Principles and Concepts of Geospatial Data Structure, Algorithms, Mining,

1
Principles and Concepts of Geospatial Data
Structure, Algorithms, Mining, Fusion

• Presented by
• GDF Learning Group

2
Geospatial Data Structure

• Entity-Based Models
• Tessellation
• Vector Mode
• Half-Plane Representation
• (Refer to Chapter Two, course textbook for
  additional information)

3
Entity-Based Models

• Zero-dimensional objects or points
• One-dimensional objects or linear objects
• Two-dimensional objects or surface objects

4
0-D Object or Point

• A point is used to represent the location of an
  object whose shape is not considered useful.

5
1-D Object or Linear Object

• Polyline
• Simple Polyline
• Monotone Polyline

6
2-D objects

• Polygon
• Convex Polygon
• Monotone Polygon

7
Tessellation

• Basically the partitioning of space into cells or
  a grid.
• Instead of using x,y coordinates, tessellation
  partitions cells and names them with numbers
  (this could be confusing).

8
Vector Mode

• Vector Mode uses an x and y axis to plot the
  coordinate of points.

9
Half-Plane Representation

• Half-Plane Representation can be defined as a set
  of points that satisfy an inequation of the form
  a1x1a2x2adxd
• Really it is an ongoing group of linked polygons
  spread out over an x,y, and z axis.
• This fives the impression that it is
  3-Dimensional, however we know that this is not
  truly so.

10
Algorithms

• Part II

11
Algorithms

• Point in polygon
• Line intersection
• Polygon intersection

12
Point in a polygon

• If the point lies on an edge of the polygon then
  the point is contained in the polygon
• If a horizontal line is drawn from the point to
  the right and intersects an even number of edges
  of the polygon it is outside the polygon
• Only non collinear lines are counted when
  intersected lines are counted

13
Point in a polygon
14
Line intersection

• A line is drawn vertically at the left most
  endpoint of the lines in question
• The y coordinate of the lines are noted
• The vertical line is moved to the right till it
  gets to the rightmost endpoint of the lines
• If the y coordinate of two lines is the same then
  the lines intersect

15
Line intersection
16
Polygon intersection

• Starts off with a synchronized scan of the
  boundaries of both polygons
• Reports the intersection points of the polygons
  and which vertexes are inside the other polygons
• Continues till all boundaries have been scanned
• If no intersections are detected then it tests if
  one polygon is completely in the other polygon

17
Polygon intersection
18
Data Mining

• Part III

19
Data Mining

• The process of discovering interesting and
  potentially useful patterns of information
  embedded in large databases
• Examples of large databases are Earth Observation
  Satellites, the U.S. Census, and weather and
  climate databases

20
Pattern Discovery

• A pattern can be a summary statistic, like the
  mean, median, or standard deviation of a dataset,
  or a simple rule such as Beach property is, on
  average, 40 percent more expensive than inland
  property

21
Data Mining Process

• Domain expert provides a database to the data
  mining analyst
• The DE and DMA must agree on a problem statement
• The DMA decides which technique and algorithm
  should be used, resulting in hypotheses of a
  potential pattern

22
Data Mining Process

• The next step is verification, refinement, and
  visualization of the pattern, usually done with
  GIS software
• The final step is interpretation of the pattern
  and deciding what action to take

23
Statistics and Data Mining

• Statistics are used to verify whether the
  hypotheses are true or not, but there are some
  false dismissals

24
Unique Features of Data Mining

• Spatial data tends to be highly self-correlated
• For example, people with similar characteristics,
  occupations, and backgrounds tend to cluster
  together in the same areas
• The first law of geography states that
  Everything is related to everything else, but
  nearby things are more related than distant
  things (Tobler, 1979)
• In spatial statistics this is called spatial
  correlation

25
Example of Spatial Data MiningBefore the
Invention of Computers

• In 1855, Asiatic cholera was all over London
• An epidemiologist marked all locations where
  disease struck
• A cluster formed around a water pump
• Water pump was turned off and the disease began
  to subside
• The goal of spatial data mining is to automate
  the discoveries of such correlations, which can
  then be examined by specialists for further
  validation and verification

26
Motivating Spatial Data Mining

• Part IV

27
Measures of Spatial Form and Autocorrelation

• The propensity of a variable to exhibit similar
  values as a function of the distance between the
  spatial locations at which it is measured
• Spatial autocorrelation is used to measure this

28
Spatial Autocorrelation

• A property that is often exhibited by variables
  which are sampled over space
• For example, soil fertility, rainfall, and air
  pressure all vary gradually over space
• Morans I is a measure used to quantify this
  interdependence
• There are both global and local Morans I

29
Spatial Statistical Models

• Often used to represent the observations in terms
  of random variables
• Can be used for estimation, description, and
  prediction based on probability theory

30
Point Process

• A model for the spatial distribution of the
  points in a point pattern
• Examples are the position of trees in a forest or
  locations of gas stations in a city

31
Lattices

• A countable collection of regular or irregular
  spatial sites
• An example is census data defined on census
  blocks
• Several spatial analysis functions can be applied
  on lattice models

32
Geostatistics

• Deals with the analysis of spatial continuity,
  which is an inherent characteristic of spatial
  data sets
• Provides a set of statistical tools for modeling
  spatial variability and interpolation
  (prediction) of attributes at unsampled locations
• Kriging is a well-known estimation procedure used
  in geostatistics

33
The Data Mining Trinity

• Classification
• Clustering
• Association rules

34
Location Prediction andThematic Classification

• The goal of classification is to estimate the
  value of an attribute of a relation based on the
  value of the relations other attributes

35
Determining the Interactionamong Attributes

• When x happens y is likely to occur also

36
Identification of Hot SpotsClusters and Outliers

• Hot spots are regions in the study space that
  stand out compared with the overall behavior
  prevalent in the space
• Outliers are observations that appear to be
  inconsistent with the remainder of the data set
• Law enforcement agencies use hot spot analysis to
  determine areas within their jurisdiction that
  have unusually high levels of crime

37
Data Fusion

• How will we apply our area into the overall
  homeland security project?

38
Fusions 2 Main Categories

• Fusion of collection of measurements done by data
  mining.
• Field data collected by actual measurements done
  by using algorithms.
• Also could be analysis of the remote sensing.

• Fusion of remote sensing images.
• Vector data
• Raster data
• Tins of areas
• (map data of routes, locations,)

39
Whats Next?

• We can apply our data (mapping and measurements)
  to a conclusion on how to solve a problem.

• We can take the acquired knowledge and continue
  crunching numbers.

40
Conclusion

• Today, we took a deeper look at principles and
  concepts of Geospatial Data Structure,
  Algorithms, Mining, Data Fusion.
• In our next presentation, we will explore
  implications of these concepts for the Homeland
  Security GIS application