1. Spatial analysis Measurements - Points: centroid, clustering, density
Lines: Length, sinuosity
Polygons: Length, perimeter, area, shape

2. The Centroid of point data
The centroid is the spatial mean. The ‘average’ location of all points.
The centroid can also be thought of as the balance point of a set of points.

3. S S xi yi x = y = n n Centroid
The spatial mean is called the centroid.
For a set of (x,y) coordinates, the mean center (x,y) is computed using: S xi
i=1
i=n n
x = S yi
i=1
i=n n
y =

4. Point Pattern Analysis
There are many ways to quantify the dispersion of points in region.
Clustered
Regular
Random

5. Applications of Point pattern analysis
1. whether the geographical incidence of disease shows any tendency towards clustering in geographical space?
2. Do cases of disease tend to occur in proximity to other cases?
3. Rural-urban migrants’ spatial clustering in the urban setting
Solutions:
Spatial Statistics such as Moran's I, Monte carlo simulation

6. Nang Rong
Bangkok
22 source villages and 1085 rural-urban migrants

7. Results: spatial clustering of migrants at village level

8. Point density
Point Density calculates the density of point features around each output raster cell.

9. Kernel Function Example
The result of applying a 150km-wide kernel to points distributed over California
A typical kernel function

10. (Gatrell et al., 1996)

11. Kernel Size
The smoothness of the resulting field depends on the width of the kernel
Wide kernels produce smooth surfaces
Narrow kernels produce bumpy surfaces

12. Kernel Size
Kernel width is 16 km instead of 150 km. This shows the S. California part of the database.

13. Kernel Density in Nicaraguan Health Facilities
Objective: assess health accessibility
Data
Facilities' staffing information
GPS receivers to collect latitude and longitude coordinates for every facility
Population data from the Nicaragua Census Bureau
(the location and population of all communities )

16. Local peaks for migrant’s locations (intensity surface)

17. Measuring Linear Objects
1D: Length
Vector
Distance measurements affected by elevation changes
Easily calculated with computer
Pythagorean theorem: the difference between x coordinates (longitude), squared + difference between the y coordinates (latitude), squared. Take the square root. The square root is the distance A B A B

18. Measuring Linear Objects
Raster
Add up # grid cells, multiply by resolution
But what about diagonal or highly sinuous lines?
Length possibly underrepresented
Take home:
Vector best for length calculations!

19. Measuring Shape: Sinuosity
Relating objects to their environment
Sinuosity
Closer to 1, less sinuous
Sometimes want to know about curvature

20. Measuring Polygons 2D: Length, width
More dimensionality, more measurements!
Orientation, elongation, perimeter, area,
shape

21. Measuring Polygons: Length
Vector
Calculate lengths of all opposing polygon vertices
Compare to see which is longest
Ratio of major to minor axes  elongation
Angular direction of polygon calculated using spherical geometry
Raster  can’t ascertain long axis easily
Raster Difficult to determine orientation because grid cell locations are relative

22. Measuring Polygons: Perimeter
Vector
Calculate & sum the distance of each line segment making up polygon
Raster
Identify perimeter cells, sum & multiply by cell resolution
Less accurate for complex polygons
Take home:
Vector best for perimeter calculations!

23. Measuring Polygons: Areas
Vector
Simple polygons (e.g., rectangle, triangle, circle)easy calculation
Complex polygonsdivide polygon into shapes easily measured with available formulas
Often calculated during the digitizing process
Perimeter/area ratio: Measure of polygon complexity
Perimeter/area ratio smallest for most compact shapes (e.g. circle)

24. Measuring Polygons: Areas
Raster
Regions
Assign a unique value to each region (recode/reclassify), then count the number of cells for each region & multiply by area
Tabulate data to find # grid cells for each attribute
Provides measure of proportion of different attribute types

25. Measuring polygon: Shape
Major axis
Along longest part of polygon
Must divide polygon in two equal parts
Minor axis
Along shortest part of polygon
Must divide the polygon in two equal parts
Major axis / Minor axis ratio
Values > 1 denote elongated polygon
Value = 1 denotes uniform polygon
Major axis
Minor axis
1.5
2.5
R = 1
3.5
R = 2.33
Graphic: Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University

26. Measuring polygon: Shape
Area = 25 sqr miles
Perimeter = 7 miles
CI = 7 / 25 = 0.28
Perimeter = 15 miles
CI = 15 / 25 = 0.60
Shape
Perimeter to Area Ratio
perimeter/area
Expression of the geographical complexity of a polygon
High ratio  complex
Low ratio  simple
Graphic: Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University

27. Final Project

28. Introduction Why you wanted to do the project
What’s the need, what purpose might the data serve?
What features are you planning to map?

29. Materials & Methods Datasets Source: Where did you obtain it from
Scale
Projection
Use the metadata!

30. Materials & Methods Notes on Metadata
Check the Data Quality Section to determine the data set's fitness-for-use as far as scale and resolution
Attribute Accuracy & Horizontal Positional Accuracy can describe the scale/resolution of the data set (either directly or indirectly).
Check the Lineage subsection
For each contributing source to the data set pertinent information must be included such as the source's title, media (paper, digital), and source scale.
Check the Process Steps in the Data Quality section.
In well-documented metadata, the Process Steps will describe not only how the data set was created (e.g. from paper maps), but also provide information or links to other documents containing information on how the contributing sources were created, as well.

31. Materials & Methods Describe your analyses
Did you have to query data out of a larger dataset?
How did you use that query to generate a separate shapefile for your analysis?

32. Results & Discussion Present whatever maps and tables you create
Discuss their meaning

33. Conclusions
What did you learn from your analysis?