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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. Introduction to GIS Modeling Week 9 — Spatial Data Mining GEOG 3110 –University of Denver. Basic Descriptive Statistics and its GIS Expression : Normalizing maps; Mapping spatial dependency.

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Introduction to GIS Modeling Week 9 — Spatial Data Mining GEOG 3110 –University of Denver

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  1. Presented byJoseph K. Berry W. M. Keck Scholar, Department of Geography, University of Denver Introduction to GIS ModelingWeek 9 — Spatial Data MiningGEOG 3110 –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

  2. Kicking at the Finish (Waning Class Moments) • The last of the “Learning Opportunities” that remain are… • Exercise #9 on Spatial Data Mining (or paper) for 50 points • Exam #2 on Surface Modeling, Spatial Data Mining and Future Directions • material for 150 points • Optional Exercises for up to 50 extra credit points (can only improve your grade) • Grad Student Presentations on a topic of their choice for 100 points (15-minute PowerPoint at last class meeting) 2nd Exam Study Questions…posted Friday 3/8 by 12:00noon. Class initiative to “group study” to collectively address the 24 study Midterm Exam …you will download and take the 2-hour exam online (honor system) sometime between 10:00 am, Friday, March 15and 5:00 pm, Tuesday, March 19 Special, special offer provided you fully participate in the study question “group study” you can choose not to take the second exam— Fine print: I will simply allocate the points for the exam according to the current percentage of all of your graded materials which means not taking the exam has no effect on your grade. If you choose to take the exam and get a grade below your current percentage of all graded materials, the exam grade will be ignored …therefore taking the exam can only improve your grade.

  3. GIS and Statistical Perspectives (SS) Spatial Statistics Operations – Numerical Context GIS Perspective: Surface Modeling (Density Analysis, Spatial Interpolation, Map Generalization) Spatial Data Mining (Descriptive, Predictive, Prescriptive) Map Analysis Toolbox Statistical Perspective: Basic Descriptive Statistics (Min, Max, Median, Mean, StDev, etc.) Basic Classification (Reclassify, Contouring, Normalization) Map Comparison (Joint Coincidence, Statistical Tests) Unique Map Statistics (Roving Window and Regional Summaries) Surface Modeling (Density Analysis, Spatial Interpolation) Advanced Classification (Map Similarity, Maximum Likelihood, Clustering) Predictive Statistics (Map Correlation/Regression, Data Mining Engines) Surface Modeling (Density Analysis, Spatial Interpolation) …last week Grid Map Layers Berry

  4. 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)

  5. 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)

  6. Linking Numeric & Geographic Distributions …aHistogramdepicts thenumeric distribution(Mean/Central Tendency focus) …aMap depicts thegeographic distribution(Variance/Variability focus) Key Concept …Data Valueslink the two views— Click anywhere on the Map and the Histogram interval is highlighted Click on the Histogram interval and the Map locations are highlighted …simply different ways to organize and analyze “mapped data” (x,y= Where and z= What) (See Beyond Mapping III, “Topic 7” for more information) (Berry)

  7. An Analytic Framework for GIS Modeling (Last week) Surface Modellingoperations involve creating continuous spatial distributions from point sampled data (univariate). (This week) Spatial Data Miningoperations involve characterizing numerical patterns and relationships among mapped data (multivariate). See www.innovativegis.com/basis/Download/IJRSpaper/ (Berry)

  8. Antenna Offset GPS Fix Delay Overlap and Multiple Passes Mass Flow Lag and Mixing Preprocessing Mapped Data (Preprocessing Types 1-3) Preprocessinginvolves conversion of raw data into consistent values that accurately represent mapped conditions(4 types of preprocessing) • Calibration1 — “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’ • Translation2 — 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) • Adjustment/Correction3— • dramatically changes the • data, such as post processing • GPS coordinates and/or Mass Flow Lag adjustment … “trolling” for data (Berry)

  9. Normalizing Mapped Data (4th type of preprocessing) • Normalization— involves standardization of a data set, usually for comparison among different types of data… • Goal…Norm_GOAL = (mapValue / 250 ) * 100 • 0-100…Norm_0-100 = ((mapValue – min) * 100) / (max – min) + 0 • SNV…Norm_SNV = ((mapValue - mean) / stdev) * 100 “apples and oranges to mixed fruit scale” 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 Since normalization involves scalar mathematics (constants), the pattern of the numeric distribution (histogram) and the spatial distribution (map) do not change …same relative distributions Key Concept 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)

