spatial statistics presentation - university of manitoba

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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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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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.php


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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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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)


Calculate ZBW_Obs

Calculate ZBB_Obs

Reject H0 if |ZBW_Obs| > Z0.025 or

|ZBB_Obs

| > Z0.025


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Analysis (4)


Use the Monte Carlo procedure

Use 10,000 permutations


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Analysis (5)


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)


Calculate ZI_Obs

Reject H0 if |ZI_Obs| > Z0.025


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Analysis (9)


Use the Monte Carlo procedure

Use 10,000 permutations


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Analysis (10)


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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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)


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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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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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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Questions

spatial statistics presentation - university of manitoba

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