Extracting Regional Knowledge from Spatial Datasets Christoph F

Extracting Regional Knowledge from Spatial Datasets Christoph F. Eick Department of Computer Science, University of Houston 1. 2. 3. 4. 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] 5. [Analyzing Related Datasets] 6. Summary 1

Ch. Eick: Extracting Regional Knowledge from Spatial Datasets 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 2

Ch. Eick: Extracting Regional Knowledge from Spatial Datasets 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” [Goodchild 03, Openshaw 99]. • Simpson’s Paradox – global models may be inconsistent with regional models [Simpson 1951]. • Therefore, it is not surprising that domain experts are mostly interested in discovering hidden patterns at a regional scale rather than a global scale. 3

Ch. Eick: Extracting Regional Knowledge from Spatial Datasets Example: Regional Association Rules Rule 1 Rule 2 Rule 3 Rule 4 Scopes of the 4 Rules in 4

Ch. Eick: Extracting Regional Knowledge from Spatial Datasets 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. 5

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

Preview: A Framework for Extracting Regional Knowledge from Spatial Datasets 7 Application 1: Supervised Clustering [EVJW 07] Application 2: Regional Association Rule Mining and Scoping [DEWY 06, DEYWN 07] Application 3: Find Interesting Regions with respect to a Continuous Variables [CRET 08] Application 4: Regional Co-location Mining Involving Continuous Variables [EPWSN 08] Application 5: Find “representative” regions (Sampling) Application 6: Regional Regression [CE 09] Application 7: Multi-Objective Clustering [JEV 09] Application 8: Change Analysis in Related Datasets [RE 09] =1. 01 RD-Algorithm =1. 04 Wells in Texas: Green: safe well with respect to arsenic Red: unsafe well Department of Computer Science UH-DMML

2. Region Discovery Framework Department of Computer Science 8 Christoph F. Eick

Region Discovery Framework 2 9 § We assume we have spatial or spatio-temporal datasets that have the following structure: (; ) 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. Department of Computer Science Christoph F. Eick

10 Region Discovery Framework 3 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 clusterings X={c 1, …, ck} as follows: q(X)= c X reward(c)= c X i(c) *size(c) with 1 Objective: Find c 1, …, ck O such that: 1. ci cj= if i j 2. X={c 1, …, ck} maximizes q(X) 3. All cluster ci X are contiguous (each pair of objects belonging to ci has to be delaunay-connected with respect to ci and to d) 4. c 1 … ck O 5. c 1, …, ck are usually ranked based on the reward each cluster receives, and low reward clusters are frequently not reported Department of Computer Science Christoph F. Eick

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 [PKDD 06] Hot spots and cool spots [ICDM 06] Scope of regional patterns [SSTDM 07, GE 011] Co-location patterns involving continuous variables [PAKDD 08, ACM-GIS 08] § High-variance regions involving a continuous variable [PAKDD 09] § Regional Regression [ACM-GIS 09] Department of Computer Science Christoph F. Eick

12 Example 1: Finding Regional Co-location Patterns in Spatial Data 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 colocation 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. Department of Computer Science Christoph F. Eick

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

Challenges for Region Discovery 1. 2. 3. 4. 5. 6. 7. 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. Department of Computer Science Christoph F. Eick

Clustering with Plug-in Fitness Functions q. 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. q. 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

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 Department of Computer Science Christoph F. Eick

Representative-based Clustering Attribute 1 17 2 1 3 4 Attribute 2 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, … Department of Computer Science Christoph F. Eick

Rinsurakawong&Eick: Correspondence Clustering , PAKDD’ 10 § § CLEVER [ACM-GIS 08] 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 § 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 Department of Computer Science Christoph F. Eick

20 Ideas SCMRG (Divisive, Multi-Resolution Grids) 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) Department of Computer Science

Code SCMRG Department of Computer Science 21

22 4. Case Studies Regional Knowledge Extraction 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! Department of Computer Science Christoph F. Eick

