Cluster Analysis Techniques for Neighborhood Change
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1 Cluster Analysis Techniques for Neighborhood Change Michael Reibel, Cal Poly Pomona Moira Regelson, Yahoo! Search Marketing
2 The Problem Define distinct types of neighborhood change in multiethnic context Seminal papers in neighborhood racial and ethnic change (Denton and Massey, 1991; Alba et al., 1995) classify neighborhoods according to a priori thresholds (e.g. > 100 persons indicates presence of group)
3 Clustering Approaches K-means clustering: For J variables, minimizes within-cluster (J dimensional) distance from the means of K clusters Number of clusters specified a priori PAM (Partitioning Around Medoid) clustering: similar to K-means clustering except uses cluster medians instead of means PAM clustering more robust (less distortion due to extreme values)
4 Problem: k-means and PAM clustering will happily divide any dataset into k clusters per analyst s instructions, regardless of whether that s appropriate or not.
5 Tibshirani Prediction Strength A supervised classificaton technique to predict number of clusters (Tibshirani et al., 2005) Use cluster reproducibility measures for different k to estimate the true number of clusters in the data set. choosing correct number of clusters > less random assignment of samples to clusters and to greater cluster reproducibility.
6 Tibshirani Prediction Strength, cont. Specify kmax and max number of iterations, B. For k in {2 kmax}, repeat B times: Randomly split data set into a training set and test set Apply clustering procedure to partition training set into k clusters, record cluster labels as outcomes Apply best fit cluster labels from training set run to observations in test set ( predicted labels) Apply the clustering procedure to the test set to arrive at the observed labels Compute a measure of agreement comparing predicted to observed labels
7 Data and Methods Census tract race and ethnic trend data for Los Angeles County (1990 counts; 2000 counts interpolated to 1990 census tracts; 2000 mixed race assigned to single races) Tracts clustered on trends for four groups: All Hispanics; NH White, Black, API Three transition moments: raw change, proportional change, relative change Tibshirani Prediction Strength to determine number of clusters, PAM clustering method
8 Selection of Cluster Numbers (Tibshirani Threshold=0.7) Clusters Raw Change Relative Change Proportional Change
9 Cluster Sizes (N J ) Cluster Raw Relative Proportional
10 Scatterplots Rotated in J Dimensional Space Raw Change, 3 clusters Raw Change, 4 clusters allhispanics allhispanics nhwhite nhwhite nhblack nhblack nhapi nhapi
11 Cluster Centers Raw Change County Median Cluster 1 Cluster 2 Cluster 3 allhispanics nhwhite nhblack nhapi
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13 Cluster Centers Relative Change (Note overall growth: Cluster 1 is fast; Cluster 3 is slow) County Median Cluster 1 Cluster 2 Cluster 3 allhispanics nhwhite nhblack nhapi
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15 Cluster Centers: Proportional Change County Median Hispanic nhwhite nhblack nhapi
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17 Discussion Initial test of this clustering approach in neighborhood research (PAM clustering using Tibshirani prediction strength) Both the number of clusters and the cluster centers (with respect to variables) are different for the various moments of change Differences between moments of change most evident in case of Blacks (dispersion out of previously segregated areas does not appear in raw change; appears differently in relative and proportional change)
18 Future Research Apply this technique, with possible modifications, to census tracts across a broader study area (e.g. regional, national) Compare metropolitan areas in terms of the relative presence or absence of clusters identified for the nation s cities Use principal clusters identified for the nation s cities as neighborhood change outcomes to categorically model covariates
19 Sources Cited Alba, R.D., Denton, N. A.,Leung, S.J., Logan, J.R Neighborhood change under conditions of mass immigration: The New York City region, International Migration Review 29: Denton, N.A. and D.S. Massey Patterns of neighborhood transition in a multiethnic world: U.S. metropolitan areas, Demography 28: Kaufman, L. and Rousseeuw, P.J Finding Groups in Data : An Introduction to Cluster Analysis (Wiley Series in Probability and Statistics) Wiley- Interscience; 2 rev edition Tibshirani, R Cluster validation by prediction strength. Journal of Computational and Graphical Statistics 14:
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