Title: Spatial Data Mining in Geo-Business

Overview  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 “level- slicing” 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 geo- business application that combines retail competition analysis and product sales prediction Paper available online at

Classified Density Levels Classify Density Map Density Surface Totals Density Surface Analysis Counts the number of customers (points) within in each grid cell Customer Street Address Customer GIS Location Customer Counts (# per cell) Geo-CodingVector to Raster 2D grid display of customer counts Roving Window Calculates the total number of customers within a roving window– customer density 2D perspective display of density contours 3D surface plot 91

Identifying Pockets of High Density Customer Density (Map Surface) Customer Density (Non-spatial Statistics) Unusually High = Mean + 1 Standard Deviation

Grid-based Analysis Frame (Keystone Concept) Customer Database (non-spatial) …appends Lat, Lon, Column, Row location to customer records …GeoCoding plots customers address on the streets map Vector (point) Raster (cell) Analysis Frame …V to R Conversion plots customers location in the analysis frame (grid) Latitude, Longitude, C, R Customer Database (spatial)

Point Samples Surface Modeling (Spatial Interpolation) Surface Map “Spikes ‘n Blanket” Avg = “Spikes” 66.3 …“maps the variance” by using geographic position to help explain the differences in the sample values.

IDW Interpolation (Inverse Distanced Weighted) 5) Move window to next grid location and repeat 2) Calculate distance from location to data points— Pythagorean Theorem #11 distance = #14 distance = #15 distance = 6.32 #16 distance = ) Weight-average values in the window based on distance to grid location— (1/Distance) 2 * Value “closer has more influence” X #11 #14 #15 #16 Sampled Data 1) Identify data points in window— #11 value = 56.9 #14 value = 22.5 #15 value = 52.3 #16 value = 66.3 #16 #15 #14 #11 x X ) Assign weight-averaged value— 53.35

Average vs. IDW Interpolated Surface Average IDW Surface Reds Avg>IDW Greens Avg<IDW Min = Max = 29.5 Difference Surface (IDW – Average) IDW - Average

IDW vs. Krig Interpolated Surfaces Krig Surface IDW Surface Min = Max = 5.0 Difference Surface (IDW – Krig) Reds Krig>IDW Greens Krig<IDW IDW - Krig

Assessing Relationships Among Maps Housing Density Home Value Home Age (Units/ac) ($K) (Years) South has Lower Density South has Higher Values South has Newer Homes

Geographic Space  Data Space Density Value Age Geographic Space – relative spatial position of measurements Point #1 Point #2 Data Space – relative numerical magnitude of measurements Comparison Point #1 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 Similarity is inversely proportional to Data Distance …as data distance increases, the map values for two locations are less similar

Assessing Map Similarity “Data Distance” determines similarity among data patterns …the farthest away point in data space (least similar) is set 0 and the comparison point is set to 100 — Data Space Percent Similar Least similar point Comparison point Least Similar Point = 4.8, 190, 51.2 Comparison Point = 2.4, 407, 18.3 …all other Data Distances are scaled in terms of their relative similarity as “percent similar” to the comparison point (0 to 100) Geographic Space

Identifying Data Patterns of Interest Housing Density Geographic Space Data Space Geographic Space Mean = StDev = 0.80 Level Min = 4.36 Unusually High 67.2 = -StDev = Level Max = Mean Home Value Unusually Low

Level-Slicing Classifier (two variables) Data Space Unusually High Housing Density Unusually Low Home Value Unusually High Density and Low Value Geographic Space

Level-Slicing Classifier (three variables) …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) = 7 (high D, low V but not high A) = 3 Data Space …identifies combinations of selected measurements (high D, low V, high A)

Spatial Data Clustering … “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) Relatively high D, low V and high A Relatively low D, high V and low A Three Clusters Four Clusters Two Clusters Data Space …plots and identifies groups of similar data values

Spatial Regression (prediction equation) Low High Low High Housing Density Home Value Home Age Loan Concentration …relationship between Loan Concentration and independent variables housing Density, Value and Age Loan Concentration vs. Housing Density Y = * X density [R 2 = 40%] V Loan Concentration vs. Home Value Y = * X value [R 2 = 46%] V Loan Concentration vs. Home Age Y = * X age [R 2 = 23%] V

Competition Analysis (Spatial Analysis Steps) 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 1 Repeat for every competitor Update every customer record with travel time to competitor store Add to every non-customer record in trading area Step 2 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 Step 3

Predictive Modeling (Spatial Statistics Steps) Build analytic dataset from customer data Geocoding information Transactions, sales, product category purchases Visitation frequency, recency, spend Customer Segment, travel times, demographics Step 4 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 5 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 Step 6

Map Analysis Framework Mapping and Geo-query While discrete sets of points, lines and polygons have served our mapping demands for over 8,000 years and keep us from getting lost… …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  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 “level- slicing” 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 geo- business application that combines retail competition analysis and product sales prediction Paper available online at

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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) AverageIDW Krig