Extracting Regional Knowledge from Spatial Datasets

1. Extracting Regional Knowledge from Spatial Datasets Christoph F. Eick Department of Computer Science, University of Houston Motivation: Why is Regional Knowledge Important? Region Discovery Framework A Family of Clustering Algorithms for Region Discovery Case Studies—Extracting Regional Knowledge: Regional Regression Regional Association Rule Mining [Regional Models of User Behaviour on the Internet] [Co-location Mining] [Analyzing Related Datasets] Summary

2. Spatial Data Mining • Definition: Spatial data mining is the process of discovering interesting patterns from large spatial datasets; it organizes by location what is interesting. • Challenges: • Information is not uniformly distributed • Autocorrelation • Space is continuous • Complex spatial data types • Large dataset sizes and many possible patterns • Patterns exist at different sets level of resolution • Importance of maps as summaries • Importance of regional Knowledge

3. Why Regional Knowledge Important in Spatial Data Mining? • It has been pointed out in the literature that “whole map statistics are seldom useful”, that “most relationships in spatial data sets are geographically regional, rather than global”, and that “there is no average place on the Earth’s surface” [Goodchild03, Openshaw99]. • Simpson’s Paradox – global models may be inconsistent with regional models [Simpson1951]. • Therefore, it is not surprising that domain experts are mostly interested in discovering hidden patterns at a regional scale rather than a global scale.

4. Rule 1 Rule 2 Rule 3 Rule 4 Example: Regional Association Rules Scopes of the 4 Rules in

5. Goal of the Presented Research Develop and implement an integrated computational framework useful for data analysts and scientists from diverse disciplines for extracting regional knowledge in spatial datasets in a highly automated fashion.

6. Related Work • Spatial co-location pattern discovery [Shekhar et al.] • Spatial association rule mining [Han et al.] • Localized associations in segments of the basket data [Yu et al.] • Spatial statistics on hot spot detection [Tay and Brimicombe et al.] • There is some work on geo-regression techniques (to be discussed later) • … Comment: Most work centers on extraction global knowledge from spatial datasets

7. Preview: A Framework for Extracting Regional Knowledge from Spatial Datasets 7 Application 1: Supervised Clustering [EVJW07] Application 2: Regional Association Rule Miningand Scoping [DEWY06, DEYWN07] Application 3: Find Interesting Regions with respect to a Continuous Variables [CRET08] Application 4: Regional Co-location Mining Involving Continuous Variables [EPWSN08] Application 5: Find “representative” regions (Sampling) Application 6: Regional Regression [CE09] Application 7: Multi-Objective Clustering [JEV09] Application 8: Change Analysis in Related Datasets [RE09] b=1.01 RD-Algorithm b=1.04 Wells in Texas: Green: safe well with respect to arsenic Red: unsafe well UH-DMML

8. 2. Region Discovery Framework 8

9. Region Discovery Framework2 9 • We assume we have spatial or spatio-temporal datasets that have the following structure: (<spatial attributes>;<non-spatial attributes>) e.g. (longitude, lattitude, class_variable) or (longitude, lattitude, continous_variable) • Clustering occurs in space of the spatial attributes; regions are found in this space. • The non-spatial attributes are used by the fitness function but neither in distance computations nor by the clustering algorithm itself. • For the remainder of the talk, we view region discovery as a clustering task and assume that regions and clusters are the same.

10. Region Discovery Framework3 10 The algorithms we currently investigate solve the following problem: Given: A dataset O with a schema R A distance function d defined on instances of R A fitness function q(X) that evaluates clusteringsX={c1,…,ck} as follows: q(X)= cXreward(c)=cXi(c) *size(c) with b1 Objective: Find c1,…,ck O such that: • cicj= if ij • X={c1,…,ck} maximizes q(X) • All cluster ciX are contiguous (each pair of objects belonging to cihas to be delaunay-connected with respect to ciand to d) • c1,…,ck  O • c1,…,ck are usually ranked based on the reward each cluster receives, and low reward clusters are frequently not reported

11. Measure of Interestingness i(c) 11 • The function i(c) is an interestingness measure for a region c, a quantity based on domain interest to reflect how “newsworthy” the region is. • In our past work, we have designed a suite of measures of interestingness for: • Supervised Clustering [PKDD06] • Hot spots and cool spots [ICDM06] • Scope of regional patterns [SSTDM07] • Co-location patterns involving variables [PAKDD08, ACM-GIS08] • High-variance regions involving a continuous variable [PAKDD09] • Regional Regression [ACM-GIS09]

