# Urban Parcel Grouping Method Based on Urban Form and Functional Connectivity Characterisation

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Materials and Methods

#### 3.1. Study Area and Data Source

#### 3.1.1. Study Area

#### 3.1.2. Experimental Urban Parcel Datasets and Environment

#### 3.2. Infiltration Behaviours of Components among Urban Parcels

**Definition**

**1.**

**Dominant function**: Urban function for individual parcels is identified by examining dominant POI types within the parcels. A dominant function within a parcel is defined as the POI type that has accounted for more than 50% of all POIs within the parcel.

**Definition**

**2.**

**Functional complementarity behaviour**: In different parcels, the types of functions and the degree of functional mixing usually differ, which produces a functional requirement between adjacent parcels. A fine-grained mixing of residential, commercial, and recreational land use may enable local residents to walk or bike to desired destinations, which increases the frequency of interaction among parcels. Over time, a functional complementarity behaviour is formed between adjacent parcels.

_{ij}= Percent of land use i in parcel j.

_{j}= Number of represented land uses in all parcels.

**Definition**

**3.**

**Imitation behaviour**: This kind of behaviour describes the similarity of the components between adjacent parcels. When two parcels are adjacent and both parcels are composed of three parts—residential area, shopping centre, and catering service—then we conclude that there are imitation behaviours between two parcels. Thus, we can construct a vector to describe the composition of a parcel. Each attribute (dimension) in the vector corresponds to a land use type. The value of each attribute is 1 or 0, where “1” indicates that a certain land use type exists in the current parcel, and “0” indicates that it does not exist (Figure 4).

#### 3.3. Expression and Establishment of Adjacent Parcel Relationship

#### 3.3.1. Identification of Adjacent Relationships among Parcels

**connecting triangle**. If two parcels were connected by connecting triangles, we named the two parcels

**conflicting parcels**, which were evaluated based on the condition of ‘whether the three vertices of a triangle belong to the same polygon boundary’. When two parcels consisted of conflicting parcels, we considered them to have an adjacent relationship. The CDT was constructed for all parcels by analysing whether an adjacent relationship existed between any two parcels. Considering that a long and thin triangle easily produces an incorrect assessment of the adjacency relationship between two parcels (refer to Figure 5), it was necessary to eliminate the long and thin triangles in connecting triangles.

_{1}and P

_{2}is obtained from the edges of the connecting triangles, such as triangle ABC (AB). The heights (h) of all connecting triangles between two adjacent parcels are calculated and used to calculate the proximity between two adjacent parcels.

#### 3.3.2. Method for Measuring the Proximity of Parcels

#### 3.4. Urban Parcel Grouping Method

#### 3.4.1. Description of Urban Parcel Grouping (UPG) Algorithm

_{1}to S

_{i}belong to the first level, S

_{i+1}belongs to the second level,

_{i+1}to S

_{i+j}belongs to the second level and S

_{i+1+j}belongs to the third level. By analogy, we obtained a hierarchical proximity sequence. The result of level-by-level tuning is illustrated in Figure 8. According to the results, we observed that the number of groups easily changed with the levels. For example, at level 1, each parcel constituted a group (see Figure 8a) or, at level 13, all parcels formed only one group (see Figure 8c). According to Gestalt theory, this was not a very good means of grouping, and could not effectively convey the compactness and proximity mutation. Therefore, an optimum number of groups should be set to make the grouping process more automated and obtain a reasonable grouping result.

#### 3.4.2. Method of Obtaining the Optimum Grouping Result

**DT**) is set for a parcel that conflicts with parcel i, the proximity is less than the DT, which is referred to as the intra-group distance (

**INDIS**), while the proximity is greater than the DT, which is referred to as the inter-group distance (

**OUTDIS**).

**mutation value**, which corresponds to the grouping result, as illustrated in Figure 10c. Among all grouping results, Figure 10c showed that the intergroup distance was larger than the intragroup distance, which was consistent with the cognitive habit and satisfies the requirements of compactness and continuity in Gestalt theory. We determined that the reason for the mutation value was that Avg_OUTDIS(i) was larger than Avg_OUTDIS(i). Therefore, to obtain a reasonable parcel grouping result, we should determine the proximity threshold, which has a mutation value in the compactness curve. Through the analysis of Table 3, we also determined that the compactness of the internal parcel grouping increased gradually, as in P1. If the number of such parcels in the grouping result also increases gradually, then the value of the curve may increase.

