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Introduction to GIS Modeling
Week 9 — Spatial Data Mining
GEOG 3110 –University of Denver
Presented by
Joseph K. Berry
W. M. Keck Scholar, Department of Geography, University of Denver
Basic Descriptive Statistics and its GIS Expression:
Normalizing maps; Mapping spatial dependency
Linking Numeric and Geographic Patterns:
Map comparison; Similarity maps; Clustering mapped data;
Investigating map correlation; Developing prediction models;
Assessing prediction results
Kicking for the Finish
Exercise #9 — to tailor your work to your interests, you can choose to not complete this
standard exercise, however in lieu of the exercise you will submit a short paper (4-8 pages)
on a GIS modeling topic of your choice. Due 12:00 midnight, Thursday, March 10th.
Optional Exercises — you can turn in these exercises for extra credit anytime before
5:00 pm, Tuesday, March 15th.
Final Exam Study Questions — covering weeks 7-10, Spatial Statistics and Future
Directions; the exam is optional and can only improve your grade. You are encouraged to
study together and exchange insights about answering the questions.
…at least three-fourths of the exam will be taken directly (verbatim) from the list of study
questions. The format will be similar to the last exam, with questions from Terminology,
Procedures and Basic Concepts, How Things Work and Mini-Exercises.
…study questions for Exam 2 are posted on the class website now; send me an email if a
question needs further explanation and I will post the clarification.
Final Exam — Covers material from weeks 7 (GIS Modeling), 8 (Surface Modeling), 9
(Spatial Data Mining) and 10 (Future Directions)
…exam posted on the class website by 10:00 am, Thursday, March 10th and must be completed by
8:00 am, Monday, March 14th.
… at the end of the last class I will be handing out a CD with all of the class material—
sort of a “graduation present” that will keep you GIS-ing for years
(Berry)
An Analytic Framework for GIS Modeling
(Last week)
Surface Modelling operations involve
creating continuous spatial distributions from
point sampled data (univariate).
(This week)
Spatial Data Mining operations
involve characterizing numerical patterns and
relationships among mapped data (multivariate).
See www.innovativegis.com/basis/Download/IJRSpaper/
(Berry)
Basic Concepts in Statistics (Standard Normal Curve)
See Beyond Mapping III , Topic 7, Linking Data Space and Geographic Space
(Berry)
Basic Concepts in Statistics (SN_Curve Shape)
Kurtosis …shape
(positive= peaked; negative= flat)
See Beyond Mapping III , Topic 7, Linking Data Space and Geographic Space
(Berry)
Basic Concepts in Statistics (SN_Curve Shape continued)
…Multi-modal
…Skewness
(positive= right;
negative= left)
See Beyond Mapping III , Topic 7, Linking Data Space and Geographic Space
(Berry)
Preprocessing Mapped Data (Preprocessing Types 1-3)
Preprocessing involves conversion of raw data into consistent units
that accurately represent mapped conditions (4 considerations)
Calibration 1 — “tweaking” the values… sort of like a slight turn on a
bathroom scale to alter the reading to what you know is your ‘true weight’
Translation 2 — converts map
values into appropriate units for
analysis, such as feet into meters
or bushels per acre (measure of
volume) into tons per hectare
(measure of mass)
Antenna Offset
GPS Fix Delay
Overlap and Multiple Passes
Mass Flow Lag and Mixing
Adjustment/Correction 3 —
dramatically changes the
data, such as post processing
GPS coordinates and/or Mass Flow Lag adjustment
(Berry)
Normalizing Mapped Data (4
th
type of preprocessing)
Normalization — involves standardization of a data set, usually for
comparison among different types of data…
“apples and oranges to mixed fruit scale”
Goal …Norm_GOAL = (mapValue / 250 ) * 100
0-100 …Norm_0-100 = ((mapValue – min) * 100) / (max – min) + 0
SNV …Norm_SNV = ((mapValue - mean) / stdev) * 100
Norm_GOAL = (Yield_Vol / 250 ) * 100
…generates a standardized map based
on a yield goal of 250 bushels/acre.
