 97 | 98 | 100 |
5 | 68 | 81 | 86 | 90 | 93 | 95 | 97 | 98 | 99 | 100 | 100 |
6 | 28 | 52 | 79 | 82 | 85 | 90 | 92 | 98 | 99 | 99 | 100 |
7 | 18 | 31 | 45 | 48 | 57 | 67 | 84 | 95 | 98 | 98 | 100 |
Independent Variable | Function | |
---|---|---|
1 | 2 | |
Mar.—3 w | 0.377 | 1.30 |
Mar.—4 w | 1.00 | 0.127 |
Apr.—1 w | −1.12 | 1.20 |
Apr.—2 w | 1.29 | −2.85 |
Apr.—3 w | 0.607 | 2.54 |
Apr.—4 w | −0.396 | −2.00 |
May | −0.870 | 0.055 |
June | 0.836 | −0.402 |
July | −0.374 | 0.333 |
August | −0.003 | 0.228 |
Independent Variable | Function | |
---|---|---|
1 | 2 | |
Mar.—3 w | 0.569 * | 0.433 |
Mar.—4 w | 0.664 * | 0.010 |
Apr.—1 w | 0.576 * | −0.260 |
Apr.—2 w | 0.617 * | −0.314 |
Apr.—3 w | 0.477 * | −0.208 |
Apr.—4 w | 0.476 * | −0.171 |
May | 0.287 | −0.082 |
June | 0.180 | −0.084 |
July | 0.067 | 0.014 |
August | 0.086 | 0.030 |
Independent Variable | Function | ||
---|---|---|---|
1 | 2 | ||
Mar.—3 w | X1 | 0.039 | 0.136 |
Mar.—4 w | X2 | 0.104 | 0.013 |
Apr.—1 w | X3 | −0.123 | 0.131 |
Apr.—2 w | X4 | 0.148 | −0.329 |
Apr.—3 w | X5 | 0.063 | 0.263 |
Apr.—4 w | X6 | −0.053 | −0.270 |
May | X7 | −0.144 | 0.009 |
June | X8 | 0.356 | −0.171 |
July | X9 | −0.190 | 0.169 |
August | X10 | −0.001 | 0.119 |
(Constant) | −14.3 | −1.76 |
Cluster | Function | |
---|---|---|
1 | 2 | |
1 | 0.336 | −2.33 |
2 | −0.367 | 1.58 |
3 | 2.39 | −0.412 |
4 | 0.702 | −0.346 |
5 | 2.41 | 1.78 |
6 | −2.15 | −3.27 |
7 | −5.74 | 0.824 |
Cluster | Predicted Group Membership | Total | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | ||||
Original | Count | 1 | 6 | 0 | 0 | 1 | 0 | 0 | 0 | 7 |
2 | 0 | 6 | 0 | 1 | 0 | 0 | 0 | 7 | ||
3 | 0 | 0 | 9 | 0 | 1 | 0 | 0 | 10 | ||
4 | 1 | 0 | 0 | 9 | 0 | 0 | 0 | 10 | ||
5 | 0 | 0 | 0 | 0 | 9 | 0 | 0 | 9 | ||
6 | 0 | 0 | 0 | 0 | 0 | 3 | 0 | 3 | ||
7 | 0 | 0 | 0 | 0 | 0 | 0 | 8 | 8 | ||
% | 1 | 85.7 | 0.0 | 0.0 | 14.3 | 0.0 | 0.0 | 0.0 | 100.0 | |
2 | 0.0 | 85.7 | 0.0 | 14.3 | 0.0 | 0.0 | 0.0 | 100.0 | ||
3 | 0.0 | 0.0 | 90.0 | 0.0 | 10.0 | 0.0 | 0.0 | 100.0 | ||
4 | 10.0 | 0.0 | 0.0 | 90.0 | 0.0 | 0.0 | 0.0 | 100.0 | ||
5 | 0.0 | 0.0 | 0.0 | 0.0 | 100.0 | 0.0 | 0.0 | 100.0 | ||
6 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 100.0 | 0.0 | 100.0 | ||
7 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 100.0 | 100.0 |
Cluster | Elevations | ||||
---|---|---|---|---|---|
<50 m | 50–100 m | 100–200 m | 200–500 m | >500 m | |
Pearson Correlation | −0.265 | −0.232 | −0.291 | 0.150 | 0.311 |
Sig. | 0.053 | 0.091 | 0.033 | 0.279 | 0.022 |
Cluster | Road Importance | Road Density | Population Density | Measured Seismic Intensities | Road Closure Rate Due to Snow |
---|---|---|---|---|---|
Pearson Correlation | 0.417 | −0.416 | −0.190 | −0.637 | 0.729 |
Sig. | 0.002 | 0.002 | 0.169 | 0.000 | 0.000 |
Cluster | Elevations | ||||
---|---|---|---|---|---|
<50 m | 50–100 m | 100–200 m | 200–500 m | >500 m | |
Pearson Correlation | −0.370 | 0.129 | 0.222 | 0.402 | 0.204 |
Sig. | 0.020 | 0.435 | 0.174 | 0.011 | 0.214 |
Cluster | Road Importance | Road Density | Population Density | Measured Seismic Intensities | Road Closure Rate Due to Snow |
---|---|---|---|---|---|
Pearson Correlation | 0.365 | −0.242 | −0.163 | −0.081 | 0.145 |
Sig. | 0.022 | 0.137 | 0.321 | 0.624 | 0.380 |
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Wu, J.; Saito, M.; Endo, N. Cluster Analysis and Discriminant Analysis for Determining Post-Earthquake Road Recovery Patterns. Sensors 2022, 22, 2213. https://doi.org/10.3390/s22062213
Wu J, Saito M, Endo N. Cluster Analysis and Discriminant Analysis for Determining Post-Earthquake Road Recovery Patterns. Sensors. 2022; 22(6):2213. https://doi.org/10.3390/s22062213
Chicago/Turabian StyleWu, Jieling, Mitsugu Saito, and Noriaki Endo. 2022. "Cluster Analysis and Discriminant Analysis for Determining Post-Earthquake Road Recovery Patterns" Sensors 22, no. 6: 2213. https://doi.org/10.3390/s22062213
APA StyleWu, J., Saito, M., & Endo, N. (2022). Cluster Analysis and Discriminant Analysis for Determining Post-Earthquake Road Recovery Patterns. Sensors, 22(6), 2213. https://doi.org/10.3390/s22062213