1. Albany New York (1) G. P. Patil

2. This report is very disappointing. What kind of software are you using?

3. Space Age and Stone Age Syndrome
Data: Space Age/Stone Age
Analysis: Space Age/Stone Age
Data Space Age Stone Age
Analysis
Space Age + +
Stone Age +

4. Geospatial Cell-based Data Kinds of Data
Cell as a Unit (Regular grid layout)
Categorical
Ordinal
Numerical
Multivariate Numerical
Cell as an Object (Irregular cell sizes and shapes)
Partially Ordered

5. Consider a 21st century digital government scenario of the following nature:
What message does a remote sensing-derived land cover land use map have about the large landscape it represents? And at what scale and at what level of detail?
Does the spatial pattern of the map reveal any societal, ecological, environmental condition of the landscape? And therefore can it be an indicator of change?

6. Consider a 21st century digital government scenario of the following nature:
How do you automate the assessment of the spatial structure and behavior of change to discover critical areas, hot spots, and their corridors?
Is the map accurate? How accurate is it? How do you assess the accuracy of the map? Of the change map over time for change detection?

7. Consider a 21st century digital government scenario of the following nature
What are the implications of the kind and amount of change and accuracy on what matters, whether climate change, carbon emission, water resources, urban sprawl, biodiversity, indicator species, or early warning, or others. And with what confidence, even with a single map/change-map?

8. The needed partnership research is expected
to find answers to these questions and a few
more that involve multicategorial raster maps
based on remote sensing and other geospatial
data. It is also expected to design a prototype
and user-friendly advanced raster map
analysis system for digital governance.

10. National Mortality Maps and Health Statistics
Health Service Areas, Counties, Zip Codes, …
Geographical Patterns for Health Resource Allocation
Study Areas for Putative Sources of Health Hazard
Balance between dilution effect and edge effect
Case Event Analysis and Ecological Analysis
Thresholds, contours, corresponding data
Regional Comparisons and Rankings with Multiple Indicators/Criteria
Choices of Reference/Control Areas

11. National Mortality Maps and Statistics Geographic Patterns—1
Mortality rate due to a specific cause of death
Elevated rates areas, patterns
Ordinal thematic maps
Transition pattern, transitionogram
Transition matrices; spatial association with varying distance
Comparatives with different causes of death

12. National Mortality Maps and Statistics Geographic Patterns—2
Surface topology and spatial structure
High mortality area delineation
Hotspots, clusters, outbreaks, corridors
Surface smoothing
Masking of true geographic patterns?
Echelon analysis, original surface, smoothed surface

13. Multiple Criteria Analysis Multiple Indicators Partial Ordering Procedures
Cells are objects of primary interest, such as countries, states, watersheds, counties, etc.
Cell comparisons and rankings are the goals
Suite of indicators are available on each cell
Different indicators have different comparative messages, i.e., partial instead of linear ordering
Hasse diagrams for visualization of partial orders. Multi-level diagram whose top level of nodes consists of all maximal elements in the partially ordered set of objects. Next level consists of all maximal elements when top level is removed from the partially ordered set, etc. Nodes are joined by segments when they are immediately comparable.

14. Multiple Criteria Analysis Multiple Indicators Partial Ordering Procedures
Issues to be addressed:
Crisp rankings, interval rankings, fuzzy rankings
Fuzzy comparisons
Echelon analysis of partially ordered sets with ordinal response levels determined by successive levels in the Hasse diagram
Hasse diagram metrics: height, width, dimension, ambiguity (departure from linear order), etc.
Hasse diagram stochastics (random structure on the indicators or random structure on Hasse diagram)
Hasse diagram comparisons, e.g., compare Hasse diagrams for different regions

17. Figure 1. Example of perfect positive and perfect negative correlation between two coordinates (variables).

18. Hasse Diagram (all countries)

21. Ranking Partially Ordered Sets – 1
S = partially ordered set (poset) with elements a, b, c, ….
How can we rank the elements of S consistent with the partial order? Such rankings are called linear extensions of the partial order.
Different people with different perceptions and priorities may choose different rankings.
How many rankings assign rank 1 to element a ? Rank 2 ? Rank 3 ? , etc.
If rankings are chosen randomly (equal probability), what is the likelihood that element x receives rank i ?