This map can be used in analysis with
other goal-normalized maps, even
from different crops
Key Concept
Since normalization involves scalar
mathematics (constants), the
pattern of the numeric distribution
(histogram) and the spatial
distribution (map) do not change
…same relative distributions
See Beyond Mapping III , Topic 18, Understanding Grid-based Data
Note: the generalized rescaling equation is…
Normalize a data set to a fixed range of Rmin to Rmax = (((X-Dmin) * (Rmax – Rmin)) / (Dmax – Dmin)) + Rmin
…where Rmin and Rmax is the minimum and maximum values for the rescaled range, Dmin and Dmax is the minimum and maximum values for the input data
and X is any value in the data set to be rescaled.
(Berry)
Assessing Localized Variation
Question 1 – Visual Map Analysis
(Spatial and Numeric distributions)
The “Scan” operation moves a window
around the yield map and calculates the
Coefficient of Variation with a 2-cell
radius of each location
…higher values indicate areas
with more localized variability
CoffVar= (StDev/Mean) * 100
Scan Yield_Volume
Coffvar
Within 2
For Yield_Coffvar
Where,
Coffvar = Stdev/mean *100
(Berry)
Data Proximity/Buffer Stratification
…proximity to field edge
Edge effects
“Sweet Spot”
(interior)
…Stratification
partitions the data
(numeric) or the project
area (spatial) into
logical groups—
…Proximity map
identifies the distance
from point, line or
polygon features to all
other locations
…unusually high yield
…proximity to high yield areas
Far
:
Close
…Yield map
> Average + 1Stdev
“High Yield”
vicinity
(Berry)
Summarizing Map Regions (template/data)
…creates a map summarizing values from a data
map (Phosphorous levels) that coincide with the
categories of a template map (Soil types)
Soil
Types
BIB
Phosphorous
levels
Soil Type Pavg
Ve
15.0
VdC
12.8
BIB
11.2
BIA
14.6
TuC
10.5
HvB
11.3
Overall BIA
Pavg = 14.6
…average phosphorous
level for each soil type
13.6
15.5
…average P-level for each soil unit
(clump first before COMPOSITE)
8.6
(Berry)
Comparing Discrete Maps (Multivariate analysis)
Thematic Categorization
…we often represent continuous
spatial data (map surfaces) as a
set of discrete polygons
Which classified map is correct?
How similar are the three maps?
Spatial Precision
(Where — boundaries)
Medium
High
Low
of Points, Lines and Areas
(polygons) is a primary
concern of GIS, but we are
often less concerned with
Thematic Accuracy
(What — map values)
See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning
(Berry)
Comparing Discrete Maps
Two ways to compare Discrete Maps…
Coincidence Summary
Proximal Alignment
693
…Coincidence Summary
generates a cross-tabular
listing of the intersection of
two maps.
Table Interpretation
Diagonal (Same)
Off-diagonal (Above/Below)
Percentages (% Same)
Overall Percentage
83%
((475+297+563)/1950)*100= 68%
((631+297+693)/1950)*100=
Raster versus Vector
See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning
(Berry)
Comparing Discrete Maps
Two ways to compare Discrete Maps…
Coincidence Summary
Proximal Alignment
Question 2
Map2: Med-- 104 + 297 + 225 = 626; (297/626) *100= 47 percent matched
631 + 297 + 693 = 1621; (1621/1950) *100= 83 percent matched
Map1
…Coincidence Summary
generates a cross-tabular
listing of the intersection of
two maps.
