The document discusses methods for analyzing co-location patterns of businesses using statistical tests and Monte Carlo simulations. It analyzes co-location patterns among gas stations, food locations, and banks in three major US cities. The analyses show that gas stations generally cluster, while food locations cluster due to competition or complementation. Food and bank locations may cluster due to urban planning.

1. 1. Candidate Generation Through Co-Location Pattern Mining:
● Used concept of participation index(pi) to find interesting co-locations
● Participation Index : Efficient, but many false positives
2. Statistical Tests of Co-Location and Clustering Patterns:
● Ripley’s K and Cross-K against Poisson Complete Spatial Randomness
● Ripley’s K : 𝐾" 𝑑 = 𝜆'( ∑
*(,-./,)
1345
● Cross-K : 𝐾" 𝑑 = 𝜆5
'(
∑
*(,-./,)
1-
345
● K Functions : Computationally expensive, very accurate
● Autocorrelation vs. Business Decision
3. Monte-Carlo Simulation:
● Shuffle businesses among their location
domain, calculate K-function value each
time
● Repeat 999 times, if above 95%
confidence, reject null hypothesis
and claim intentional clustering
Introduction and Background Discussion
Dixon, P. M. (2014). Ripley's K Function. Wiley StatsRef:
Statistics Reference Online.
Huang, Y., Shekhar, S., & Xiong, H. (2004). Discovering
colocation patterns from spatial data sets:
a general approach. IEEE Transactions on Knowledge and
Data Engineering, 16(12), 1472-1485.
Metropolis, N., & Ulam, S. (1949). The monte carlo method.
Journal of the American Statistical Association, 44(247),
335-341.
Methods and Analysis Techniques
References
1. Gas stations in general tend to be
clustered or inconclusive. Main gas
stations tend to be inconclusive or
declustered. Small gas businesses lack
access to extensive land choice and/or
data
2. Food locations tend to cluster due to
competition or complementation
3. Food and Bank location may be clustered
due urban commercial region planning by
cities
Co-Location Pattern:
A co-location is a set of spatial
features that frequently occur together (e.g.
Walmart and Subway)
Figure 1 : Walmart and Subway Co-Location
Retrieved from http://www.kptv.com/story/33335477/affidavit-man-pointed-gun-at-subway-manager-inside-walmart-shot-at-pumpkins
Objectives and Significance:
Discover previously unknown business location
patterns among:
1. Specific brands within industries
2. Specific brands across industries
3. Different Industries
4. Same Industries
Help small businesses choose location by
revealing location patterns of large brands
Data Set:
Dataset for three largest cities in the US
obtained through querying Google Places API.
Heat maps of locations shown in Figures 2, 3, 4.
Brightness indicates density
Figure 2 : New York City Figure 3 : Los Angeles
Figure 4 : Chicago
Understanding business location patterns through co-location pattern mining
Jeffrey Chiu1, Amin Vahedian Khezerlou2, Xun Zhou2
Irvington High School1 - Department of Management Sciences, The University of Iowa2
Figure 6 : Flow of Analysis in this project
Figure 5 : Example Monte-Carlo K Function
Retrieved from resources.esri.com/help/9.3/arcgisdesktop/com/gp_toolref/spatial_statistics_tools/
Results
Figure 7 : Ripley’s K Function for All Gas Stations and Major Gas Stations Only
(a) NYC All (b) NYC Major (c) LA All (d) LA Major (f) Chicago Major(f) Chicago All
Figure 8 : Cross-K Functions within food Industry
(a) Chipotle/Le Paine
Quotidien NYC
(b) Juice Press/Le Paine
Quotidien NYC
(c) McDonalds/BR NYC (d) Dunkin/Subway
NYC
Further Directions
(d) Dunkin/Subway
Chicago
(e) Starbucks/Subway
LA
1. Find interesting co-location patterns
among other cities and find overarching
patterns among cities
2. Work with economics researchers to
generate economic theories behind co-
location patterns
3. Submit for publication to an academic
journal after further results and analysis
Acknowledgements
Figure 9 : Cross-K Function across Industries
(a) Chipotle/HSBC
Bank NYC
(b) Jimmy Johns/
Chase Chicago
(c) Starbucks/ Wells
Fargo LA
Special thanks to Amin and Dr. Zhou for their
guidance on this project. Thanks to SSTP for
allowing me to have such a wonderful opportunity.
Figure 10 : Cross-K Function of types food and bank
(a) New York City (b) Los Angeles (c) Chicago