2. Spatial Data Mining Practical Approaches for Analyzing Relationships Within and Among Maps Berry & Associates // Spatial Information Systems 2000 S. College Ave, Suite 300, Fort Collins, CO 80525 Phone: (970) 215-0825 Email: jberry@innovativegis.com …visit our Website at www.innovativegis.com/basis “GIS technology is rapidly moving beyond mapping and spatial database management to analytical capabilities that assess spatial relationships within decision-making contexts” (JKB) Presented by Joseph K. Berry W.M. Keck Scholar in Geosciences, University of Denver

3. Visually Comparing Maps But just how similar are the maps? …what proportion has the same classification? …where are they different? …where are they the same? and of course, your response should be objective and repeatable I bet you've seen and heard it a thousand times before  a speaker waves a laser pointer at a couple of maps and says something like "see how similar the patterns are." (Berry)

4. Approach for Comparing Discrete Maps (Berry)

5. Coincidence Summary Results (Table 1) (Berry) (Table 1)

6. Proximal Alignment Results (Table 2) (Berry) (Table 2)

7. Approach for Comparing Map Surfaces (Berry)

8. Statistical Test Results (Table 3) …Statistical Tests of entire surface or partitioned areas (Berry) (Table 3)

9. Percent Difference Results (Table 4) (Berry) …Percent Difference between two map surfaces (Table 4)

10. Surface Configuration Results (Table 5) (Berry) The two superimposed maps at the left side of figure show the normalized differences in the slope and aspect angles (dark red being very different). The map of the overall differences in surface configuration (Sur_Fig Index) is the average of the two maps. Note that over half of the map area is classified as low difference (0-20) suggesting that the two surface maps align fairly well overall. (Table 4)

11. Visualizing Spatial Relationships (Berry) What spatial relationships do you see? Interpolated Spatial Distribution Phosphorous (P) …do relatively high levels of P often occur with high levels of K and N? …how often? …where?

12. 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)

13. Identifying Map Similarity (Berry) The green tones indicate field locations with fairly similar P, K and N levels; red tones indicate dissimilar areas. …the relative data distance between the comparison point’s data pattern and those of all other map locations form a Similarity Index (See Map Analysis, “Topic 16, Calculating Map Similarity” for more information) Topic 16Topic 16

14. Clustering Maps for Data Zones (Berry) (Cyber-Farmer, Circa 1990) Variable Rate Application …fertilization rates vary for the different clusters “on-the-fly” …groups of “floating balls” in data space identify locations in the field with similar data patterns– data zones …a map stack is a spatially organized set of numbers

15. Evaluating Clustering Results (Berry)

16. Map Surface Correlation/Regression Histogram/Map View-- Data Space (joint magnitude of values) are linked to Geographic Space (position of values) (Berry)

17. Creating Prediction Models (Scatter Plot) …a Scatter Plot identifies the “joint condition” at each map location; the trend in the plot forms a prediction equation (Berry)

18. Deriving a Predictive Index (NDVI) …an index combining the Red and NIR maps can be used to generate a better predictive model Normalized Difference Vegetation Index NDVI= ((NIR – Red) / (NIR + Red)) for the sample grid location NDVI= ((121-14.7) / (121 + 14.7))= 106.3 / 135.7=.783 (Berry)

19. Evaluating Prediction Maps (Spatial error analysis) …the regression equation is evaluated and the predicted map is compared to the actual measurements to generate an error map Error = Predicted - Actual for the sample grid location Y est = 55 + (180 *.783) = 196 …error is 196 – 218 = 22 bu/ac Note that the average error is 2.62 and 67% of the predictions are within +/- 20 bu/ac Also, most of the error is concentrated along the edge of the field (Berry) Exercise #8c, page 30 – Create a regression model relating Yield and NDVI (See Map Analysis, “Topic 16, Predicting Maps” for more information) Topic 16Topic 16

20. Stratifying Maps for Better Predictions (Berry) Stratifying by Error Zones Other ways to stratify mapped data— 1) Geographic Zones, such as proximity to the field edge; 2) Dependent Map Zones, such as areas of low, medium and high yield; 3) Data Zones, such as areas of similar soil nutrient levels; and 4) Correlated Map Zones, such as micro terrain features identifying small ridges and depressions. The Error Zones map is used as a template to identify the NDVI and Yield values used to calculate three separate prediction equations. A Composite Prediction map is created by applying the equations to the NDVI data respecting the template map zones. (See Map Analysis, “Topic 16, Stratifying Maps for Better Predictions” for more information) Topic 16Topic 16

21. Assessing Prediction Results (Berry) Whole Field Prediction Stratified Prediction Actual Yield none Error Map for Stratified Prediction 80% Error Map

22. 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 feet. This map 4) is combined with soil, terrain and other maps to derive a 5) “Prescription Map” that is used to maps to derive a 5) “Prescription Map” that is used to 6) adjust fertilization levels every few feet in the field. 6) adjust fertilization levels every few feet in the field. Variable Rate Application Step 6) (Berry) Cyber-Farmer, Circa 1992 …come a long ways baby Prescription Map Step 5) Zone 1 Zone 3 Zone 2 Farm dB Step 4) Map Analysis On-the-Fly Yield Map Steps 1)–3)

23. Spatial Data Mining …making sense out of a map stack (Berry) 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

24. Spatial Data Mining Practical Approaches for Analyzing Relationships Within and Among Maps Berry & Associates // Spatial Information Systems 2000 S. College Ave, Suite 300, Fort Collins, CO 80525 Phone: (970) 215-0825 Email: jberry@innovativegis.com …visit our Website at www.innovativegis.com/basis Presented by Joseph K. Berry W.M. Keck Scholar in Geosciences, University of Denver