  10. …unusually high yield …proximity to high yield …Yield map > Average + 1Stdev Proximity Stratification …proximity to field edge …Stratificationpartitions the data (numeric) or the project area (spatial) into logical groups— Edge effects “Sweet Spot” (interior) …Proximity mapidentifies the distance from point, line or polygon features to all other locations Far : Close “High Yield” vicinity (Berry)

  11. …creates a map summarizing values from a data map (Phosphorous levels) that coincide with the categories of a template map (Soil types) or stratification partitioning BIB Soil Type Ve VdC BIB BIA TuC HvB Pavg 15.0 12.8 11.2 14.6 10.5 11.3 …average phosphorous level for each soil type Summarizing Map Regions(template/data) Soil Types Phosphorous levels Individual BIA clumps Overall BIA Pavg = 14.6 13.6 15.5 8.6 …average P-level for each soil unit (clump first before COMPOSITE) (Berry)

  12. 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 practicesin agriculture and numerous other fields from business to epidemiology and natural resources (Berry)

  13. 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) of Points, Lines and Areas (polygons) is a primary concern of GIS, but we are often less concerned with Thematic Accuracy (What — map values) High Medium Low (Berry) See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning

  14. Comparing Discrete Maps Two ways to compare Discrete Maps… Coincidence Summary Proximal Alignment …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 ((631+297+693)/1950)*100= 83% ((475+297+563)/1950)*100=68% Raster versus Vector 693 See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning (Berry)

  15. Comparing Discrete Maps (Coincident Summary) Two ways to compare Discrete Maps… Coincidence Summary Proximal Alignment Map2: Med-- 104 + 297 + 225 = 626; (297/626) *100= 47 percent matched 631 + 297 + 693 = 1621; (1621/1950) *100= 83 percent matched 475 + 297 + 563 = 1335; (1335/1950) *100= 68 percent matched Map3: Med-- 260 + 297 + 335= 912; (297/912) *100= 33 percent matched …helpful in answering Question 2 Map1 …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 ((631+297+693)/1950)*100= 83% ((475+297+563)/1950)*100=68% Raster versus Vector Map2 Map1 Map3 See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning (Berry)

  16. Comparing Discrete Maps (Proximal Alignment) Two ways to compare Discrete Maps… Coincident Summary Proximal Alignment …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) Proximity_Map1_Category1 * Binary_Map3_Category1 …non-zero values identify changes and how far away (Berry) See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning

  17. 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.) …must be quantitativeisopleth data Table 1 Box-and-whisker graphs (Berry) See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning

  18. Comparing Map Surfaces (%Difference) Three ways to compare Map Surfaces… Statistical Tests Percent Difference Surface Configuration …Percent Difference capitalizes on the spatial arrangement of the values by comparing the values at each map location— %Difference Map, %Difference Table Question 3 Table 2 (Berry) See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning

  19. 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 Table 3 (Berry) See Beyond Mapping III , Topic 10, Analyzing Map Similarity and Zoning

  20. GIS and Statistical Perspectives (SS) Spatial Statistics Operations – Numerical Context GIS Perspective: Surface Modeling (Density Analysis, Spatial Interpolation, Map Generalization) Spatial Data Mining (Descriptive, Predictive, Prescriptive) Map Analysis Toolbox Statistical Perspective: Basic Descriptive Statistics (Min, Max, Median, Mean, StDev, etc.) Basic Classification (Reclassify, Contouring, Normalization) Map Comparison (Joint Coincidence, Statistical Tests) Unique Map Statistics (Roving Window and Regional Summaries) Surface Modeling (Density Analysis, Spatial Interpolation) Advanced Classification (Map Similarity, Maximum Likelihood, Clustering) Predictive Statistics (Map Correlation/Regression, Data Mining Engines) Surface Modeling (Density Analysis, Spatial Interpolation) …last week Grid Map Layers Berry

  21. 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 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) Surface Modeling Discrete Point Map Continuous Map Surface Multivariate Spatial Data Mining 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) See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships

  22. Interpolated Spatial Distribution Phosphorous (P) What spatial relationships do you see? Visualizing Spatial Relationships …do relatively high levels of P often occur with high levels of K and N? …how often? …where? (Berry) See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships

  23. Identifying Unusually High Measurements …isolate areas with mean + 1 StDev (tail of normal curve) (Berry) See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships

  24. Level Slicing …simply multiply the two maps to identify joint coincidence 1*1=1 coincidence (any 0 results in zero) Question 4 2-dimensional data space Box (Berry) See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships

  25. Multivariate Data Space …sum of a binary progression (1, 2 ,4 8, 16, etc.) provides level slice solutions for many map layers 3-dimensional space Cube (Parallel piped ) (Berry) See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships

  26. 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) See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships

