# Parallel Cellular Automata Markov Model for Land Use Change Prediction over MapReduce Framework

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Background Technologies

#### 2.1. Study Area and Data

#### 2.2. MapReduce

_{1}, v

_{1}) and processes it to generate a key-value pair (k

_{2}, v

_{2}) as an intermediate result. Then, the corresponding values of all the same intermediate keys (k

_{2}) are aggregated to generate a list of values for the k

_{2}key list (v

_{2}), which is used as an input to the Reduce function and processed by the Reduce function to obtain the final result list (k

_{3}, v

_{3}). The process can be expressed by the following formula:

#### 2.3. CA Markov Model

## 3. Methods

#### 3.1. Parallel CA-Markov Model Overview

#### 3.1.1. Parallel CA-Markov Structure

#### 3.1.2. Parallel CA-Markov Workflow

- (1)
- Data-processing: Preprocessing and interpreting remote-sensing images to land-use maps, designing multicriteria-evaluation factors, and storing images, land-use data, and multicriteria-evaluation factors into the Hadoop HDFS.
- (2)
- Parallel Markov: Using the overlay method, analyzing two-phase images and land-use data to obtain each cell’s land-use-type transition probability, and calculating the total number of cells in each land-use-type transition direction, and counting the area transition-probability matrix of each land-use type.
- (3)
- Parallel CA: In Cloud-CELUC, C-ENID was used to calculate the cell’s neighborhood influence value. C-MCE was designed to calculate multicriteria-evaluation values, including constraint-evaluation and suitability-evaluation values. These values were then used to calculate the statistical table of comprehensive evaluation of land use.
- (4)
- Transition-direction determination stage: Loop reading each cell’s transition probability from the statistical table of comprehensive-evaluation values in the parallel CA stage and combining the area transfer-probability matrix of each land-use type in the parallel Markov stage to decide a cell’s land-use-type transition direction.
- (5)
- Land-use-change prediction: In our experiment, we used data from 2006 to predict 2013 land-use changes and then evaluate the precision of the parallel CA-Markov model with a Kappa coefficient. Land-use change prediction for 2020 was then obtained.

#### 3.2. Markov Model Parallel Processing (Cloud-Markov)

_{1}represents all cells’ land-use type of the earlier raster image, T

_{2}represents all cells’ land-use type of the later raster image, C

_{mk}represents the cell conversion from land-use type m to land-use type k, i indicates the cell transfer number of C

_{mk}, M is the number of land-use types in a MapReduce node, s is the total cell number of C

_{mk}in a MapReduce node, L is the total number of land-use types, and q is the combined value of the total number of cells and transition probability for C

_{mk}conversion in the entire study area. For example, “100-3.12%” means that there were 100 cells with C

_{mk}conversion, and transition probability was 3.12%. Figure 5 is the flow of Cloud-Markov algorithm. After summing the number of same land-use type transition direction in each node, the area transition matrix was calculated at the Reduce stage.

- (1)
- Map stage:
- ①
- Input <Key,Value>
- ②
- Raster cell’s land-use type conversion analysis

_{mk}. If the value of C

_{mk}is ‘B-A’, it means that the land-use-type of the cell with the same position in different raster images is converted from B into A.

- ③
- Output <Key,Value>

_{mk}, and Value is an integer equal to 1.

- (2)
- Combiner stage:
- ①
- Enter <Key,Value>
- ②
- Calculate the number of each land-use-type conversion direction in each node

_{mk},s), where C

_{mk}is the conversion direction and s is the total number of cells in a MapReduce node where the C

_{mk}land-use-type conversion direction occurs.

- ③
- Output <Key,Value>

_{mk},s).

- (3)
- Reduce stage:
- ①
- Enter <Key,Value>
- ②
- Calculate transition probability

_{mk}is the value that summed C

_{mk}from all MapReduce nodes and S

_{m}is the number of the initial raster image’s cells whose land-use type is m.

- ③
- Output <Key,Value>

_{mk},P

_{mk}), where V

_{mk}is the land-use-type area-conversion matrix and P

_{mk}is the transition-probability matrix.

#### 3.3. Cloud-CELUC

#### 3.3.1. Cell Neighborhood Processing

_{x}were from line K − 1, K, and K + 1, were recorded as K − 1

_{x−1}, K − 1

_{x}, K − 1

_{x+1}, K

_{x−1}, K

_{x+1}, K + 1

_{x−1}, K + 1

_{x}, and K + 1

_{x+1}, and then stored as an array structure into the HDFS.

