1. Spatially Constrained Clustering and Upper Level Set Scan Hotspot Detection in Surveillance GeoInformatics
G.P.Patil, Penn State University
Reza Modarres, George Washington University
Pushkar Patankar, Penn State University
Yun Cai, Penn State University
W.L. Myers, Penn State University

2. Spatially Constrained Clustering
Constrained clustering is part of a family of methods whose purpose is to delimit homogeneous regions on a univariate or multivariate surface, by forming blocks of pieces that are also adjacent in space or in time. (Legendre, 1987)
Besides the similarity of measured variables, the clustering is spatially constrained if the cells within a cluster are adjacent to each other.

3. Motivations
Spatially constrained clustering is useful in applications in ……
Landscape Ecology
Geospatial Environment
Image Analysis
Spatial Economics
Public Policy in Geospace
Geography of Disease ……

4. Comparing the Two Methods…
The result of method I is better interpreted in the variable space, but it tends to give small patches and splinters.
Method II yields tighter clusters, but it is harder to interpret.
As far as programming is concerned, method I has programs ready to use, and it is more computationally efficient.
Usually, the two methods do not yield the same result.

5. Spatially Constrained Clustering in Hotspot Detection
Definition: A hotspot is that portion of the study region with an elevated risk of an adverse outcome.
A major task of geospatial hotspot detection is to delineate areas that exhibit elevated risks over geographical regions.
Upper Level Set (ULS) scan turns out to be a special case of spatially constrained clustering.

6. NSF Digital Government surveillance geoinformatics project, federal agency partnership and national applications for digital governance.

7. Geoinformatic hotspot surveillance system

8. Geographic and Network Surveillance for Arbitrarily Shaped Hotspots
Center for Statistical Ecology and Environmental Statistics
G.P. Patil, R. Acharya, W.L. Myers, P. Patankar, Y. Cai, and S.L. Rathbun
The Penn State University, University Park, PA 16802
R. Modarres
George Washington University, Washington, D.C.
Overview
Geospatial Surveillance
Upper Level Set Scan Statistic System
Spatial-Temporal Surveillance
Typology of Space-Time Hotspots
Hotspot Prioritization
Ranking Without Having to Integrate Multiple Indicators
Surveillance Geoinformatics for Hotspot Detection, Prioritization, Early Warning and Sustainable Management
Upper Level Set Scan System
Definition: A hotspot is that portion of the study region with an elevated risk of an adverse outcome
Example: West Nile Virus
First isolated in 1937, this mosquito born disease, indigenous to north Africa, the Middle East and west Asia was first introduced into the United States in 1999.
Example: Lyme Disease
Infections from the bacterium Borelia burgdorfei vectored by ticks from the genus Ixodes.
Example: Human-environment indicator values for 16 European countries.
Changing Connectivity of ULS as Level Drops g
Comparison of ULS Scan with Cylindrical Scan
ULS Scan
Disease Count Quintiles
Population Quintiles
Year
Disease Rates
Cylindrical Scan
Features of ULS Scan Statistic:
Identifies arbitrarily shaped hotspots
Applicable to data on a network
Confidence sets and hotspot ratings
Computationally efficient
Generalizes to space-time scan
1997
1998
Haase Diagram
Poset Prioritization System
Objective: Prioritize or rank hotspots based on multiple indicator and stakeholder criteria without having to integrate indicators into an index, using Haase diagrams and partially ordered sets.
Example: Prioritization of disease clusters with Multiple Indicators
Disease Rate Quintiles
Likelihood Quintiles
1999
2000
There are a total of 3,764,448 admissible linear extensions. The cumulative rank function for Sweden exceeds that of all remaining countries. The crf’s of all countries dominate that of Ireland. The remaining countries cannot be uniquely ordered based on their crf’s. Belgium, Netherlands and United Kingdom have identical crf’s.
Comparison of ULS Scan with Circular Scan
2001
ULS Scan
Circular Scan
Admissible linear extensions are comprised of rankings compatible with the rankings of all indicators. Treating each linear extension as a voter, the cumulative rank function is obtained from the frequencies at which each object receives each rank.
2002
2003
The crf’s also form a partially ordered set. There are only 182 admissible linear extensions for this poset, yielding the cumulative rank function:
Federal Agency Partnerships
CDC DOD EPA NASA NIH NOAA USFS USGS
Confidence set for ULS Hotspot
Hotspot Membership Rating
National Applications and Case Studies
Biosurveillance
Carbon Management
Costal Management
Community Infrastructure
Crop Surveillance
Disaster Management
Disease Surveillance
Ecosystem Health
Environmental Justice
Sensor Networks
Robotic Networks
Environmental Management
Environmental Policy
Homeland Security
Invasive Species
Poverty Policy
Public Health
Public Health and Environment
Syndromic Surveillance
Social Networks
Stream Networks
One more iteration yields the rankings in the data table.