Map2
Map1
Map3
Table Interpretation
Diagonal (Same)
Off-diagonal (Above/Below)
Percentages (% Same)
Overall Percentage
475 + 297 + 563 = 1335; (1335/1950) *100= 68 percent matched
Map3: Med-- 260 + 297 + 335= 912; (297/912) *100= 36 percent matched
See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning
83%
((475+297+563)/1950)*100= 68%
((631+297+693)/1950)*100=
Raster versus Vector
(Berry)
Coincidence Table (idealized conditions)
Low
Med
High
Total
Low
208
0
0
208/208
= 100%
Med
0
208
0
208/208
= 100%
0
0
208
208/208
= 100%
High
Diagonal elements in the map comparison matrix identify
agreement (matches) between two progressive ordinal maps
Off-diagonal elements in the map comparison matrix identify
disagreement (miss-matches) between two progressive ordinal maps
Low
Med
High
Total
…ALL MISMATCHES where
there is an opposite
relationship
Overall coincidence = 0%
Low
69
70
69
69/208
= 33%
Med
70
69
69
69/208
= 33%
High
69
69
70
69/208
= 33%
Total
69/208
= 33%
69/208
= 33%
208/208 208/208 208/208 624/624
Total = 100% = 100% = 100% = 100%
…PERFECT COINCIDENCE
where all of the increasing
ordinal steps are matched
(diagonal) and there is no
mismatches (off-diagonal).
Overall coincidence is 624/624 = 100%
found by the sum of the diagonal
elements (matches); the other totals
indicate percent agreement by
category on each map
Low
Med
High
Total
104 104
0/208
= 0%
Low
0
…EQUALLY BALANCED
matches and mismatches
where there is no pattern
relationship
Med
104
High
104 104
Overall coincidence = 33%
partially matched and mismatched
Total
0/208
= 0%
69/208 208/624
= 33% = 33%
0
0/208
= 0%
104
0/208
= 0%
0
0/208
= 0%
0/208
= 0%
0/624
= 0%
(Berry)
Comparing Discrete Maps
Two ways to compare Discrete Maps…
Coincident Summary
Proximal Alignment
Proximity_Map1_Category1 * Binary_Map3_Category1
…non-zero values identify changes and how far away
…Proximal Alignment
isolates a category on one
of the maps, generates its
proximity, then identifies
the proximity values that
align with the same
category on the other map.
Table Interpretation
Zeros (Agreement)
Values (> Disagreement)
PA Index (average)
See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning
(Berry)
Comparing Map Surfaces (Statistical Tests)
Three ways to compare Map Surfaces…
Statistical Tests
Percent Difference
Surface Configuration
…Statistical Tests compare one set of cell values to that of another based on the
differences in the distributions of the data— 1) data sets (partition or coincidence;
continuous or sampled) 2) statistical procedure (t-Test, f-Test, etc.)
Box-and-whisker
graphs
See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning
(Berry)
Comparing Map Surfaces (%Difference)
Three ways to compare Map Surfaces…
Statistical Tests
Percent Difference
Surface Configuration
Question 3
…Percent Difference capitalizes on the spatial arrangement of the values by
comparing the values at each map location— %Difference Map, %Difference Table
See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning
(Berry)
Comparing Map Surfaces (Surface Configuration)
Three ways to compare Map Surfaces…
Statistical Tests
Percent Difference
Surface Configuration
…Surface Configuration capitalizes on the spatial arrangement of the values by
comparing the localized trend in the values — Slope Map, Aspect Map, Surface
Configuration Index
See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning
(Berry)
Comparing Map Surfaces (Temporal Difference)
1997_Yield_Volume
- 1998_Yield_Volume
= Yield_Diff
Map Variables… map values within an analysis grid
can be mathematically and statistically analyzed
…green indicates
areas of increased
production
…yellow indicates
minimal change
…red indicates
decreased production
See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships
(Berry)
Data Analysis (establishing relationships)
On-farm studies, such as seed hybrid performance, can be conducted using actual farm conditions…
…management action recommendations are based on local relationships instead of
Experiment Station research hundreds of miles away
…is radically changing research and management practices in agriculture and
numerous other fields from business to epidemiology and natural resources
(Berry)
Spatial Dependency
Spatial Variable Dependence — what occurs at a location
in geographic space is related to:
• the conditions of that variable at nearby locations, termed
Spatial Autocorrelation (intra-variable dependence)
• the conditions of other variables at that location, termed
Spatial Correlation (inter-variable dependence)
Map Stack– relationships among maps are investigated by
aligning grid maps with a common configuration…
#cols/rows, cell size and geo-reference.