23 4. 1 REG^2: A Framework of Regional Regression § § 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. 120000 100000 95, 773 80000 70, 000 66, 923 60000 40000 29, 500 20000 13, 157 6, 500 2, 173 5, 378 0 GLS Discovered Regions and Regression Functions q Clustering algorithms with plug-in fitness functions are REG^2 Arsenic Data Random GWR Boston Housing REG^2 Outperforms Other Models in SSE_TR employed to find such region; the employed fitness functions reward regions with a low generalization error. AIC Fitness VAL Fitness Reg. VAL Fitness WAIC Fitness q Various schemes are explored to estimate the Arsenic 5. 01% 11. 19% 3. 58% 13. 18% generalization error: example weighting, regularization, penalizing model complexity and using validation sets, … Boston 29. 80% 35. 69% 38. 98% 36. 60% Skip! Regularization Improves Prediction Accuracy Department of Computer Science Christoph F. Eick

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

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

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

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

28 Motivation Example 2: Houston House Price Estimate v Dependent variable: House_Price v Independent variables: no. Of. Rooms, square. Footage, year. Built, have. Pool, attached. Garage, etc. .

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

31 Motivation Example 2: Houston House Price Estimate $350, 000 $180, 000 q Houses A, B have very similar characteristics q OLS produces single parameter estimates for predictor variables like no. Of. Rooms, square. Footage, year. Built, etc

32 Motivation Example 2: Houston House Price Estimate v If we use zip code as regions, they are in same region v If we use a grid structure v 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 v More importantly, the house around U-shape lake show similar pattern and should be in the same region, we miss important information.

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 n 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.

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

35 Methodology So, what Can we use as Interestingness? v The natural first candidate is Adjusted R 2. R-sq is a measure of the extent to which the total variation of the dependent variable is explained by the model. v 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 v There are better model selection criteria to balance the tradeoff between bias and the variance.

36 Methodology Fitness Function Candidates v. R 2 -based fitness functions v. Fitness functions that additionally consider model complexity, in addition to goodness of fit, such as AIC or BIC v. Regularization approaches that penalize large coefficients. v. Fitness functions that employ validation sets that provide a better measure for the generalization error—the model’s performance on unseen examples v. An improvement of the previous approach that additionally considers training set/test set similarity v Combination of approaches mentioned above

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

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

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

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

41 Experiments & Results Generalization Error Results - Boston Housing Data β SSE_TE SSE % of objects (GL) (REG 2) Improvement better prediction 1. 1 17, 182 12, 566 27% 72% 1. 7 17, 182 14, 799 26% 65% Generalization Error Improvement (SSE_TE) v Discovered regions and their regional regression coefficients perform better prediction compared to the global model v Some regions with very high error reduce the overall accuracy but still 27% improvement. (future work item) v Relationship between variables spatially varies

42 Experiments & Results Generalization Error Results – Arsenic Data β SSE_TE (GL) SSE_TE (REG 2) SSE Improvement % of objects better prediction 1. 1 102, 578 98, 879 3. 6% 57% 1. 25 102, 578 92, 200 8. 01% 61% v Regional regression coefficients perform just slightly better prediction v Some due to external factors, e. g. toxic waste, power plant (analyzed previously using PCAFitness approach, MLDM 09) v Some regions with very high error reduce the overall accuracy v Still around 60% of objects are better predicted v Open for improvement; new fitness functions (next)

4. 2 A Framework for Regional Association Rule Mining and Scoping [Geo. Informatica 10] Step 1: Region Discovery Arsenic hot spots An association rule a is discovered. Scope of the rule a Step 2: Regional Association Rule Mining Step 3: Regional Association Rule Scoping Department of Computer Science 43

Arsenic Hot Spots and Cool Spots 44 Step 1: Region Discovery Step 2: Regional Association Rule Mining Step 3: Regional Association Rule Scoping Department of Computer Science Christoph F. Eick

Example Regional Association Rules 45 rule 1 Step 1: Region Discovery Step 2: Regional Association Rule Mining rule 2 rule 3 Step 3: Regional Association Rule Scoping rule 4 Department of Computer Science Christoph F. Eick

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. Department of Computer Science Christoph F. Eick

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 d 1=d 2=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. Department of Computer Science Christoph F. Eick