12. Example1: Finding Regional Co-location Patterns in Spatial Data 12 Figure 1: Co-location regions involving deep and shallow ice on Mars Figure 2: Chemical co-location patterns in Texas Water Supply Objective: Find co-location regions using various clustering algorithms and novel fitness functions. Applications: 1. Finding regions on planet Mars where shallow and deep ice are co-located, using point and raster datasets. In figure 1, regions in red have very high co-location and regions in blue have anti co-location. 2. Finding co-location patterns involving chemical concentrations with values on the wings of their statistical distribution in Texas’ ground water supply. Figure 2 indicates discovered regions and their associated chemical patterns.

13. Example 2: Regional Regression 13 • Geo-regression approaches: Multiple regression functions are used that vary depending on location. • Regional Regression: • To discover regions with strong relationships between dependent & independent variables • Construct regional regression functions for each region • When predicting the dependent variable of an object, use the regression function associated with the location of the object

14. Challenges for Region Discovery 14 • Recall and precision with respect to the discovered regions should be high • Definition of measures of interestingness and of corresponding parameterized reward-based fitness functions that capture “what domain experts find interesting in spatial datasets” • Detection of regions at different levels of granularities (from very local to almost global patterns) • Detection of regions of arbitrary shapes • Necessity to cope with very large datasets • Regions should be properly ranked by relevance (reward) • Design and implementation of clustering algorithms that are suitable to address challenges 1, 3, 4, 5 and 6.

15. Clustering with Plug-in Fitness Functions • In the last 5 years, my research group developed families of clustering algorithms that find contiguous spatial clusters that by maximizing a plug-in fitness function. • This work is motivated by a mismatch between evaluation measures of traditional clustering algorithms (such as cluster compactness) and what domain experts are actually looking for. 15

16. 3. Current Suite of Clustering Algorithms 16 • Representative-based: SCEC, SRIDHCR, SPAM, CLEVER • Grid-based: SCMRG, SCHG • Agglomerative: MOSAIC, SCAH • Density-based: SCDE, DCONTOUR Density-based Grid-based Representative-based Agglomerative-based Clustering Algorithms

17. Representative-based Clustering 17 2 Attribute1 1 3 Attribute2 4 Objective: Find a set of objects OR such that the clustering X obtained by using the objects in OR as representatives minimizes q(X). Characteristic: cluster are formed by assigning objects to the closest representative Popular Algorithms: K-means, K-medoids, CLEVER,…

18. Rinsurakawong&Eick: Correspondence Clustering , PAKDD’10 CLEVER [ACM-GIS08] • Is a representative-based clustering algorithm, similar to PAM. • Searches variable number of clusters and larger neighborhood sizes to battle premature termination and randomized hill climbing and adaptive sampling to reduce complexity. • In general, new clusters are generated in the neighborhood of the current solution by replacing, inserting, and replacing representatives. • Searches for optimal number of clusters 18

19. Advantages of Grid-based Clustering Algorithms 19 • fast: • No distance computations • Clustering is performed on summaries and not individual objects; complexity is usually O(#populated-grid-cells) and not O(#objects) • Easy to determine which clusters are neighboring • Shapes are limited to union of grid-cells

20. Ideas SCMRG (Divisive, Multi-Resolution Grids) 20 Cell Processing Strategy 1. If a cell receives a reward that is larger than the sum of its rewards its ancestors: return that cell. 2. If a cell and its ancestor do not receive any reward: prune 3. Otherwise, process the children of the cell (drill down)

21. Code SCMRG 21

22. 4. Case Studies Regional Knowledge Extraction 22 4.1 Regional Regression 4.2 Regional Association Rule Mining & Scoping 4.3 Association-List Based Discrepancy Mining of User Behavior 4.4 Co-location Mining to be skipped!

23. 4.1 REG^2: A Framework of Regional Regression 23 • Motivation: Regression functions spatially vary, as they are not constant over space • Goal:To discover regions with strong relationships between dependent & independent variables and extract their regional regression functions. Discovered Regions and Regression Functions REG^2 Outperforms Other Models in SSE_TR • Clustering algorithms with plug-in fitness functions are employed to find such region; the employed fitness functions reward regions with a low generalization error. • Various schemes are explored to estimate the generalization error: example weighting, regularization, penalizing model complexity and using validation sets,… Regularization Improves Prediction Accuracy Skip!