Data Shishkebab– each map represents a variable, each grid
space a case and each value a measurement with all of the
rights, privileges, and responsibilities of non-spatial
mathematical , numerical and statistical analysis
See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships
(Berry)
Visualizing Spatial Relationships
Interpolated Spatial Distribution
Phosphorous (P)
What spatial
relationships do you
see?
…do relatively high levels
of P often occur with high
levels of K and N?
…how often?
…where?
See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships
(Berry)
Identifying Unusually High Measurements
…isolate areas with mean + 1 StDev (tail of normal curve)
See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships
(Berry)
Level Slicing
…simply multiply the two maps to identify joint coincidence
1*1=1 coincidence (any 0 results in zero)
See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships
Question 4
(Berry)
Multivariate Data Space
…sum of a binary progression (1, 2 ,4 8, 16, etc.) provides
level slice solutions for many map layers
See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships
(Berry)
Calculating Data Distance
…an n-dimensional plot depicts the multivariate distribution; the distance
between points determines the relative similarity in data patterns
…the closest floating ball is the least similar (largest data distance) from the comparison point
See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships
(Berry)
Identifying Map Similarity
Question 5
…the relative data distance between the comparison point’s data pattern
and those of all other map locations form a Similarity Index
The green tones indicate field locations with fairly similar P, K and N levels; red tones indicate dissimilar areas.
See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships
(Berry)
Clustering Maps for Data Zones
Question 6
…a map stack is a spatially organized set of numbers
…groups of “floating balls” in data space
identify locations in the field with similar data
patterns– data zones
…fertilization rates vary for the different
clusters “on-the-fly”
See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships
Cyber-Farmer, Circa 1992
Variable Rate Application
(Berry)
Assessing Clustering Results
…Clustering results can be roughly evaluated using basic statistics
Average, Standard Deviation, Minimum and Maximum values within each cluster are calculated. Ideally
the averages between the two clusters would be radically different and the standard deviations small—large
difference between groups and small differences within groups.
Standard
Statistical Tests
of two data sets
Box and
Whisker Plots
to visualize
differences
See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships
(Berry)
How Clustering Works (IsoData algorithm)
The scatter plot
shows Height
versus Weight
data that might
have been
collected in
your old
geometry class
The data
distance to
each
weight/height
measurement
pair is
calculated and
the point is
assigned to the
closest
arbitrary
cluster center
The average
X,Y
coordinates of
the assigned
students is
calculated and
used to
reposition the
cluster centers
Repeat data
distances,
cluster
assignments
and
repositioning
until no change
in cluster
membership
(centers do not
move)
See Beyond Mapping III , Topic 7, Linking Data Space and Geographic Space
(Berry)
Spatial Data Mining (The Big Picture)
…making sense out of a map stack
Mapped data that
exhibits high spatial
dependency create
strong prediction
functions. As in
traditional statistical
analysis, spatial
relationships can be
used to predict
outcomes
…the difference is
that spatial statistics
predicts where
responses will be
high or low
See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships
(Berry)
An Analytic Framework for GIS Modeling
This Week
Spatial Data Mining operations involve
characterizing numerical patterns and
relationships among mapped data.
