The document discusses using an optimization clustering method to detect ethnic residential clusters. It begins by reviewing existing measures of segregation and their limitations. It then introduces an optimization approach that identifies clusters with distinctively higher data values than other areas by optimizing a clustering quality index. The method is demonstrated on census data for Pacific and Korean populations in Auckland, New Zealand. The results are compared using different parameters and initialization methods.

1. 최적화 기법을 이용한 거주지
군집의 탐색
홍성연 (hong.seongyun@gmail.com)
2012/05/22

2. 거주지 분화에 관한 연구의 일반적인 흐름
Patterns of segregation – which population
group is separated from other population
groups?
Causes of segregation – what are the
underlying reasons for the residential
separation?
Consequences of segregation – what does
that imply in our society?

3. Measures of segregation
Duncan and Duncan’s
index of dissimilarity
(1955)
White’s index of spatial
Morrill’s adjusted proximity (1983)
index of
dissimilarity
(1991) Wong’s adjusted
index of
dissimilarity (1993)
Reardon and O’Sullivan’s
spatial segregation indices
(2004)

4. Enclave vs. Ethnoburb
Enclave Ethnoburb
Dynamics Forced segregation Voluntary segregation
Spatial form Small scale Small to medium scale
Population High density Medium density
Location Inner city Suburbs
Economy Labour-intensive sectors Business of all kinds
Internal stratification Minimum Very stratified
Interaction Mainly within group Both within- & inter-groups
Tension Between groups Inter- & intra-group
Community Mainly inward Both inward and outward
Example Traditional Chinatown San Gabriel Valley
Source: Li, 1997

5. Some candidates …
• GAM and Kulldorff’s scan statistic?
• Originally developed for epidemiological or ecological studies where
clustering is often very rare
• Often utilised in a situation where data are generated from observations,
such as the occurrence of a disease
• Getis-Ord’s local G* statistic and local Moran’s I?
• Designed to detect statistically significant clustering of the sample points
assuming no autocorrelation in the study region
• At least appeared in the relevant literature

6. 기존 방법의 문제점
Source: Poulsen et al., 2010
P(z < –5.17) = 0.000000117047
P(z > 10.32) = 2.861158 x 10–25
P(z > 20.64) = 6.003128 x 10–95

7. 거주지 분화에 관한 연구의 특징
• Often employ census data as the primary source of information
• The presence is usually very apparent even on a simple choropleth
map of the population.
• Difficulties arise in delineating the boundaries of residential clusters,
because those located in suburban areas have no clear borders.
• The question that should be addressed by a statistical tool is more
related to the extent of residential clustering than its presence or
approximate location.

8. 최적화 기법의 활용
• Suppose that the study region is divided into n census tracts, Ω = {x1,
x2, x3, . . . , xn}, and the aim is to identify a particular number of groups
whose data values are distinctively larger than those of the remaining
census tracts.
• The idea behind the proposed clustering method is that the quality of
a given clustering can be represented by numerical indices, and the
best possible subsets can be found by optimising the index values.
• Which index should we use?

9. 최적화 기법의 활용
• Within-group sum of absolute deviations:
𝑔 𝑛𝑖
𝑤 = � � 𝑎 𝑖𝑖 𝜇 𝑖 − 𝑏 𝑖𝑖
𝑖=0 𝑗=1
where ni is the number of census tracts in Ai, aij is the weight of the
corresponding census tract and bij is the data value of interest, such
as the population density of an ethnic group; μi refers to the
weighted mean of all data values in Ai.

10. 최적화 기법의 활용
• Because we cannot investigate all possible combinations, we need to
use an alternative algorithm.
• The one I implemented for demonstration worked as follows:
• Step 1: Choose starting points
• Step 2: Calculate and compare the clustering measure
• Step 3: Expand the current cluster
• Step 4: Repeat the procedures for each cluster

11. Synthetic data sets
• Patterns generated from an exponential distribution with λ = 0.005

12. Synthetic data sets
• (More) patterns from the same exponential distribution

13. Local G* with a distance-based adjacency f.
• Centre-to-centre distance less than 1, 2, 8 m

14. Local G* with a queen-contiguity matrix

15. Local G* with a queen-contiguity matrix

16. Proposed approach

17. Proposed approach

18. Population composition in Auckland
Table 1. Index of dissimilarity (D) for major ethnic groups in Auckland,
2001
Asian
European Chinese Indians Korean All
D 0.387 0.330 0.358 0.453 0.300
Pacific peoples
Māori Samoan Tongan Cook Island All
D 0.321 0.490 0.511 0.484 0.527

19. Pacific peoples in Auckland
• Geographic distribution of
Pacific peoples in the Auckland
urban areas, 2006

20. Results

21. Results

22. Koreans in Auckland
• Geographic distribution of
Koreans in the Auckland urban
areas, 2006

23. Results

24. Results

25. How many iterations?
• Pacific peoples in Auckland, 2006 (based on 100 simulations)

26. How many iterations?
• Pacific peoples in Auckland, 2006 (based on 100 simulations)

27. How many iterations?
• Koreans in Auckland, 2006 (based on 100 simulations)

28. How many iterations?
• Koreans in Auckland, 2006 (based on 100 simulations)

29. How many clusters (partitions)?

30. How many clusters (partitions)?

31. Random seeds vs. manual seeds
• Some unpublished figures for Pacific peoples ...

32. Random seeds vs. manual seeds
• Some unpublished figures for Korean ...

33. 결과 정리
• Same as most other local statistics in the sense that it attempts to
identify a set of geographically close observations with high (or low,
depending on the context) data values in relation to the rest of the
data
• Does not require defining ‘close’ or ‘high’ prior to its application, and
this feature provides an advantage over the other traditional methods
in terms of delineating the boundaries of arbitrarily shaped clusters

34. 결과 정리
• Possible to obtain similar results from other recently developed
clustering methods (e.g. Tango and Takahashi 2005, Mu and Wang
2008, Yao et al. 2011), but they set the upper limit of cluster size for
computational reasons or adopt inferential statistics as a clustering
criterion.
• Maybe reasonable for epidemiological research, where the cluster to be
found can be small and the data are usually derived from samples, but
probably not for residential clusters of population groups
• Computation is more straightforward than the other (scan statistic-based)
‘flexible’ approaches.

35. Albany
적용가능한 사례 Buffalo
• Similar to k-means
Albany Buffalo N ’hood
Type
Cincinnati New ark

36. Computer implementation
• Some ‘proof-of-concept’ level functions have been written in R.
• Working but slow ...
• More stable versions will be included in the ‘seg’ package, hopefully
before August of this year.

37. 참고 문헌
Duncan OD, and Duncan B. 1955. A methodological analysis of
segregation indexes. American Sociological Review 20: 210-217.
White MJ. 1983. The measurement of spatial segregation. The
American Journal of Sociology 88: 1008-1018.
Reardon SF, and O'Sullivan D. 2004. Measures of Spatial Segregation
Sociological Methodology 34: 121-162.
Poulsen M, Johnston R, and Forrest J. 2010. The intensity of ethnic
residential clustering: exploring scale effects using local indicators of
spatial association. Environment and Planning A 42: 874-894.
Hong S-Y, and O'Sullivan D. 2012. Detecting ethnic residential clusters
using an optimisation clustering method. International Journal of
Geographical Information Science: 1-21.