24. 24 Motivation Regional Knowledge & Regression • 1st law of geography: “Everything is related to everything else but nearby things are more related than distant things” (Tobler) • Coefficient estimates in geo-referenced datasets spatially vary  we need regression methods to discover regional coefficient estimates that captures underlyingstructure of data. • Using human-made boundaries (zip code etc.) is not good idea since spatial variation is rarely rectangular.

25. 25 Motivation Other Geo-Regression Analysis Methods • Regression Trees • Data is split in a top-down approach using a greedy algorithm • Discovers only rectangle shapes • Geographically Weighted Regression(GWR) • an instance-based, local spatial statistical technique used to analyze spatial non-stationarity. • generates a separate regression equation for a set of observation points-determined using a grid or kernel • weight assigned to each observation is based on a distance decay function centered on observation.

26. 26 Motivation Example 1: Why We Need Regional Knowledge? Arsenic Fluoride Regression Result: A positive linear regression line (Arsenic increases with increasing Fluoride concentration)

27. 27 Motivation Example 1: Why We Need Regional Knowledge? Location 1 Location 2 Arsenic Fluoride • A negative linear Regression line in both locations (Arsenic decreases with increasing Fluoride concentration) • A reflection of Simpson’s paradox.

28. 28 Motivation Example 2: Houston House Price Estimate • Dependent variable: House_Price • Independent variables: noOfRooms, squareFootage, yearBuilt, havePool, attachedGarage, etc..

29. 29 Motivation Example 2: Houston House Price Estimate • Global Regression (OLS) produces the coefficient estimates, R2 value, and error etc.. a single global model • This model assumes all areas have same coefficients • E.g. attribute havePool has a coefficient of +9,000 • (~having a pool adds $9,000 to a house price) • In reality this changes. A house of $100K and a house of $500K or different zip codes or locations. • Having a pool in a house in luxury areas is very different (~$40K) than having a pool in a house in Suburbs(~$5K).

30. 31 Motivation Example 2: Houston House Price Estimate $350,000 $180,000 • Houses A, B have very similar characteristics • OLS produces single parameter estimates for predictor variables like noOfRooms, squareFootage, yearBuilt, etc

31. 32 Motivation Example 2: Houston House Price Estimate • If we use zip code as regions, they are in same region • If we use a grid structure • They are in different regions but some houses similar to B (lake view) are in same region with A and this will effect coefficient estimate • More importantly, the house around U-shape lake show similar pattern and should be in the same region, we miss important information.

32. 33 Motivation Our Approach: Capture the True Pattern Structure! • We need to discover arbitrary shaped regions, and not rely on some a priori defined artificial boundaries Problems to be solved: 1. Find regions whose objects have a strong relationship between the dependent variable and independent variables 2. Extracting Regional Regression Functions 3. Develop a method to select which regression function to use for a new object to be predicted.

33. 34 Skip! Methodology The REGional REGression Framework (REG^2) Employs a two-phased approach: • Phase I:Discovering regions using a clustering alg. Maximizing a regression based (R-sq or AIC ) fitness functions ( along with regional coefficient estimates) • Phase II: Applying techniques to select correct regional regression function and improve prediction for unseen data

34. 35 Methodology So, what Can we use as Interestingness? • The natural first candidate is Adjusted R2. R-sq is a measure of the extent to which the total variation of the dependent variable is explained by the model. • R-sq alone is not a good measure to assess the goodness of fit; only deals with the bias of the model & ignores the complexity of model which leads to overfitting • There are better model selection criteria to balance the tradeoff between bias and the variance.

35. 36 Methodology Fitness Function Candidates • R2-based fitness functions • Fitness functions that additionally consider model complexity, in addition to goodness of fit, such as AIC or BIC • Regularization approaches that penalize large coefficients. • Fitness functions that employ validation sets that provide a better measure for the generalization error—the model’s performance on unseen examples • An improvement of the previous approach that additionally considers training set/test set similarity • Combination of approaches mentioned above

36. 37 Methodology • R-sq Based Fitness Function • Given; and • The interestingness is: • To battle the tendency towards having small size regions with high correlation (false correlation): • used scaled version of the fitness function • employed a parameter to limit the min. size of the region • The Rsq-based fitness function then becomes;