48 Regional Association Rule Scoping Ogallala Aquifer Gulf Coast Aquifer Department of Computer Science Christoph F. Eick

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. Department of Computer Science Christoph F. Eick

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 as well as basded on socio-ecomic factors. Our subtopic: As usual, we are interested in extracting knowledge concerning the „regional variation of clicking behavior“. Department of Computer Science Christoph F. Eick

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. Department of Computer Science Christoph F. Eick

Research Goals ALDM 52 1. Develop algorithms that generate groups and association lists that characterize those groups 2. Propose similarity measures for association lists to compare different groups 3. Compare different regional groups with respect to discrepancies of user behavior to: § Extract regional knowledge from the groups § Extract discrepancy knowledge that describes Ø how the behavior of different users differs in different regions Ø How regional behavior differs from global behavior 4. Develop regional prediction techniques § By using knowledge that has been obtained in step 2 § By generalizing our regional prediction work, presented in part 4. 1 Department of Computer Science Christoph F. Eick

5. Methodologies and Tools to Analyze Related Datasets 53 Subtopics: • Disparity Analysis/Emergent Pattern Discovery (“how do two groups differ with respect to their patterns? ”) [SDE 10] • Change Analysis ( “what is new/different? ”) [CVET 09] • Correspondence Clustering (“mining interesting relationships between two or more datasets”) [RE 10] • Meta Clustering (“cluster models of multiple datasets”) • Analyzing Relationships between Polygonal Cluster Models Example: Analyze Changes with Respect to Regions of High Variance of Earthquake Depth. Time 1 Time 2 Novelty (r’) = (r’—(r 1 … rk)) Emerging regions based on the novelty change predicate Department of Computer Science Christoph F. Eick

6. Summary 54 1. A framework for region discovery that relies on additive, reward-based fitness functions and views region discovery as a clustering problem has been introduced. 2. Families of clustering algorithms and families of measures of interestingness are provided that form the core of the framework. 3. Evidence concerning the usefulness of the framework for regional association rule mining, regional regression, and colocation mining has been presented. 4. The special challenges in designing clustering algorithms for region discovery have been identified. 5. The ultimate vision of this research is the development of region discovery engines that assist data analysts and scientists in finding interesting regions in spatial datasets. Department of Computer Science Christoph F. Eick

Other Contributors to the Work Presented Today 55 Graduated Ph. D Students: § Wei Ding (Regional Association Rule Mining, Grid-based Clustering) § Rachsuda Jiamthapthaksin (Agglomerative Clustering, Multi-Run Clustering) § Oner Ulvi Celepcikay (Regional Regression) Current Ph. D Students § Chun-sheng Chen (Density based Clustering, Regional Knowledge Extraction from Ads) § Vadeerat Risurongkawong (Analyzing Multiple Datasets, Change Analysis) Graduated Master Students § Rachana Parmar (CLEVER, Co-location Mining) § Seungchan Lee (Grid-based Clustering, Agglomerative Clustering) § Dan Jiang (Density-based Clustering, Co-location Mining) § Jing Wang (Grid-based and Representative-based Clustering) Software Platform and Software Design § Abraham Bagherjeiran (Ph. D student UH, now at Yahoo!) Domain Experts § Tomasz Stepinski (Lunar and Planetary Institute, Houston, Texas) § J. -P. Nicot (Bureau of Economic Geology, UT, Austin) § Michael Twa (College of Optometry, University of Houston) Department of Computer Science Christoph F. Eick

CLEVER Pseudo Code Inputs: Dataset O, k’, neighborhood-size, p, p’, Outputs: Clustering X, fitness q Algorithm: 1. Create a current solution by randomly selecting k’ representatives from O. 2. Create p neighbors of the current solution randomly using the given neighborhood definition. 3. If the best neighbor improves the fitness q, it becomes the current solution. Go back to step 2. 4. If the fitness does not improve, the solution neighborhood is re-sampled by generating p’ more neighbors. If re-sampling does not lead to a better solution, terminate returning the current solution; otherwise, go back to step 2 replacing the current solution by the best solution found by resampling. Department of Computer Science 56