Integrating Cellular Automata with Unsupervised Deep-Learning Algorithms: A Case Study of Urban-Sprawl Simulation in the Jingjintang Urban Agglomeration, China
Abstract
:1. Introduction
2. Methodology
2.1. DBN
- Unsupervised pretraining stage: (1) Train the bottom RBM with CD on training data v being the visible units; (2) freeze weights matrix W and bias a, b of the first RBM, and the state of the hidden units is inferred and used as the input of the next higher RBM; (3) next higher RBM is stacked on top of the previous lower RBM after training; (4) iterate Steps 2 and 3 for the desired number of layers, each time upward propagating either samples or mean values.
- Supervised fine-tuning stage: After an unsupervised pretraining stage, all parameters need to be slightly adjusted in supervised manner until DBN loss function reaches its minimum. In this paper, a logistic regression layer periodically works in the top-level RBM during the supervised fine-tuning stage.
2.2. SDA
- Unsupervised pretrain stage: (1): Train the bottom DAE through the above steps, and an encoder is obtained when the first layer is trained; (2) the feature representation vector is obtained by this encoder on the original input data and regarded as the hidden layer vector, which is used to obtain and train the encoder of the second SDA layer; (3) iterate Steps 1 and 2 for the desired number of SDA layers.
- Supervised fine-tuning stage: When the entire pretraining stage is over, the top layer is the final output layer. With this output as the base layer for logistic regression errors throughout the SDA structure, fine-tuning global parameters are adjusted.
2.3. Proposed Geographical CA Model
2.4. Accuracy Assessment
3. Proposed-Model Implementation
3.1. Study Area
3.2. Data Preprocessing
3.2.1. Land-Use Data
3.2.2. Neighborhood Conditions
3.2.3. Global Spatial Variables
3.3. Model Design and Computational Environment
3.4. Simulation Results and Comparisons
4. Discussion and Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Spatial Variable | Value Range |
---|---|
Urban sprawl in 2000–2010 | Remained nonurban area: 0; converted to urban area: 1; remained urban area: 2 |
Distance to airport | 0–175,594 m |
Distance to city administrative center | 0–129,142 m |
Distance to town administrative center | 0–47,261 m |
Distance to county administrative center | 0–63,279 m |
Distance to reservoir | 0–44,457 m |
Distance to river | 0–88,911 m |
Distance to railway station | 0–109,976 m |
Distance to motorway | 0–70,052 m |
Distance to trunkway | 0–21,979 m |
Distance to railway | 0–33,278 m |
Urban cells in neighborhood | 0–48 |
Land use type | urban area: 1; nonurban area: 0 |
Elevation | −52–2224 m |
Slope | 0–69 |
Description | Symbol | DBN | SDA |
---|---|---|---|
Input dimension | n_ins | 11 | 11 |
Output dimension | n_out | 3 | 3 |
Intermediate layer size | hidden_layer_sizes | [30, 30, 30] | [30, 30, 30] |
Number of epochs for pretraining | pre-training_epochs | 300 | 300 |
Maximal number of iterations of running optimizer | training_epochs | 3000 | 3000 |
Learning rate used in pretraining | pretrain_lr | 0.01 | 0.001 |
Learning rate used in fine-tuning stage | finetune_lr | 0.1 | 0.01 |
SDA-CA | DBN-CA | ANN-CA | LR-CA | |
---|---|---|---|---|
2005 | ||||
Beijing | 0.583 | 0.385 | 0.243 | 0.415 |
Tianjin | 0.581 | 0.403 | 0.280 | 0.505 |
Tangshan | 0.579 | 0.367 | 0.320 | 0.315 |
2010 | ||||
Beijing | 0.468 | 0.343 | 0.277 | 0.294 |
Tianjin | 0.523 | 0.364 | 0.313 | 0.440 |
Tangshan | 0.432 | 0.332 | 0.299 | 0.199 |
SDA–CA | DBN–CA | ANN–CA | LR–CA | |
---|---|---|---|---|
2005 | ||||
Hit | 244528 | 230445 | 219001 | 230811 |
Miss | 20247 | 34330 | 45774 | 35547 |
False alarm | 12555 | 16195 | 11364 | 33964 |
Correcct rejection | 4514091 | 4510451 | 4515282 | 4491099 |
2010 | ||||
Hit | 255148 | 236676 | 231238 | 235346 |
Miss | 28638 | 47110 | 52548 | 48440 |
False alarm | 32785 | 36148 | 42303 | 64997 |
Correcct rejection | 4474850 | 4471487 | 4465332 | 4442638 |
NP | ED | LSI | AWMPFD | AI | S_i | |
---|---|---|---|---|---|---|
2005 | ||||||
observed | 142 | 1.019 | 23.889 | 1.175 | 95.539 | - |
SDA-CA | 179 | 0.855 | 20.385 | 1.159 | 96.166 | |
DBN-CA | 193 | 0.815 | 19.842 | 1.154 | 96.196 | |
ANN-CA | 229 | 0.818 | 20.614 | 1.155 | 95.905 | |
LR-CA | 365 | 0.591 | 13.801 | 1.089 | 97.513 | |
2010 | ||||||
observed | 179 | 1.174 | 26.579 | 1.186 | 95.187 | - |
SDA-CA | 191 | 0.831 | 18.725 | 1.145 | 96.688 | |
DBN-CA | 229 | 0.884 | 20.384 | 1.148 | 96.281 | |
ANN-CA | 215 | 0.635 | 14.613 | 1.122 | 97.390 | |
LR-CA | 361 | 1.080 | 23.705 | 1.101 | 95.846 |
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Ou, C.; Yang, J.; Du, Z.; Zhang, X.; Zhu, D. Integrating Cellular Automata with Unsupervised Deep-Learning Algorithms: A Case Study of Urban-Sprawl Simulation in the Jingjintang Urban Agglomeration, China. Sustainability 2019, 11, 2464. https://doi.org/10.3390/su11092464
Ou C, Yang J, Du Z, Zhang X, Zhu D. Integrating Cellular Automata with Unsupervised Deep-Learning Algorithms: A Case Study of Urban-Sprawl Simulation in the Jingjintang Urban Agglomeration, China. Sustainability. 2019; 11(9):2464. https://doi.org/10.3390/su11092464
Chicago/Turabian StyleOu, Cong, Jianyu Yang, Zhenrong Du, Xin Zhang, and Dehai Zhu. 2019. "Integrating Cellular Automata with Unsupervised Deep-Learning Algorithms: A Case Study of Urban-Sprawl Simulation in the Jingjintang Urban Agglomeration, China" Sustainability 11, no. 9: 2464. https://doi.org/10.3390/su11092464