37. 38 Methodology • AIC Based Fitness Function (AICFitness) • We prefer Akaike’s Information Criterion (AIC) because; • it takes model complexity (number of observations etc..) into consideration more effectively • AIC provides a balance between bias and variance, and is estimated using the following formula: • Variations of AIC including AICu [McQuarrie] which is used for small size data is available  good fit for our small size regions

38. 39 Methodology • AIC Based Fitness Function (AICFitness) • AIC-based Interestingness – iAIC (r) • AICFitness function then becomes • AICFitness function repeatedly applies regression analysis during the search for the optimal set of regions which overall provides best AIC values (minimum)

39. 40 Methodology • Controlling Regional Granularity • β is used to control the number of regions to be • discovered, thus overall model complexity. • Finding a good value for β means striking the right • balance between underfitting and overfitting for a given • dataset. • Small values for  small number of regions; large • values for large number of regions Reminder—Region Discovery Framework Fitness Function: q(X)= cXreward(c)=cXi(c) *size(c)

40. 41 Experiments & Results Generalization Error Results - Boston Housing Data Generalization Error Improvement (SSE_TE) • Discovered regions and their regional regression coefficients perform better prediction compared to the global model • Some regions with very high error reduce the overall accuracy but still 27% improvement. (future work item) • Relationship between variables spatially varies

41. 42 Experiments & Results Generalization Error Results – Arsenic Data • Regional regression coefficients perform just slightly better prediction • Some due to external factors, e.g. toxic waste, power plant (analyzed previously using PCAFitness approach, MLDM09) • Some regions with very high error reduce the overall accuracy • Still around 60% of objects are better predicted • Open for improvement; new fitness functions (next)

42. 4.2 A Framework for Regional Association Rule Mining and Scoping [GeoInformatica10] 43 Step 1: Region Discovery Arsenic hot spots Step 2: Regional Association Rule Mining An association rule a is discovered. Step 3: Regional Association Rule Scoping Scope of the rule a

43. Arsenic Hot Spots and Cool Spots 44 Step 1: Region Discovery Step 2: Regional Association Rule Mining Step 3: Regional Association Rule Scoping

44. Example Regional Association Rules 45 rule 1 rule 2 rule 3 rule 4 Step 1: Region Discovery Step 2: Regional Association Rule Mining Step 3: Regional Association Rule Scoping

45. Region vs. Scope 46 • Scope of an association rule indicates how regional or global a local pattern is. • The region, where an association rule is originated, is a subset of the scope where the association rule holds.

46. Association Rule Scope Discovery Framework 47 Let a be an association rule, r be a region, conf(a,r) denotes the confidence of a in region r, and sup(a,r) denotes the support of a in r. Goal: Find all regions for which an associate rule a satisfies its minimum support and confidence threshold; regions in which a’s confidence and support are significantly higher than the min-support and min-conf thresholds receive higher rewards. Association Rule Scope Discovery Methodology: For each rule a that was discovered for region r’, we run our region discovery algorithm that defines the interestingness of a region ri with respect to an association rule a as follows: Remarks: • Typically d1=d2=0.9; =2 (confidence increase is more important than support increase) • Obviously the region r’ from which rule a originated or some variation of it should be “rediscovered” when determining the scope of a.

47. Regional Association Rule Scoping 48 Ogallala Aquifer Gulf Coast Aquifer

48. Fine Tuning Confidence and Support 49 • We can fine tune the measure of interestingness for association rule scoping by changing the minimum confidence and support thresholds.

49. Regional Models for User Behaviour on the Internet 50 Problem: We are interested in predicting a performance variable based on some performance context that is described using a set of binary variables Example: We try to predict is a user clicks on an ad based on the keywords that occur in the ad. Our ancle: As usual, we are interested in extracting knowledge concerning the „regional variation of clicking behavior“

50. Association List Based Discrepancy Mining (ALDM) 51 Given a set of key-words with an associated performance measure for a group G of transactions, we create association lists; for example: G:=((A 0.002 17 2)(B 0.001 222 1)) that models user behavior for group G on the internet, such as clicking of ads in Texas Meaning—for the group G analyzed: • If A was present the performance variable has an average value of 0.002, A is present in 17 objects, the average value of the performance measure if A is present is twice as high as its average value for all transactions. • If B was present the performance variable has an average value of 0.01, B is present in 222 objects, the average value of the performance measure if B is present is the same as the average value for all transactions.