9. ULS Connectivity Tree -- 1
Ingredients:
Tessellation of a geographic region:
Intensity value G on each cell. Determines a cellular (piece-wise constant) surface with G as elevation.
Imagine surface initially inundated with water
Water evaporates gradually exposing the surface which appears as islands in the sea
How does connectivity (number of connected components) of the exposed surface change with falling water level? a c b k d e f g h i j
a, b, c, … are cell labels

10. ULS Connectivity Tree -- 2
Think of the tessellated surface as a landform
Initially the entire surface is under water
As the water level recedes, more and more of the landform is exposed
At each water level, cells are colored as follows:
Green for previously exposed cells (green = vegetated)
Yellow for newly exposed cells (yellow = sandy beach)
Blue for unexposed cells (blue = under water)
For each newly exposed cell, one of three things happens:
New island emerges. Cell is a local maximum. Morse index=2. Connectivity increases.
Existing island increases in size. Cell is not a critical point. Connectivity unchanged.
Two (or more) islands are joined. Cell is a saddle point Morse index=1. Connectivity decreases.

11. ULS Connectivity Tree -- 3
Newly exposed island
ULS Tree g j a f d h b c a i e k
Island grows a g j f d h
b,c b c a i e k

12. ULS Connectivity Tree -- 4
Second island appears
ULS Tree a g j d f d h
b,c b c a
New leaf node (local maximum) i e k
Both islands grow a g
b,c j d f d h e b
f,g c a i e k

13. ULS Connectivity Tree -- 5
ULS Tree
Islands join – saddle point a
b,c g j d f d h e
f,g b c a i e h k
Junction node a
Exposed land grows
b,c g d j f d h e
f,g b a c i e h k
Root node
i,j,k

14. Changing Connectivity of ULS as Level Drops
Hotspot zones at level g (Connected Components of upper level set)

15. ULS Connectivity Tree
Schematic intensity “surface”
N.B. Intensity surface is cellular (piece-wise constant), with only finitely many levels A, B, C are junction nodes where multiple zones coalesce into a single zone A B C

16. Demonstration Example
Disease Rate

17. Demonstration Example Upper Level Set Tree: Method I12 9 2 1 3 4 5 6 7 8 13 14 15 16 17 18 19 11 10
Level 1: 3
Level 2: 18
Level 3: 8 0
Level 4:
Level 5:
Level 6:
Level 7: 9 11
Level 8: 1
Level 9: 10
Level 10: 6
Level 11: 13
Level 12: 2

18. Demonstration Example Upper Level Set Tree: Method II12 9 2 1 3 4 5 6 7 8 13 14 15 16 17 18 19 11 10
[3]
[3,18]
[3,18,0]
[17]
[17,16]
[14]
[17,16;14;15]
[3,18,0,4,8,7,19,5;17,16,14,15;11]
[8]
[3,18,0,4]
[3,18,0,4;8,7;19]
[8,7]

19. The Two Methods Give the Same Results Using the ULS Tree
The ULS tree is different from general classification methods in the way that it defines its similarity matrix. The similarity matrix is determined by the exceedance of incidence rates.
It does not matter at what stage the spatial constraint is applied, either at the end or as you go along, the result is the same.

20. Maximum Likelihood Estimate and Resultant Cluster Partition

21. ULS Scan on Multivariate Data Spatial Coincidence
In a scenario of multivariate data, ULS is operated as many times as the dimensions of the data, with every individual run of ULS operating only on one dimension. Finally the clusters are those that are the intersection of the clusters obtained by the runs of ULS.

22. Conclusion
In many situations, the usual clustering analysis is not sufficient. The spatial structure needs to be taken into consideration and accounted for. Therefore, spatially constrained clustering has been introduced. It can be accomplished by method I and method II. These give rise to different results.
In the hotspot detection work, the upper level set scan approach has been adopted. ULS is a spatially constrained clustering method based on upper level sets of rates. Similarity is defined by exceedance. It delivers identical clusters in both methods.

23. References
De Soete, Carroll, G., J.D. and DeSarbo, W.S. (1987). Least squares algorithms for constructing constrained ultrametric and additive tree representations of symmetric proximity data. Journal of Classification, 4, pp
BoundarySeer (2005). Software for Geographic Boundary Analysis. TerraSeer. Ann Arbor MI.
Everitt, B., Landau,S., and Leese, M. (2001). Cluster Analysis. Arnold, London, pp
Kulldorff, M. and Nagarwalla, N. (1995). Spatial disease clusters: detection and inference. Statistics in Medicine, 14, pp799–810.
Lebart, L. (1978). Programme d’agrégation avec constraints (C.A.H. contiguïté). Cah. Anal. Donnée, 3,
Legendre, P. (1987). Constrained clustering in Developments in Numerical Ecology. P. and L. Legendre, eds. Springer-Verlag, Berlin. pp
Legendre, P. and Legendre, L.(1998). Numerical Ecology. Elservier. NY. 853pp.
Patil, G.P. and Taillie, C.(2004). Upper level set scan statistic for detecting arbitrarily shaped hotspots. Environmental and Ecological Statistics, 11,
Urban, D.L. (2004). Multivariate Analysis. Nonhierarchical Agglomeration. Spatially Constrained Classification.