1. Topic 4 – Geographical Data Analysis
A – The Nature of Spatial Analysis
B – Basic Spatial Analysis

2. For personal and classroom use only
Conditions of Usage
For personal and classroom use only
Excludes any other forms of communication such as conference presentations, published reports and papers.
No modification and redistribution permitted
Cannot be published, in whole or in part, in any form (printed or electronic) and on any media without consent.
Citation
Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University.

3. The Nature of Spatial Analysis
1. Spatial Analysis and its Purpose
2. Spatial Location and Reference
3. Spatial Patterns
4. Topological Relationships

4. Spatial Analysis and its Purpose1
Spatial Analysis and its Purpose
Conceptual framework
Search of order amid disorder.
Organize information in categories.
Method
Inducting or deducting conclusions from spatially related information.
Deduction: Deriving from a model or a rule a conclusion.
Induction: Learning new concepts from examples.
Spatial analysis as a decision-making tool.
Help the user make better decisions.
Often involve the allocation of resources.

5. Spatial Analysis and its Purpose1
Spatial Analysis and its Purpose
Requirements
1) Information to be analyzed must be encoded in some way.
2) Encoding implicitly requires a spatial language.
3) Some media to support the encoded information.
4) Qualitative and/or quantitative methods to perform operations over encoded information.
5) Ways to present to results in an explicit message.
Information
Encoding
Media
Methods
Message

6. Spatial Analysis and its Purpose1
Spatial Analysis and its Purpose
Geographic Techniques
GIS
Cartography
Quantitative
methods
Remote sensing
Physical Geography
Geomorphology
Climatology
Biogeography
Soils
Spatial
Analysis
Human Geography
Historical
Political
Economic
Behavioral
Population

7. Mapping Deaths from Cholera, London, 1854 (Snow Study)

8. Spatial Analysis and its Purpose1
Spatial Analysis and its Purpose
Data Retrieval
Browsing; windowing (zoom-in & zoom-out).
Query window generation (retrieval of selected features).
Multiple map sheets observation.
Boolean logic functions (meeting specific rules).
Map Generalization
Line coordinate thinning of nodes.
Polygon coordinate thinning of nodes.
Edge-matching. DB HD
SHP

9. Spatial Analysis and its Purpose1
Spatial Analysis and its Purpose
Map Abstraction
Calculation of centroids.
Visual editing & checking.
Automatic contouring from randomly spaced points.
Generation of Thiessen / proximity polygons.
Reclassification of polygons.
Raster to vector/vector to raster conversion.
Map Sheet Manipulation
Changing scales.
Distortion removal/rectification.
Changing projections.
Rotation of coordinates.

10. Spatial Analysis and its Purpose1
Spatial Analysis and its Purpose
Buffer Generation
Generation of zones around certain objects.
Geoprocessing
Polygon overlay.
Polygon dissolve.
“Cookie cutting”.
Measurements
Points - total number or number within an area.
Lines - distance along a straight or curvilinear line.
Polygons - area or perimeter. 6
4.5 5
7.5

11. Spatial Analysis and its Purpose1
Spatial Analysis and its Purpose
Raster / Grid Analysis
Grid cell overlay.
Area calculation.
Search radius.
Distance calculations.
Digital Terrain Analysis
Visibility analysis of viewing points.
Insolation intensity.
Grid interpolation.
Cross-sectional viewing.
Slope/aspect analysis.
Watershed calculation.
Contour generation. 15

12. 3 Spatial Patterns Relativity of objects Main patterns
Definition of an object in view of another.
Create spatial patterns.
Main patterns
Size.
Distribution/spacing : Uniform, random and clustered.
Proximity.
Density: Dense and dispersed.
Shape.
Orientation.
Scale.
Size
Form
Orientation
Scale
Proximity

13. Positive autocorrelation3
Spatial Patterns
Spatial autocorrelation
Set of objects that are spatially associated.
Relationship in the process affecting the object.
Negative autocorrelation.
Positive autocorrelation.
Uniform
Clustered
Positive autocorrelation
Random

14. Topological Relations4
Topological Relations
Proximity
Qualitative expression of distance.
Link spatial objects by their mutual locations.
Nearest neighbors.
Buffer around a point or a line.
Directionality

15. Topological Relations4
Topological Relations
Adjacency
Link contiguous entities.
Share at least one common boundary.
Intersection
Containment
Link entities to a higher order set.
City B
City A

16. Topological Relations4
Topological Relations
Connectivity
Adjacency applied to a network.
Must follow a path, which is a set of linked nodes.
Shortest path.
All possible paths. 1 2 3 4 5 6

17. Topological Relations4
Topological Relations
Arable land
Flat land
Intersection
What two geographical objects have in common.
Union
Summation of two geographical objects.
Complementarity
What is outside of the geographical object.
Suitable for agriculture
Land
Non arable land

18. Elementary Spatial AnalysisB
Elementary Spatial Analysis
1. Statistical Generalization
2. Data Distribution
3. Spatial Inference

19. Statistical Generalization1
Statistical Generalization
Maps and statistical information
Important to display accurately the underlying distribution of data.
Data is generalized to search for a spatial pattern.
If the data is not properly generalized, the message may be obscured.
Balance between remaining true to the data and a generalization enabling to identify spatial patterns.
Thematic maps are a good example of the issue of statistical generalization.

