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8/8/2019 Spatial Statistics Presentation - University of Manitoba
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Spatial StatisticalAnalysis of a CellularNetwork
Presenters: Julian Benavides, Bryan DemianykCourse: STAT 7240Date: December 3, 2010
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Presentation Outline
Overview
Objectives
Methods
Analysis
Results
Conclusion
Future Work
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Overview (1)
The Internet Innovation Centre (IIC) research lab at the
University of Manitoba
Agent Based Modeling (disease spread)
Telecommunications
Demographics
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Overview (2)
The IIC has recently obtained a very large set of
information from MTS
More than 46 million records in total
Only a duration of 5 days
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Overview (3)
Data consists of call information1
Tower ID, tower location (GPS)
Caller ID, time of call, etc.
1 This information does NOT contain any personal or confidential information about
MTS or their customers
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Presentation Outline
Overview
Objectives
Methods
Analysis
Results
Conclusion
Future Work
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Objectives (1)
Apply concepts weve learned in class to the data
we have
Try to determine if there is any spatial relationshipbetween cellular towers
Have an interesting, and relative project
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Presentation Outline
Overview
Objectives
Methods
Analysis
Results
Conclusion
Future Work
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Methods (1)
Created a database to store all data
Manage the huge amount of data we have
Perform queries to get relevant chunks of data
at a time
Avoid timeouts for time-consuming queries
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Methods (2)
We need to refine, organize, and represent the
data we will be analyzing
Look only at a 1 day window
Look only at towers within Winnipeg
Used the number of calls/tower as our variable
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Methods (3)
We want to spatially represent the data we have
Google maps
Using different icons
VoronoiThiessen polygons
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Methods (4)
Google maps
Plot the precise locations of the towers
Allow the user to interact with it
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Google Maps (1)
http://130.179.131.96/stats/map.php
http://130.179.131.96/stats/map.phphttp://130.179.131.96/stats/map.php8/8/2019 Spatial Statistics Presentation - University of Manitoba
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Methods (5)
We have the number of calls/tower, and the
location of each tower
We want to partition our coordinate space andassociate a certain area with a single tower
Voronoi-Thiessen polygons
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Methods (6)
Created an application to create the Voronoi
diagram for a given data set of coordinates
CGAL and Qt 4 libraries
Allow user to create the Voronoi diagram
manually, or automatically from a data set
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Voronoi Diagram (1)
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Voronoi Diagram (2)
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Methods (7)
Need to find out which towers are adjacent to one
another for our analysis
Do notwant to do this by hand
Delaunay Triangulation
Conveniently, the dual of the Voronoi diagram
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Voronoi-Delaunay (1)
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Voronoi-Delaunay (2)
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Methods (8)
Determine any autocorrelation using Joins Count
approach, and Morans I statistic
Wrote R programs to do this
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Presentation Outline
Overview
Objectives
Methods
Analysis
Results
Conclusion
Future Work
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Analysis (1)
Joins Count approach (non-free sampling)
Let average calls/tower = Calls
Region Ri = B if # of calls for tower in Ri Calls
Region Ri
= W if # of calls for tower in Ri
< Calls
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Analysis (2)
Joins Count approach (non-free sampling) contd
Let null hypothesis H0 state that the spatial
arrangement of regions with an above averagenumber of calls is random and the alternate
hypothesis H1 state that the arrangement is
clustered
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Analysis (3)
Joins Count approach (non-free sampling) contd
Calculate ZBW_Obs
Calculate ZBB_Obs
Reject H0 if |ZBW_Obs| > Z0.025 or
|ZBB_Obs
| > Z0.025
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Analysis (4)
Joins Count approach (non-free sampling) contd
Use the Monte Carlo procedure
Use 10,000 permutations
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Analysis (5)
Joins Count approach (non-free sampling) contd
Calculate ZBW_Gen
Calculate ZBB_Gen
Reject H0
if |ZBW_Gen
| > Z0.025
or
|ZBB_Gen| > Z0.025
