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Title: Spatial Data Mining in Geo-Business Overview Paper available online at www.innovativegis.com/basis/present/GeoTec08/ Twisting the Perspective of Map Surfaces — describes the character of spatial distributions through the generation of a customer density surface Linking Numeric and Geographic Distributions — investigates the link between numeric and geographic distributions of mapped data Interpolating Spatial Distributions — discusses the basic concepts underlying spatial interpolation Interpreting Interpolation Results — describes the use of “residual analysis” for evaluating spatial interpolation performance Characterizing Data Groups — describes the use of “data distance” to derive similarity among the data patterns in a set of map layers Identifying Data Zones — describes the use of “levelslicing” for classifying locations with a specified data pattern (data zones) Mapping Data Clusters — describes the use of “clustering” to identify inherent groupings of similar data patterns Mapping the Future — describes the use of “linear regression” to develop prediction equations relating dependent and independent map variables Mapping Potential Sales — describes an extensive geobusiness application that combines retail competition analysis and product sales prediction Density Surface Analysis Customer Street Address Customer GIS Location Geo-Coding Density Surface Totals Customer Counts (# per cell) Vector to Raster Roving Window Classified Density Levels Classify Calculates the total number of customers within Counts the number of customers (points) within in each grid cell a roving window– customer density 91 3D surface plot 2D grid display of customer counts 2D perspective display of density contours Density Map Identifying Pockets of High Density Unusually High = Mean + 1 Standard Deviation Customer Density (Non-spatial Statistics) Customer Density (Map Surface) Grid-based Analysis Frame (Keystone Concept) Raster (cell) Analysis Frame Latitude, Longitude, C, R Vector (point) …GeoCoding plots customers address on the streets map …appends Lat, Lon, Column, Row location to customer records Customer Database Customer Database (non-spatial) (spatial) …V to R Conversion plots customers location in the analysis frame (grid) Surface Modeling (Spatial Interpolation) …“maps the variance” by using geographic position to help explain the differences in the sample values. Surface Map Avg = 42.9 66.3 Point Samples 66.3 “Spikes” “Spikes ‘n Blanket” IDW Interpolation (Inverse Distanced Weighted) #14 #15 #16 x #11 1) Identify data points in window— #11value = 56.9 #14value = 22.5 #15value = 52.3 #16value = 66.3 Sampled Data 1 2 3 4 5 6 7 8 9 10 11 12 4) Assign weight-averaged value— 53.35 3) Weight-average values in the window based on distance to grid location— (1/Distance)2 * Value “closer has more influence” 2) Calculate distance 13 14 15 16 X from location to data points— Pythagorean Theorem #11distance = 22.80 #14distance = 26.08 #15distance = 6.32 #16distance = 14.14 #11 #16 #14 #15 5) Move window to next grid location and repeat Average vs. IDW Interpolated Surface Difference Surface (IDW – Average) Average Min = -26.1 Max = 29.5 IDW Surface IDW - Average Reds Avg>IDW Greens Avg<IDW IDW vs. Krig Interpolated Surfaces Difference Surface (IDW – Krig) Krig Surface Min = -14.8 Max = 5.0 IDW Surface IDW - Krig Reds Krig>IDW Greens Krig<IDW Assessing Relationships Among Maps Housing Density (Units/ac) South has Lower Density Home Value ($K) South has Higher Values Home Age (Years) South has Newer Homes Geographic Space Data Space Point #2 Geographic Space – relative spatial position of measurements Point #1 Density Data Similarity is inversely proportional to Data Distance …as data distance increases, the map values for two locations are less similar Value Comparison Point #1 Age D= Low (2.4 units/ac) V= High ($407,000) A= Low (18.3 years) Least Similar Point #2 D= High (4.8 units/ac) V= Low ($190,000) A= High (51.2 years) Data Space – relative numerical magnitude of measurements Assessing Map Similarity “Data Distance” determines similarity among data patterns Data Space Least Similar Point = 4.8, 190, 51.2 Percent Similar …the farthest away point in data space (least similar) is set 0 and the comparison point is set to 100 — …all other Data Distances are scaled in terms of their relative similarity as “percent similar” to the comparison point (0 to 100) 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Comparison Point = 2.4, 407, 18.3 Geographic Space Identifying Data Patterns of Interest Housing Density Unusually High Mean = 3.56 +StDev = 0.80 LevelMin = 4.36 Geographic Space Data Space 67.2 = -StDev 