#### 3.3.2. Multicriteria Evaluation Factors

#### 3.3.3. Parallel Cloud-CELUC Algorithm

_{1}is the cell-state value to be calculated, and H

_{2}and H

_{3}indicate the uplink and downlink cell-state values of H

_{1}. H

_{4}, … H

_{m}are various constraint factors and suitability factors corresponding to the cell, and L

_{m}is the value combined by the cell’s composite-evaluation value of the transition direction and the cell’s corresponding transition direction. For example, If L

_{1}is ‘ba-1.2234’, the evaluation value of the cell (i, j) from the initial land-use type ‘b’ to the final land-use type ‘a’ is ‘1.2234’.

- ①
- Enter <Key,Value>
- ②
- Calculate neighborhood-influence evaluation value (NID)

_{1}and H

_{3}, the neighborhood-influence degree of each cell in H

_{2}was calculated. The calculation formula for the evaluation value of the neighborhood-influence degree of the cell (i,j) corresponding to a class at a certain time is as follows:

- ③
- Calculate Suitability-Evaluation Value (SEV)

- ④
- Calculate constraint-evaluation value (CEV)

- ⑤
- Calculate comprehensive-evaluation value (CELUC)

- ⑥
- Output <Key,Value>

#### 3.4. Cell Land-Use-Type Conversion

- ①
- Calculating the maximum evaluation value from the table of statistical summary of comprehensive evaluation that was obtained from Cloud-CELUC.
- ②
- Loop reading each row of the table. Each row was a key-value pair ((i, j), CELUCs), where (i, j) is the position of the cell, CELUCs means cell (i, j) has N kinds of land-use conversion possibilities (CELUC), and CELUCi means the ith CELUC of the cell.
- ③
- Determining whether the area of the converted land-use type reached the upper area limit of this land-use-type conversion or not.

_{mk}, P

_{mk}) where V

_{mk}is the land-use-type area conversion matrix and P

_{mk}is the land-use transition-probability matrix at the CLOUD-Markov stage.

- ④
- If reaching the upper area limit, the CELUCi of the cell should be marked as 0, meaning that one of the cell (i, j)’s CELUCi was deleted to make sure the CELUCi would not be used in the subsequent steps. Then, it returns to the first step.

- ⑤
- Repeating the above steps until all cells completed conversion, and finally obtaining the prediction of the whole land-use-change distribution, which was stored as an array. Each item of the array was a key-value pair ((i, j), CELUC).

## 4. Results and Discussion

#### 4.1. Model-Efficiency Analysis

#### 4.2. Precision Evaluation and Result Analysis

#### 4.2.1. Precision Evaluation

#### 4.2.2. Land-Use-Change Prediction

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 10.**Running efficiency and acceleration ratio of Cloud-Markov relative to serial-Markov. (

**a**) Running efficiency comparison, (

**b**) acceleration ratio.

**Figure 11.**Running efficiency and acceleration ratio of serial-CELUC relative to Cloud-CELUC. (

**a**) Running efficiency comparison, (

**b**) acceleration ratio.

Level 1. | Level 2 | Definition |
---|---|---|

Construction land (B) | Land for construction (B1), land for transportation (B2) | Land for buildings and structures. |

Agricultural land (A) | Cultivated land (A1), garden (A2) | Land for agricultural production. |

Water area (W) | Waters (W1), swampland (W2) | River surface, lake surface, swamp. |

Nature reserve (N) | Forest (N1), grassland (N2), unused land (N3) | Land with little or no human activity that did not include agricultural land, construction land, and waters. |

Factor Name | Definition | Classification |
---|---|---|

FreLev | Distance from cell to highway. | Cell distance from main road or town center: 0–250, 250–500, 500–750, 750–1000, and 1000–1250 m. |

TownLev | Distance from cell to town center. | |

SubLev | Distance from cell to subway station. | Cell distance to subway or bus station, other roads: 0–100, 100–200, 200–300, 300–400, and 400–500 m. |

BusLev | Distance from cell to bus stop. | |

MainLev | Distance from cell to other roads. | |

TraLev | Distance from cell to train station. | Cell distance to train or bus station: 0–200, 200–400, 400–600, 600–800, and 800–1000 m. |

StaLev | Distance from cell to bus station. | |

CityLev | Distance from cell to county center. | Cell distance to main road or county center: 500–1000, 1000–1500, 1500–2000, and 2000–2500 m. |

Factor Name | Agricultural Land | Construction Land | Nature Reserve |
---|---|---|---|