## 4. Results

#### 4.1. Analysis of Infiltration Behaviour

**Definition 3**(refer to Section 3.2), in this study, values greater than 0.5 represent a high degree of similarity, which is denoted by the red line in the figures (Figure 12); 0.3 to 0.5 indicates a moderate similarity, which is denoted by the blue line; and less than 0.3 represents a low degree of similarity or dissimilarity, which is denoted by the grey line. According to the results (refer to Figure 12), Parcel 1 has 33 instances of high-degree imitation behaviours, and Parcel 2 has 192 instances of high-degree imitation behaviours. The higher degree of similarity primarily occurred in clusters, and a large proportion occurred in adjacent parcels, from a global perspective. In addition, a dissimilarity or lower similarity of components existed in parcels that were not directly adjacent.

#### 4.2. Results of Urban Parcel grouping Method

#### 4.2.1. Parcel grouping Method Based on the Centroid Proximity

#### 4.2.2. Analysis of the UPG Method

#### 4.3. Practical Application of the UPG

## 5. Discussion

## 6. Conclusions and Further Research

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of study area (Xicheng District, Beijing) and the description of POI data. (Key to abbreviated names is in Table 1).

**Figure 7.**Urban parcel grouping method: (

**a**) Construction process of the parcels adjacent matrix; (

**b**) diagrammatic sketch of parcel grouping trees; and (

**c**) description of parcel grouping algorithm.

**Figure 8.**Illustration of step-by-step tuning within 13 levels: (

**a**) parcel grouping at level 1; (

**b**) parcel grouping at level 4; (

**c**) parcel grouping at level 13.

**Figure 9.**Illustration of three types of grouping results: (

**a**) grouping result when Avg_OUTDIS is 0; (

**b**) grouping result when Avg_INDIS is 0; (

**c**) grouping result when Avg_OUTDIS is greater than Avg_INDIS.

**Figure 10.**Illustration of grouping results with different proximity thresholds: (

**a**) ungrouped parcels; (

**b**) proximity threshold = d1; (

**c**) proximity threshold = d2; (

**d**) proximity threshold = d3; (

**e**) proximity threshold = d4; (

**f**) proximity threshold = d5; (

**g**) the relationship between compactness and proximity threshold.

**Figure 11.**Illustration of mixed land use (red numbers within parcels represent the MLU less than 0.5): (

**a**) MLU of Parcel 1, and (

**b**) MLU of Parcel 2.

**Figure 12.**Illustration of imitation behaviour among parcels: (

**a**) imitation behaviour of Parcel 1, and (

**b**) imitation behaviour of Parcel 2.

**Figure 13.**Illustration of dominant function within parcels: (

**a**) dominant functions of Parcel 1, and (

**b**) dominant functions of Parcel 2. In the legend, “--” represents that there is no POI in this parcel.

**Figure 14.**Illustration of parcel grouping results based on the k-means++ algorithm: (

**a**) grouping result of Parcel 1 (k = 8) and (

**b**) grouping result of Parcel 2 (k = 10). Numbers within a group illustrate the MLU index of the group. The left part of the figures illustrates the process of choosing the optimal cluster number.

**Figure 15.**The ignored imitation behaviours among groups: (

**a**) grouping result of Parcel 1 and (

**b**) grouping result of Parcel 2.

**Figure 16.**Compactness curve generated by two datasets: (

**a**) compactness curve of parcel 1; (

**b**) compactness curve of Parcel 2.

**Figure 17.**Illustration of grouping results based on UPG: (

**a**) grouping result of Parcel 1 and (

**b**) grouping result of Parcel 2. Numbers within groups represent the MLU index.

**Figure 18.**The ignored imitation behaviours among parcel group: (

**a**) grouping result of Parcel 1 and (

**b**) grouping result of Parcel 2.

**Figure 19.**Xicheng District’s parcel grouping results are generated by UGP: (

**a**) mixed land use of Xicheng District (red numbers within parcels represent the MLU less than 0.5); (

**b**) a CDT constructed for the study area; (

**c**) parcel grouping result at level 22, numbers within groups represent the MLU index; and (

**d**) compactness curve.

**Figure 20.**Illustration of relationship between parcel groups and functional region: (

**a**) two groups merge into a large functional region; (

**b**) hard segmentation.

**Figure 21.**Illustration of contrast experiment results: (

**a**) k-means++ result (k = 7), the left parts of the figures illustrate the process of choosing the optimal cluster number; (