  27. 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. (Berry) See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships

  28. …a map stack is a spatially organized set of numbers Cyber-Farmer, Circa 1992 …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” Variable Rate Application Clustering Maps for Data Zones Question 6 (Berry) See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships

  29. 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 (Berry) See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships

  30. How Clustering Works (IsoData algorithm) 1) The scatter plot shows Height versus Weight data that might have been collected in your old geometry class 2) The data distance to each weight/height measurement pair is calculated and the point is assigned to the closest arbitrary cluster center Data Space 4) Repeat data distances, cluster assignments and repositioning until no change in cluster membership (centers do not move) 3) The average X,Y coordinates of the assigned students to each “working” cluster is calculated and used to reposition the cluster centers (Berry) See Beyond Mapping III , Topic 7, Linking Data Space and Geographic Space

  31. Localized Correlation Map Correlation (How it works) Spatially Aggregated Correlation Roving Window Elevation (Feet) Slope (Percent) X elev = 2,063 feet …625 small data tables within 5 cell reach = 81map values for localized summary Yslope = 38% Point- by-Point = .562 localized r = …one large data table with 25rows x 25 columns = 625 map values for map wide summary = .432 map wide …where x = Elevation value and y = Slope value and n = number of value pairs (Berry)

  32. Map Correlation (Aggregated and Localized results) Spatially Aggregated Correlation Scalar Value– one value represents the overall non-spatial relationship between the two map surfaces r = .432 map wide Strong Positive Map Variable– a continuous quantitative surface represents the localized spatial relationship between the two map surfaces Minimal Correlation Strong Positive Strong Negative Strong Negative r = .562 Localized Localized Correlation (Berry)

  33. An Analytic Framework for GIS Modeling Spatial Data Mining operations involve characterizing numerical patterns and relationships among mapped data. See www.innovativegis.com/basis/Download/IJRSpaper/ (Berry)

  34. 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)

  35. Non-spatial…R-squared value looks at the deviations from the regression line; data patterns about the regression line Evaluating Prediction Maps (non-spatial) (Berry)

  36. The Dependent Map variable is the one that you want to predict… …derive from customer data …from a set of existing or easily measured Independent Map variables Map Variables Question 7 (Berry) See Beyond Mapping III , Topic 28, Spatial Data Mining in Geo-Business

  37. Scatter plots and regression equations relating Loan Density to three candidate driving variables (Housing Density, Value and Age) 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) Map Regression Results (Bivariate) Question 7 Creates the Loan Concentration map surface Question 8 Creates regression equation and R2 index (Berry) See Beyond Mapping III , Topic 28, Spatial Data Mining in Geo-Business

  38. 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 (Berry) See Beyond Mapping III , Topic 28, Spatial Data Mining in Geo-Business

  39. Evaluating Regression Results (multiple linear) …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 Optional Question 9-1 (Berry) See Beyond Mapping III , Topic 28, Spatial Data Mining in Geo-Business

  40. 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 Optional Question 9-2 (Berry) See Beyond Mapping III , Topic 28, Spatial Data Mining in Geo-Business

  41. 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 (Berry) See Beyond Mapping III , Topic 16, Characterizing Patterns and Relationships

  42. An Analytic Framework for GIS Modeling Spatial Data Mining operations involve characterizing numerical patterns and relationships among mapped data. See www.innovativegis.com/basis/Download/IJRSpaper/ (Berry)

  43. 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… • Descriptivemath/stat models summarize existing mapped data • (e.g., Standard Normal Variable Map for Unusual Conditions and Clustering for Data Zones) • Predictivemath/stat models develop equations relating mapped data • (e.g., Map Regression for Equity Loan Prediction and Probability of Product Sales ) • Prescriptivemath/stat models identify management actions based on descriptive/predictive relationships (e.g., Retail Marketing and Precision Ag)… • Discrete Actions: If <condition(s)> Then <Action(s)> • If P is 0-4ppm, then apply 50 lbs P2O5/Acre • If P is 4-8ppm, then apply 18 lbs P2O5/Acre • If P is 8-12ppm, then apply 7 lbs P2O5/Acre • If P is >12 ppm, then apply 0 lbs P2O5/Acre 50 50 7 0 18 0 • Continuous Actions: Equation defining action(s) • Negative linear equation of the form:y = aX • Negative exponential equation of the form: y = e-x 0 P 12 more Phosphorous (P) P2O5/ 50 P2O5/ 0 (Berry) 0 P 12 more

  44. Grid-Based Map Analysis • Spatial Analysisinvestigates 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 Modelingmaps the “spatial distribution” 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 Mininginvestigates 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)

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