22. Ranking Partially Ordered Sets – 2 An Example
Poset (Hasse Diagram)
Some linear extensions a a a b b a b c c b a a c d b e c c c e b d d e e f d d e e d f f f f f
Jump Size:
Jump or Imputed Link ( ) is a link in the ranking that is not implied by the partial order

23. Ranking Partially Ordered Sets – 5
Poset (Hasse Diagram)
Linear extension decision tree a b a b c d c b a d e b c d c d a e f b e d e d c e d c c d d e f d e f e d e f e f e f f f f f e f f e f e f f e f e f e
Jump Size:

24. Ranking Partially Ordered Sets – 3
In the example from the preceding slide, there are a total of 16 linear extensions, giving the following frequency table.
Rank
Element 1 2 3 4 5 6
Totals a 9 16 b 7 c d e f 10
Each (normalized) row gives the rank-frequency distribution for that element
Each (normalized) column gives a rank-assignment distribution across the poset

25. Ranking Partially Ordered Sets – 3a Rank-Frequency Distributions
Element a
Element b
Element c
Element d
Element e
Element f
Rank
Rank

26. Cumulative Rank Frequency Operator – 5 An Example of the Procedure
In the example from the preceding slide, there are a total of 16 linear extensions, giving the following cumulative frequency table.
Rank
Element 1 2 3 4 5 6 a 9 14 16 b 7 12 15 c 10 d e f
Each entry gives the number of linear extensions in which the element (row label) receives a rank equal to or better that the column heading

27. Cumulative Rank Frequency Operator – 6 An Example of the Procedure16
The curves are stacked one above the other and the result is a linear ordering of the elements: a > b > c > d > e > f

28. Original Poset (Hasse Diagram)
Cumulative Rank Frequency Operator – 8 An example where F results in ties
Original Poset (Hasse Diagram) a c b d a
b, c (tied) d F
Ties reflect symmetries among incomparable elements in the original Hasse diagram
Elements that are comparable in the original Hasse diagram will not become tied after applying F operator

29. Original Poset (Hasse Diagram)
Cumulative Rank Frequency Operator – 7 An example where F must be iterated a f e b d c h g F
F 2
Original Poset (Hasse Diagram) a f e b d c h g a f e b c g d h

31. Ranking Possible Disease Clusters in the State of New York
Data Matrix

32. Composite Indexes -- 1
I1, I2, . . ., Ip indicators for ranking elements of some set
G(I1, I2, . . ., Ip) = composite index
Many possible choices for G:
Only general requirement is that G must be increasing in each indicator separately

33. Composite Indexes -- 2
Each choice of G determines a set of G-contours in indicator space and thereby determines a set of substitution or trade-off rules among the indicators
Contour of constant G x substitutes for y
 y
Indicator 2 (y)
 x
 y
 x
Indicator 1 (x)

34. Comparison of Ranking Methods
Composite Indicator Approach
Requires choice of composite index G
Implicitly or explicitly, requires choice of substitution rules among different indicators (this is often like comparing apples and oranges)
Difficult to achieve a consensus on choice of G. Final decision is often made on basis of mathematical simplicity instead of scientific substance
Once G is chosen, future elements are easily incorporated into the ranking without changing relative ranks of earlier elements

35. Comparison of Ranking Methods
Poset Cumulative Rank Frequency Approach
Entirely objective---no arbitrary choices involved
Computationally challenging (typically requires combinatorial MCMC)
Final ranking applies only to the given set of elements and reflects overall structure of entire Hasse diagram
If new elements are added to the collection to be ranked, all computations must be redone and relative rankings of earlier elements may change

36. Incorporating Judgment Poset Cumulative Rank Frequency Approach
Certain of the indicators may be deemed more important than the others
Such differential importance can be accommodated by the poset cumulative rank frequency approach
Instead of the uniform distribution on the set of linear extensions, we may use an appropriately weighted probability distribution  , e.g.,

37. Second stage screening
Multiple Criteria Analysis Multiple Indicators and Choices Health Statistics Disease Etiology, Health Policy, Resource Allocation
First stage screening
Significant clusters by SaTScan and/or
upper surface level echelon sets
Second stage screening
Multicriteria noteworthy clusters by partially ordered sets and Hass diagrams
Final stage screening
Follow up clusters for etiology, intervention
based on multiple criteria using Hass diagrams