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Analysis (6)
Morans I statistic (assumption R)
Let the null hypothesis H0 state that the
probability that a tower receiving a certainnumber of calls is the same for each tower and
the number of calls is fixed independently of all
the other number of calls for all other towers
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Analysis (7)
Morans I statistic (assumption R) contd
Let the alternate hypothesis H1 state that the
probability that a tower receiving a certainnumber of calls is the same for each tower and
the number of calls is depends on all the other
number of calls for all other towers
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Analysis (8)
Morans I statistic (assumption R) contd
Calculate ZI_Obs
Reject H0 if |ZI_Obs| > Z0.025
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Analysis (9)
Morans I statistic (assumption R) contd
Use the Monte Carlo procedure
Use 10,000 permutations
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Analysis (10)
Morans I statistic (assumption R) contd
Calculate ZI_Gen
Reject H0 if |ZI_Gen| > Z0.025
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Analysis (11)
Semivariogram
Calculate the observed semivariogram
Calculate the omnidirectional semivariogram
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Analysis (12)
Semivariogram contd
Calculate the empirical semivariogram for the 4
major compass directions (N/S, E/W, NE/SW,SE/NW)
Look for any trends or indications of anisotropy
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Presentation Outline
Overview
Objectives
Methods
Analysis
Results
Conclusion
Future Work
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Results (1)
Joins Count approach (non-free sampling)
JBW_Obs = 90
E(JBW_Obs) = 86.74654, V(JBW_Obs) = 38.57732
ZBW_Obs = 0.52382
Since |ZBW_Obs| < 1.96, do not reject H0
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Results (2)
Joins Count approach (non-free sampling) contd
JBB_Obs = 25
E(JBB_Obs) = 25.57911, V(JBB_Obs) = 12.44333
ZBB_Obs = -0.16417
Since |ZBB_Obs| < 1.96, do not reject H0
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Results (3)
Joins Count approach (Monte Carlo)
JBW_Obs = 90
E(JBW_Gen) = 86.66820, V(JBW_Gen) = 38.57897 ZBW_Gen = 0.53642
Since |ZBW_Gen| < 1.96, do not reject H0
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Results (4)
Joins Count approach (Monte Carlo) contd
JBB_Obs = 25
E(JBB_Gen) = 25.57290, V(JBB_Gen) = 12.64095 ZBB_Gen = -0.16113
Since |ZBB_Gen| < 1.96, do not reject H0
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Results (5)
Morans I statistic (assumption R)
IObs = -0.01296
E(IObs) = -0.01613, V(IObs) = 0.00496 ZI_Obs = 0.04506
Since |ZI_Obs| < 1.96, do not reject H0
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Results (6)
Morans I statistic (Monte Carlo)
IObs = -0.01296
E(IGen) = -0.01640, V(IGen) = 0.00490 ZI_Gen = 0.04927
Since |ZI_Gen| < 1.96, do not reject H0
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Results (7)
Semivariogram
Plotted the semivariogram
Plotted the omnidirectional, N/S, E/W, NE/SW,
SE/NW semivariograms
The semivariogram looks interesting
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Semivariogram (1)
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Semivariogram - Omni (2)
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Semivariogram N/S (3)
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Semivariogram E/W (4)
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Semivariogram NE/SW (5)
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Semivariogram SE/NW (6)
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Presentation Outline
Overview
Objectives
Methods
Analysis
Results
Conclusion
Future Work
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Conclusion (1)
We conducted the statistical analysis on subset of
the data due to the processing implication that one
may have analyzing really big sets of information at
one time
The Joins Count approach indicated that the spatial
arrangement of regions with an above average
number of calls was random
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Conclusion (2)
Morans I statistic indicated that the number of
calls a tower received was independent of the
number of calls received by every other tower
The semivariograms indicated anisotropy because
they seemed to change with direction
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Presentation Outline
Overview
Objectives
Methods
Analysis
Results
Conclusion
Future Work
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Future Work (1)
Extend our analysis to longer time windows as wereceive more data
Weeks, months, and maybe even years
Repeat analysis using a finer grained time window
Bi-daily, hourly, and maybe even minutely
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Future Work (2)
Try to extract some demographic information fromthe data and analyze it
One day be able to extract trajectories of
individuals from the data
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Demographics (1)
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Demographics (2)
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