FreLev | 0.0485 | 0.0461 | 0.0781 |

TownLev | 0.1239 | 0.1332 | 0.1010 |

SubLev | 0.0621 | 0.1320 | 0.0133 |

BusLev | 0.0721 | 0.1110 | 0.0513 |

MainLev | 0.0921 | 0.1102 | 0.0749 |

TraLev | 0.0423 | 0.1333 | 0.0201 |

StaLev | 0.0623 | 0.1321 | 0.0203 |

StaLev | 0.0923 | 0.2021 | 0.0103 |

IP Address | Node Role | CPU | RAM |
---|---|---|---|

192.168.128.1 | Master/Namenode/Jobtracker | Four-core 2.4 Ghz | 4 G |

192.168.128.2 | Slaves/Datanode/Tasktracker | Four-core 2.4 Ghz | 4 G |

192.168.128.3 | Slaves/Datanode/Tasktracker | Four-core 2.4 Ghz | 4 G |

192.168.128.4 | Slaves/Datanode/Tasktracker | Four-core 2.4 Ghz | 4 G |

192.168.128.5 | Slaves/Datanode/Tasktracker | Four-core 2.4 Ghz | 4 G |

2013 | Agricultural Land | Construction Land | Nature Reserve | Total | |
---|---|---|---|---|---|

2006 | |||||

Agricultural land | 1282.95 | 409.71 | 95.67 | 1788.33 | |

Construction land | 210.94 | 1381.69 | 12.52 | 1605.15 | |

Nature-reserve land | 93.39 | 50.79 | 4409.60 | 4553.78 | |

Total | 1587.28 | 1842.19 | 4517.79 | 7947.26 |

2013 | Agricultural Land | Construction Land | Nature Reserve | |
---|---|---|---|---|

2006 | ||||

Agricultural land | 71.74 | 22.91 | 5.35 | |

Construction land | 13.14 | 86.08 | 0.78 | |

Nature-reserve land | 2.05 | 1.12 | 96.83 |

Simulated Data | Nature Reserve | Non-Nature Reserve | Total | Accuracy | Kappa | |
---|---|---|---|---|---|---|

Classified Data | ||||||

Nature-reserve land | 4221.35 | 288.47 | 4509.82 | 93.60% | 0.86 | |

Non-nature-reserve land | 296.44 | 3431.50 | 3727.94 | 92.05% | ||

Total | 4517.79 | 3717.97 |

Simulated Data | Construction Land | Non-Construction Land | Total | Accuracy | Kappa | |
---|---|---|---|---|---|---|

Classified Data | ||||||

Construction land | 1391.41 | 452.77 | 1844.18 | 75.45% | 0.68 | |

Non-construction land | 450.78 | 5942.80 | 6393.58 | 92.95% | ||

Total | 1842.19 | 6395.57 |

Simulated Data | Agricultural Land | Non-Agricultural Land | Total | Accuracy | Kappa | |
---|---|---|---|---|---|---|

Classified Data | ||||||

Agricultural land | 1152.64 | 427.17 | 1579.81 | 72.96% | 0. 66 | |

Non-agricultural land | 434.65 | 6223.30 | 6657.95 | 93.47% | ||

Total | 1587.29 | 6650.47 |

2020 | Agricultural Land | Construction Land | Nature Reserve | Total | |
---|---|---|---|---|---|

2013 | |||||

Agricultural land | 1133.35 | 361.94 | 84.52 | 1579.81 | |

Construction land | 242.35 | 1587.45 | 14.38 | 1844.18 | |

Nature-reserve land | 92.49 | 50.30 | 4367.03 | 4509.82 | |

Total | 1468.19 | 1999.69 | 4465.93 | 7933.81 |

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## Share and Cite

**MDPI and ACS Style**

Kang, J.; Fang, L.; Li, S.; Wang, X.
Parallel Cellular Automata Markov Model for Land Use Change Prediction over MapReduce Framework. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 454.
https://doi.org/10.3390/ijgi8100454

**AMA Style**

Kang J, Fang L, Li S, Wang X.
Parallel Cellular Automata Markov Model for Land Use Change Prediction over MapReduce Framework. *ISPRS International Journal of Geo-Information*. 2019; 8(10):454.
https://doi.org/10.3390/ijgi8100454

**Chicago/Turabian Style**

Kang, Junfeng, Lei Fang, Shuang Li, and Xiangrong Wang.
2019. "Parallel Cellular Automata Markov Model for Land Use Change Prediction over MapReduce Framework" *ISPRS International Journal of Geo-Information* 8, no. 10: 454.
https://doi.org/10.3390/ijgi8100454