**b**) k-means++ result (k = 51).

Category | Subclass ID | Abbreviated Name |
---|---|---|

Park and Plaza | ‘7300’ | PPZ |

Famous Scenery | ‘9080’ | FAS |

Transport Services | ‘4102’, ‘1202’, ‘4500’, ‘8085’, ‘4082’, ‘8087’, ‘8083’, ‘8100’, ‘8301’, ‘8401’ | TRA |

Hotel | ‘5380’ | HOT |

Catering and Entertainment | ‘1380’, ‘6081’ | CAT |

Business and Shopping | ‘1199’, ‘1600’, ‘2003’, ‘1980’ | BAS |

Research and Education | ‘1701’ | EDU |

Residential Area | ‘1900’ | RES |

Governmental Agencies | ‘7085’ | GOV |

Medical Service | ‘7280’ | MED |

Others | ‘7180’, ‘7880’ | OTR |

Parcel ID | Number of Parcels | Number of POIs | Main Components |
---|---|---|---|

parcel 1 | 46 | 3182 | ① Business & Shopping; ② Catering & Entertainment |

parcel 2 | 157 | 6527 | ① Business & Shopping; ② Catering & Entertainment; ③ Famous Scenery; ④ Residential Area |

Proximity Threshold | Compactness(P_{i}) | Average of Compactness(Pi) | ||||
---|---|---|---|---|---|---|

P1 | P2 | P3 | P4 | P5 | ||

d1 | $1-\frac{d1}{d2}$↓^{1} | $1-\frac{2*d1}{d2+d3}$↓ | 1 | 1 | 1 | ≈ $1-\frac{3*d1}{10*d2}$≈ 0.7 |

d2 | $1-\frac{d1+d2}{2*d3}$↑ | $1-\frac{d1+d2}{2*d3}$↑ | $1-\frac{2*d2}{d3+d4}$↓ | 1 | 1 | ≈$0.89-\frac{d1}{15*d2}$ ≈ 0.82 |

d3 (≈3*d2) | $1-\frac{d1+d2}{2*d4}$↑ | $1-\frac{d1+d2+d3}{3*d4}$↑ | $1-\frac{d2+d2+d3}{3*d4}$↓ | $1-\frac{2*d3}{d5}$↓ | 1 | ≈$0.75-\frac{d1}{36*d2}$≈ 0.72 |

d4 (≈2*d3) | −1 | −1 | −1 | −1 | −1 | −1 |

d5 (≈1.5*d4) | −1 | −1 | −1 | −1 | −1 | −1 |

**Red arrows represent changes in Compactness(Pi) compared with previous grouping results: upward pointing arrows indicate larger values and downward pointing arrows indicate smaller values.**

^{1}Parcel ID | Average Increase of MLU within Groups | Whether Same Dominant Functions were Separated | Ratio (times) of Ignored the High-Degree Imitation Behaviours |
---|---|---|---|

Parcel 1 | +0.38 | No | 45.45% (15) |

Parcel 2 | +3.87 | Yes | 21.88% (42) |

Parcel ID | Average Increase of MLU within Groups | Whether Same Dominant Functions were Separated | Ratio (times) of Ignored the High-Degree Imitation Behaviours |
---|---|---|---|

Parcel 1 | +0.24 | No | 27.27% (9) |

Parcel 2 | +2.45 | No | 16.15% (31) |

Method | Number of Groups (k) | Number of Hard Segmentations | Ratio (Number of Hard Segmentation/k) |
---|---|---|---|

k-means++ | k = 7 | 4 | 57.14% |

k-means++ | k = 51 | 20 | 39.22% |

UPG | k = 51 | 5 | 9.80% |

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## Share and Cite

**MDPI and ACS Style**

Wu, P.; Zhang, S.; Li, H.; Dale, P.; Ding, X.; Lu, Y.
Urban Parcel Grouping Method Based on Urban Form and Functional Connectivity Characterisation. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 282.
https://doi.org/10.3390/ijgi8060282

**AMA Style**

Wu P, Zhang S, Li H, Dale P, Ding X, Lu Y.
Urban Parcel Grouping Method Based on Urban Form and Functional Connectivity Characterisation. *ISPRS International Journal of Geo-Information*. 2019; 8(6):282.
https://doi.org/10.3390/ijgi8060282

**Chicago/Turabian Style**

Wu, Peng, Shuqing Zhang, Huapeng Li, Patricia Dale, Xiaohui Ding, and Yuanbing Lu.
2019. "Urban Parcel Grouping Method Based on Urban Form and Functional Connectivity Characterisation" *ISPRS International Journal of Geo-Information* 8, no. 6: 282.
https://doi.org/10.3390/ijgi8060282