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Grid-based Map Analysis Techniques and
Modeling Workshop
Part 1 – Maps as Data
Part 2– Surface Modeling
Part 3 – Spatial Data Mining
Linking geographic and data space
Map similarity
Clustering mapped data
Map regression
Future geo-statistical tools
Part 4 – Spatial Analysis
Part 5 – GIS Modeling
Grid-Based Map Analysis
Surface Modeling maps the spatial distribution and pattern of point data…
 Map Generalization— characterizes spatial trends (e.g., titled plane)
 Spatial Interpolation— deriving spatial distributions (e.g., IDW, Krig)
 Other— roving window/facets (e.g., density surface; tessellation)
Data Mining investigates the “numerical” relationships in mapped data…
 Descriptive— aggregate statistics (e.g., average/stdev, similarity, clustering)
 Predictive— relationships among maps (e.g., regression)
 Prescriptive— appropriate actions (e.g., optimization)
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; map-wide)
 Distance— proximity and connectivity (movement; optimal paths; visibility)
 Neighbors— ”roving windows” (slope/aspect; diversity; anomaly)
(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; Spatial Data Mining
…understanding relationships among sets of map layers)
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
(Berry)
Linking Data and Map Distributions
A histogram depicts the numerical distribution
A map depicts the geographical distribution
…the data values
link the two
views—
Click anywhere
on the map and
the histogram
interval is
highlighted; click
on a histogram
interval and the
map locations
are highlighted
(See Map Analysis, “Topic 7” for more information)
(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?
(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
(Berry)
Identifying Map Similarity
…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 Map Analysis, “Topic 16, Calculating Map Similarity” for more information)
(Berry)
Clustering Maps for Data Zones
…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
…apply different management actions
for different “data zones”
Variable Rate Application
(Berry)
Evaluating Clustering Results
…graphical and statistics procedures
assess how “distinct” clusters are—
clustering performance
…distinct in
K, fairly
distinct in N
but not
distinct in P
(overlap)
(Berry)
The Precision Ag Process (Fertility example)
As a combine moves through a field 1) it uses GPS to check its location then 2) checks
the yield at that location to 3) create a continuous map of the yield variation every few
feet. This map 4) is combined with soil, terrain and other
maps to derive a 5) “Prescription Map” that is used to
Steps 1)–3)
adjust fertilization levels every few feet in the field.
Prescription Map
(Cyber-Farmer, Circa 1990)
45.00
On-the-Fly
Yield Map
40.00
Map Analysis
Step 4)
Farm dB
Step 5)
35.00
Zone 3
30.00
25.00
Zone 2
20.00
15.00
10.00
5.00
Variable Rate Application
Zone 1
5.00
10.00
15.00
20.00
25.00
30.00
(See http://www.innovativegis.com/basis, Precision Farming Primer, Appendix D)
(Berry)
Simple Linear Regression
(Berry)
Multivariate Map Regression
…considering all three map variables at the same time
(Berry)
Stratifying Regression based on Error Map
…in a somewhat analogous manner, Regression Trees are derived by
recursively analyzing the data to successively break the entire area
into subgroups that form the prediction relationship
(Berry)
Spatial Data Mining
…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 Map Analysis, Topic 10 for more information)
(Berry)