# A Perimeter-Based Clustering Index for Measuring Spatial Segregation: A Cognitive GIS Approach:

Abstract: Many efforts have been made to develop segregation indices that incorporate spatial interaction based on the contiguity concept. Contiguity refers to how similar the concentration of the subject of...

## Summary (2 min read)

### 1 Introduction

- A new index to measure the degree of clustering is developed and then compared with the existing indices of segregation.
- In section 5, four existing indices to be compared with the new clustering index are discussed briefly, and the clustering index and the four other indices are compared in two hypothetical settings including binary distribution in a regular lattice, and semicontiguous distribution in a regular lattice.
- In section 6, the five indices are compared in a real-world application, the five boroughs of New York City.

### 2 Operational definition of clustering

- Here, adjacent areal units showing a high concentration of the subject form a few clusters on the map.
- Once clusters are obtained, one needs to quantify the size, shape, and closeness of the clusters.
- A measure that combines these three factors is the total perimeter of the clusters.
- When shape and adjacency of the clusters are the same, the total perimeter (P) of the clusters is a proper measure of the total size [see figures 1(a) and 1(b)].
- When the size and adjacency of the clusters are constant, circular shapes have the minimum possible values [see figures 1(c) and 1(d)].

### EEIWA

- Only the boundary between a pair of adjacent tracts which have different / values (high concentration versus low concentration) remains.
- One advantage of this measure for an irregular polygon layout is that the degree of proximity between polygons is automatically taken into account during the merging process.
- The authors apply the Monte Carlo method to establish the distribution of the index based on the assumption of a stochastic process, as the distribution is not obtainable analytically.
- Based on the assumption that each member of an object group can be located freely, the probability that a member can be placed in a certain areal unit is proportional to the ratio of the total number of the object group in the tract to the citywide total.
- In the following section, some special examples of the segregated distributions are chosen to compare the clustering index with other existing segregation indices.

### 5 Comparisons in hypothetical space

- In the first setting, only binary distribution is allowed on the regular lattice.
- In the second setting, contiguous distribution is allowed, while the total number in an object group remains constant.
- Therefore each tract can contain any number of people (not exceeding 10) in the object group.
- The total number of people in the object group in the city should remain constant.
- These two settings are chosen to analyze the effects of the marginal change of spatial setting.

### 5.1 Binary distribution in a regular lattice

- The total number in an object group varies in each distribution.
- It may be misleading, because an index obtained in a city having, for example, a 20% black population may not be quite comparable with that in another city with a 40% black population.
- As an example, one can assume that two cities have identical geographical settings; however, one has 9 minority people, whereas the other has 4 minority people.
- If they can choose their locations freely, the likelihood of all minority people choosing to live in a single tract is lower in the city populated with 9 people than in the city populated with 4 people.

### 5.2 Semicontinuous distribution in a regular lattice

- Overall, the distribution of the black population generates a fairly consistent ranking of each borough, and the distribution of the origins generates the most mixed rankings over the indices.
- 7 sp and I M produce similar rankings to each other and underestimate the highly concentrated enclaves such as the origins in Staten Island.
- I c produces distinctive rankings and is very sensitive to the separation of clusters such as the three clusters of origins in Manhattan, which produce the lowest ranking for P among the boroughs.

### 6.2 Intersubject comparison

- As shown in this intersubject comparison, each index shows quite a different degree of segregation for each subject.
- This result implies that the choice of an index is a critical issue when the degrees of segregation of different subjects of interest are compared.
- As an example, a policymaker may need to choose between a populationbased program (targeting people under the poverty level) and a neighborhood-based program (targeting the neighborhoods which generate more homeless people) for the prevention of homelessness.
- Based on the clustering index, origins of the homeless form tighter enclaves than poverty in New York City, in contrast to other indices.

### 7 Conclusion

- The proposed clustering index tends to give more weight to enclaveness than contiguity alone.
- This may be a good property for those cases in which the primary concern of an investigator is the formation of enclaves of a socioeconomic subject, including minority populations, poverty, crime, epidemics, and mortgage red-lining.
- Additionally, its property of robustness to the city wide rate allows us to perform properly an intercity comparison of a given subject by index score, even when the citywide rate varies significantly, unlike in the case of the other measures.
- Further research is therefore required for detailed refinements of the clustering index to better capture enclaveness of a subject of interest.

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##### Citations

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### Cites background from "A Perimeter-Based Clustering Index ..."

...However, some scholars have been skeptical about whether spatial autocorrelation and local spatial statistical approaches can improve the measurement of segregation levels [35,67], arguing that a high degree of positive spatial autocorrelation does not always indicate a high level of segregation....

[...]

...However, some scholars have been skeptical about whether spatial autocorrelation and local spatial statistical approaches can improve the measurement of segregation levels [35,67], arguing that a high degree of positive spatial autocorrelation does not always indicate a high level of segregation....

[...]

35 citations

32 citations

### Cites background from "A Perimeter-Based Clustering Index ..."

...Introduction Geographic Information Systems (GIS) provide powerful and flexible tools for measuring, analysing and displaying urban residential segregation (Wong, 1997a; Wong and Chong, 1998; Lee and Culhane, 1998)....

[...]

...Geographic Information Systems provide powerful and flexible tools for measuring, analyzing and displaying urban residential segregation (Wong, 1997a; Wong and Chong, 1998; Lee and Culhane, 1998)....

[...]

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