Spatial Data Mining Practical Approaches for Analyzing Relationships Within and Among Maps

1. Spatial Data MiningPractical Approaches for Analyzing Relationships Within and Among Maps “GIS technology is rapidly moving beyond mapping and spatial database management to analytical capabilities that assess spatial relationships within decision-making contexts”(JKB) Presented byJoseph K. Berry W.M. Keck Scholar in Geosciences, University of Denver Berry & Associates // Spatial Information Systems2000 S. College Ave, Suite 300, Fort Collins, CO 80525Phone: (970) 215-0825 Email: jberry@innovativegis.com…visit our Website atwww.innovativegis.com/basis

2. Visually Comparing Maps 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." 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 (Berry)

3. Approach for Comparing Discrete Maps (Berry)

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

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

6. Approach for Comparing Map Surfaces (Berry)

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

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

9. Surface Configuration Results (Table 5) 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. (Table 4) 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. (Berry)

10. Phosphorous (P) Visualizing Spatial Relationships Interpolated Spatial Distribution 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)

11. 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)

12. 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)

13. …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 (Cyber-Farmer, Circa 1990) Variable Rate Application Clustering Maps for Data Zones …fertilization rates vary for the different clusters “on-the-fly” (Berry)

14. Evaluating Clustering Results (Berry)

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

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

17. 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 IndexNDVI= ((NIR – Red) / (NIR + Red)) for the sample grid locationNDVI= ((121-14.7) / (121 + 14.7))= 106.3 / 135.7= .783 (Berry)

18. 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 locationYest = 55 + (180 * .783) = 196 …error is 196 – 218 = 22 bu/ac Exercise #8c, page 30– Create a regression model relating Yield and NDVI 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 (See Map Analysis, “Topic 16, Predicting Maps” for more information) (Berry)

19. 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. Stratifying Maps for Better Predictions 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) (Berry)

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

21. The Precision Ag Process(Fertility example) Steps 1)–3) Step 5) Prescription Map On-the-Fly Yield Map Map Analysis Step 6) Cyber-Farmer, Circa 1992 …come a long ways baby Step 4) Farm dB Zone 3 Zone 2 Zone 1 Variable Rate Application 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 6) adjust fertilization levels every few feet in the field. (Berry)

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

23. Spatial Data MiningPractical Approaches for Analyzing Relationships Within and Among Maps Presented byJoseph K. Berry W.M. Keck Scholar in Geosciences, University of Denver Berry & Associates // Spatial Information Systems2000 S. College Ave, Suite 300, Fort Collins, CO 80525Phone: (970) 215-0825 Email: jberry@innovativegis.com…visit our Website atwww.innovativegis.com/basis