20. Statistical Generalization1
Statistical Generalization
Data
Classification
Spatial Pattern 15 25 88 34 56 7 92 61 45 77 39 21
0-30
31-65
65-

21. Statistical Generalization1
Statistical Generalization
Number of classes
Too few classes: contours of data distribution is obscured.
Too many classes: confusion will be created.
Most thematic maps have between 3 and 7 classes.
8 shades of gray are generally the maximum possible to tell apart.

22. Statistical Generalization1
Statistical Generalization
Classification methods
Thematic maps developed from the same data and with the same number of classes, will convey a different message if the ranging method is different.
Each ranging method is particular to a data distribution.

23. 2 Data Distribution Histogram
The first step in producing a thematic map.
See how data is distributed.
Use of basic statistics such as mean and standard deviation.
An histogram plots the value against the frequency.
Uniform
Normal
Exponential
Value
Frequency

24. 2 Data Distribution Equal interval
Each class has an equal range of values.
Difference between the lowest and the highest value divided by the number of categories.
(H-L)/C
Easy to interpret.
Good for uniform distributions and continuous data.
Inappropriate if data is clustered around a few values. C1 C2 C3 C4
Frequency L H
Value

25. 2 Data Distribution Quantiles Equal area
Equal number of observations in each category.
n(C1) = n(C2) = n(C3) = n(C4).
Relevant for evenly distributed data.
Features with similar values may end up in different categories.
Equal area
Classes divided to have a similar area per class.
Similar to quantiles if size of units is the same.
n(C1)
n(C2)
n(C3)
n(C4) C1 C2 C3 C4
Frequency
Value

26. 2 Data Distribution Standard deviation
The mean (X) and standard deviation (STD) are used to set cutpoints.
Good when the distribution is normal.
Display features that are above and below average.
Very different (abnormal) elements are shown.
Does not show the values of the features, only their distance from the average. C1 C2 C3 C4 X
-1STD
+1STD
Frequency
Value

27. 2 Data Distribution Arithmetic and geometric progressions
Width of the class intervals are increased in a non linear rate.
Good for J shaped distributions. C1 C2 C3 C4
Frequency
Value

28. 2 Data Distribution Natural breaks Complex optimization method.
Minimize the sum of the variance in each class.
Good for data that is not evenly distributed.
Statistically sound.
Difficult to compare with other classifications.
Difficult to choose the appropriate number of classes. C1 C2 C3 C4
Frequency
Value

29. 2 Data Distribution User defined Using classification
The user is free to select class intervals that fit the best the data distribution.
Last resort method, because it is conceptually difficult to explain its choice.
Analysts with experience are able to make a good choice.
Also used to get round numbers after using another type of classification method.
$5,000 - $10,000 instead of $4,982 - $10,123.
Using classification
Classification can be used to deliberately confuse or hide a message.

30. 2 Data Distribution “no problems” - Equal steps
“there is a problem” - Quantiles

31. 2
Data Distribution
“everything is within standards” - standard deviation

32. 3 Spatial Inference Filling the gaps Interpolation and extrapolation
Sampling shortens the time necessary to collect data.
Requires methods to “fill the gaps”.
Interpolation and extrapolation
Data at non-sampled locations can be predicted from sampled locations.
Interpolation:
Predict missing values when bounding values are known.
Extrapolation:
Predict missing values outside the bounding area.
Only one side is known.

33. Spatial Inference: Interpolation and Extrapolation3
Spatial Inference: Interpolation and Extrapolation
Height
Location
Interpolation line
Sample
Number of vehicles
Delay at the traffic light
Extrapolation line
Interpolation line
Sample

34. Spatial Inference: Best Fit3
Spatial Inference: Best Fit
112
110
y = x 2
108 R =
106
Sex Ratio
104
102
100 98 96
-130
-120
-110
-100
-90
-80
-70
-60
Longitude

35. 3 Spatial Inference Aggregation Conversion
Data within a boundary can be aggregated.
Often to form a new class.
Conversion
Data from a sample set can be converted for a different sample set.
Changing the scale of the geographical unit.
Switching from a set of geographical units to another.

36. Spatial Inference: Aggregation and Conversion3
Spatial Inference: Aggregation and Conversion
Boreal Forest
Pine Trees
Poplar Trees
District A
District B1
District B2
District B