Problem
The New Haven data set contains point patterns of four types of crime events: breaches of the peace, family disputes, forced-entry burglaries and non-forced-entry burglaries. To allocate crime-prevention resources, the New Haven Police Dept. would like to identify clusters of census blocks that have similar crime profiles. For example, if certain blocks have a high number of family disputes but no other crime, the NHPD might devote resources to reducing domestic violence in these blocks but not resources for reducing other types of crime. Note that the set of blocks that constitute a cluster may not be contiguous.
Important: When you are ready to finalize your answers to the questions below, please seed the random number generator using: set.seed(456), and then run your code. Seeding the random number generator will ensure that your answers are reproducible. Here's an example of how this works:
# Without seeding the random number generator, the following line
# produces a different number between 0,1 each time:
runif(1)
# Running the following two lines will always give the same number:
set.seed(456)
runif(1)
Task
i. Develop a scree plot by plotting within-group sum of squares (y axis) against number of kmeans clusters (x axis), for values of k ranging from 2 to 15. Based on the scree plot, what is an appropriate number of clusters for this data set, and why?
ii. Cluster your data set using a k-means algorithm, with k chosen based on question 1. How many blocks are in each cluster?
iii. What are the mean counts of each crime type in each cluster? Based on this, can you come up with a name for each cluster that would be meaningful or useful for the NHPD?
iv. Develop a color-patch map in which the color of a census block reflects the cluster to which it belongs. Are the clusters you identify spatially contiguous? Briefly discuss whether the clusters you identify might be meaningful or useful to the NHPD.