Hotspot/cluster detection methods(1) • Spatial Scan Statistics: Hypothesis testing – Input: data – Using continuous Poisson model • • Null hypothesis H0: points are randomly distributed (CSR) Alternative hypothesis H1: points are clustered in zone Z • Enumerate all the zones and find the one that maximizes likelihood ratio – L = p(H1|data)/p(H0|data) • Test statistical significance: Monte Carlo simulation – Generate the data for 1000 times and see how many times can we get a higher L

Hotspot/cluster detection methods(2) • DBSCAN: Density-based spatial clustering of application with noise – Input: data, radius, min_neighbors – For each data point P: • If neighbors min_neighbors then add P’s neighbor to C’s neighborhood

SatScan Result 1 clusters found But insignificant

DBSCAN results: CSR 100 DBSCAN output on CSR dataset: min neighbors=3, radius=4 90 80 70 60 50 40 30 20 10 0 0 20 40 60 80 100 X 2 clusters found

DBSCAN results: CSR 100 DBSCAN output on CSR dataset: min neighbors=3, radius=7 90 80 70 60 50 40 30 20 10 0 0 20 40 60 80 100 X 6 clusters found

DBSCAN results: CSR 100 DBSCAN output on CSR dataset: min neighbors=3, radius=10 90 80 70 60 50 40 30 20 10 0 0 20 40 60 80 100 X 7 clusters found

100 90 80 70 60 50 40 30 20 10 0 0 Results from SatScan and DBSCAN A Clustered Dataset 20 40 X 60 80 100

SatScan results

DBSCAN result

100 DBSCAN output on clustered dataset: min neighbors=3, radius=1 90 20 10 0 0 80 70 60 50 40 30 20 40 60 80 X 100 5 clusters found

DBSCAN result

DBSCAN output on clustered dataset: min neighbors=3, radius=4 100 90 80 70 60 50 40 30 20 10 0 0 20 40 60 80 100 X 3 clusters found

DBSCAN result

40 30 20 10 0 0 DBSCAN output on clustered dataset: min neighbors=3, radius=7 100 90 80 70 60 50 20 40 60 80 100 X 6 clusters found

DBSCAN result

100 DBSCAN output on clustered dataset: min neighbors=3, radius=10 90 80 70 60 50 40 30 20 10 0 0 20 40 60 80 100 X 6 clusters found