189.8 = LevelMax 257.0 = Mean Home Value Geographic Space Unusually Low Level-Slicing Classifier (two variables) Unusually High Housing Density Unusually Low Home Value Unusually High Density and Low Value Data Space Geographic Space Level-Slicing Classifier (three variables) Data Space …identifies combinations of selected measurements (high D, low V, high A) 1+2+4=7 (high D, low V but not high A) 1+2+0=3 …common “data zones” can be mapped by identifying specific levels of each mapped variable then adding the binary maps Geographic Space …locates combinations of selected measurements (high D, low V, high A) Spatial Data Clustering Data Space …plots and identifies groups of similar data values Relatively high D, low V and high A Relatively low D, high V and low A Three Clusters Four Clusters …“data clusters” are identified as groups of neighboring data points in Data Space, and then mapped as corresponding grid cells in Geographic Space Geographic Space …maps common data patterns (clusters) Two Clusters Spatial Regression (prediction equation) …relationship between Loan Concentration and independent variables housing Density, Value and Age Loan Concentration High Loan Concentration vs. Housing Density Housing Density V Y = 26 -5.7 * Xdensity [R2 = 40%] Loan Concentration vs. Home Value Low Home Value V Y = -13 +0.074 * Xvalue [R2 = 46%] High Loan Concentration vs. Home Age V Home Age Y = 17 - 0.074 * Xage [R2 = 23%] Low Competition Analysis (Spatial Analysis Steps) Step 1 Build travel time maps for entire market area • Compute travel time from every location to our store • This requires grid-based map analysis software • Update customer record with travel time to our store • Add this to every non-customer record in trading area Step 2 Repeat for every competitor • Update every customer record with travel time to competitor store • Add to every non-customer record in trading area Step 3 Compute Travel Time Gain for travel to main store • Every customer and non-customer record is updated • The greater gain indicates lower travel effort to visit our store Predictive Modeling (Spatial Statistics Steps) Step 4 Build analytic dataset from customer data • Geocoding information • Transactions, sales, product category purchases • Visitation frequency, recency, spend • Customer Segment, travel times, demographics Step 5 Build predictive models • Probability of Visitation (not possible for this demo) • Probability of Purchase by Product Category • Expected Sales and Transactions • Use store travel time and all competitive differences Step 6 Map the scores • The distribution of the scores provide visual evidence of the effects of travel time and competitive pressure • Spatial hypotheses can be tested and evaluated Map Analysis Framework While discrete sets of points, lines and polygons have served our mapping demands for over 8,000 years and keep us from getting lost… Mapping and Geo-query …the expression of mapped data as continuous spatial distributions (surfaces) provides a new foothold for the contextual and numerical analysis of mapped data— “Thinking with Maps” References Paper available online at www.innovativegis.com/basis/present/GeoTec08/ Twisting the Perspective of Map Surfaces — describes the character of spatial distributions through the generation of a customer density surface Linking Numeric and Geographic Distributions — investigates the link between numeric and geographic distributions of mapped data Interpolating Spatial Distributions — discusses the basic concepts underlying spatial interpolation Interpreting Interpolation Results — describes the use of “residual analysis” for evaluating spatial interpolation performance Characterizing Data Groups — describes the use of “data distance” to derive similarity among the data patterns in a set of map layers Identifying Data Zones — describes the use of “levelslicing” for classifying locations with a specified data pattern (data zones) Mapping Data Clusters — describes the use of “clustering” to identify inherent groupings of similar data patterns Mapping the Future — describes the use of “linear regression” to develop prediction equations relating dependent and independent map variables Mapping Potential Sales — describes an extensive geobusiness application that combines retail competition analysis and product sales prediction www.innovativegis.com/basis/present/GeoTec08/ …to download this PowerPoint slide set Spatial Data Mining in Geo-Business Weighted Average Calculations for Inverse Distance Weighting (IDW) Spatial Interpolation Technique Evaluating Interpolation Performance …Residual Analysis is used to evaluate interpolation performance (Krig at .03 Normalized Error is best) Average IDW Krig