See www.innovativegis.com/basis/Download/IJRSpaper/
(Berry)
Regression (conceptual approach)
A line is “fitted” in data space that balances the data so the differences from the
points to the line (residuals) for all the points are minimized
and the sum of the differences is zero…
…the equation of the regression line is used to predict the
“Dependent” variable (Y axis) using one or more “Independent” variables (X axis)
(Berry)
Evaluating Prediction Maps (non-spatial)
Non-spatial …R-squared value looks at the
deviations from the regression line; data
patterns about the regression line
(Berry)
Map Variables
The Dependent Map variable is the one that you want to predict…
Question 7
…derive from
customer data
…from a set of existing or easily measured Independent Map variables
See Beyond Mapping III , Topic 28, Spatial Data Mining in Geo-Business
(Berry)
Map Regression Results (Bivariate)
Scatter plots and regression equations relating Loan Density
to three candidate driving variables (Housing Density, Value and Age)
Question 8
Loans= fn( Housing Density )
Loans= fn( Home value )
Loans= fn( Home Age )
The “R-squared index” provides a general measure of how good the predictions ought to be—
40%, 46% indicates a moderately weak predictors; 23% indicates a very weak predictor
(R-squared index = 100% indicates a perfect predictor; 0% indicates an equation with no predictive capabilities)
See Beyond Mapping III , Topic 28, Spatial Data Mining in Geo-Business
(Berry)
Generating a Multivariate Regression
…a regression equation using all three independent map variables using
multiple linear regression is used to generate a prediction map
Question 9
See Beyond Mapping III , Topic 28, Spatial Data Mining in Geo-Business
(Berry)
Evaluating Regression Results (multiple linear)
Optional Question 9-1
…a regression equation using all three independent map variables using multiple
linear regression is used to generate a prediction map
…that is compared to the actual dependent variable data — Error Surface
See Beyond Mapping III , Topic 28, Spatial Data Mining in Geo-Business
(Berry)
Using the Error Map to Stratify
One way to improve the predictions, however, is to stratify the data set by breaking it
into groups of similar characteristics …and then generating separate regressions
…generate a different regression for
each of the stratified areas– red,
yellow and green
…other stratification techniques include indigenous knowledge,
level-slicing and clustering
See Beyond Mapping III , Topic 28, Spatial Data Mining in Geo-Business
(Berry)
An Analytic Framework for GIS Modeling
This Week
Spatial Data Mining operations involve
characterizing numerical patterns and
relationships among mapped data.
See www.innovativegis.com/basis/Download/IJRSpaper/
(Berry)
Prescriptive Mapping
Four primary types of applied spatial models:
 Suitability— mapping preferences (e.g., Habitat and Routing)
 Economic— mapping financial interactions (e.g., Combat Zone and Sales Propensity)
 Physical— mapping landscape interactions (e.g., Terrain Analysis and Sediment Loading)
 Mathematical/Statistical— mapping numerical relationships…
― Descriptive
math/stat models summarize existing mapped data
(e.g., Standard Normal Variable Map for Unusual Conditions and Clustering for Data Zones)
― Predictive
math/stat models develop equations relating mapped data
(e.g., Map Regression for Equity Loan Prediction and Probability of Product Sales )
― Prescriptive
math/stat models identify management actions based on
descriptive/predictive relationships (e.g., Retail Marketing and Precision Ag)…
Phosphorous (P)
Continuous Actions: Equation defining action(s)
Negative linear equation of the form: y = aX
P2O5/
If P is 0-4 ppm, then apply 50 lbs P2O5/Acre
If P is 4-8 ppm, then apply 30 lbs P2O5/Acre
If P is 8-12 ppm, then apply 15 lbs P2O5/Acre
If P is >12 ppm, then apply 0 lbs P2O5/Acre
50
50
0
0
30
15
0
P
12
more
P
12
more
50
P2O5/
Discrete Actions: If <condition(s)> Then <Action(s)>
Negative exponential equation of the form: y = e-x
0
(Berry)
0
Grid-Based Map Analysis
Spatial analysis investigates the “contextual” relationships in mapped data…
 Reclassify— reassigning map values (position; value; size, shape; contiguity)
 Overlay— map overlay (point-by-point; region-wide)
 Distance— proximity and connectivity (movement; optimal paths; visibility)
 Neighbors— ”roving windows” (slope/aspect; diversity; anomaly)
Surface modeling maps the spatial distribution and pattern of point data…
 Density Analysis— count/sum of points within a local window
 Spatial Interpolation— weighted average of points within a local window
 Map Generalization— fits mathematical relationship to all of the point data
Spatial data mining investigates the “numerical” relationships in mapped data…
 Descriptive— summary statistics, comparison, classification (e.g., clustering)
 Predictive— math/stat relationships among map layers (e.g., regression)
 Prescriptive— appropriate actions (e.g., optimization)
(Berry)