BY YING VUONG ARASH FAYZ REAL WORLD

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BY: YING VUONG ARASH FAYZ

REAL WORLD DATA • Overall Long Beach Data burglaries: 1790000 1780000 1770000 1760000 1750000 1740000 1730000 1720000 1710000 1700000 6483618 6493618 6503618 6513618 6523618 6533618 Total number of burglaries (2000 -2005) 6543618 6553618

Multiple Robberies distinguished by color 1785000 1783000 1781000 1779000 1777000 1775000 1773000 1771000 1769000 1767000 1765000 1 1763000 2 1761000 3 1759000 1757000 1755000 4 5 1753000 6 1751000 7 1749000 8 1747000 9 1745000 1743000 1741000 1739000 10 11 20 1737000 1735000 1733000 1731000 1729000 1727000 1725000 6492000 6494000 6496000 6498000 6500000 6502000 6504000 6506000 6508000 6510000 6512000 6514000 6516000 6518000 6520000 6522000 6524000 6526000 6528000 6530000 6532000 6534000 6536000 6538000 6540000 6542000 6544000

Long Beach Burglaries from the Year 2000, Number of Times Victimized LEGEND Blue – 1 Cyan – 2 Red – 3 Yellow – 4

AVERAGE FREQUENCY OF ROBBERIES • The following Excel file shows Frequency of the houses burgled with respect to weeks between robberies

OVERALL DATA ANALYSIS • • The following Frequency graph plotted using the average data More burglaries occur in rapid succession rather than long intervals. 35 30 25 20 Freq 15 Series 1 10 5 0 0 5 10 Time Interval Btw Robberies (Weeks) 15 20

AVERAGE NUMBER OF ROBBERIES The following Excel File shows the Average number of robberies for all five years.

AVERAGE NUMBER OF ROBBERIES PLOT 2500 2000 Robberies 1500 Series 1 1000 500 0 0 1 2 3 Sites 4 5 6 7

MY MODEL Ø Virtual robbers are placed on a line of length L meant to represent houses Ø robber can do 4 things at each step, essentially: stay put where he/she is, move left or right, or rob the house where he/she is at Ø The probability of moving to a neighboring location is calculated based on the “attractiveness” of the neighbor houses as follows: Ø After all the robbers have robbed and moved, the houses will update their b values according to this formula:

COMPARISON OF MY MODEL AND REAL WORLD DATA Robbers=800; Blue Model Houses=13000; Black Data Time=One year; η=. 5 =0. 5; =. 01; b 0=. 01 �

COMPARISON OF MY MODEL AND REAL WORLD DATA Number of Robberies per site for the same parameters as before Binning number time robbed: 1 2046, 2 296, 3 75, 4 19, 5 2, 6 1

What is a Hot Spot?

Hot Spot Definition 1: Areas with high percentages of multiple burglaries

Hot Spot 1 Ø 100 x 100 grid Ø Each cell is approximately 485 x 500 ft Ø Each cell represents the number of multiple burglaries divided by the total number of burglaries

Hot Spot Definition 2: Clusters of burglaries where one burglary is within 500 ft of another

Clustering Algorithm

Clustering Algorithm 1. Chooses a random point 2. Finds all points within 500 ft

Clustering Algorithm

Clustering Algorithm 1. Chooses a random point NOT already within a cluster 2. Finds all points within 500 ft

Clustering Algorithm

Clustering Algorithm Eventually, all points are in clustered in some groups

Clustering Algorithm Re-checks that points within 500 ft are in the same cluster

Clustering Algorithm Some different clusters might be within 500 ft of each other

Clustering Algorithm Clusters within 500 ft of each other are combined into one cluster

Long Beach Burglary Clusters for the year 2000 • Total of 521 Clusters, top 10 are displayed • The biggest cluster consisted of 76 housing units • 500 ft is about the size of a block • Are these hot spots?