1. Clustering Algorithms Minimize distance But to Centers of Groups

2. Clustering • First need to identify clusters • Can be done automatically • Often clusters determined by problem • Then simple matter to measure distance from new observation to each cluster • Use same measures as with memory-based reasoning

3. Partitioning • Define new categorical variables • Divide data into fixed number (k) of regions • K-means clustering

4. Clustering Uses • Segment customers • Find profitability of each, treat accordingly • Star classification: • Red giants, white dwarfs, normal • Brightness & temperature used to classify • U.S. Army • Identify sizes needed for female soldiers • (males – one size fits all)

5. Tires • Segment customers into product categories • High end (they would buy Michelins) • Intermediate & Low • Standardize data (as in memory-based reasoning)

6. Raw Tire Data

7. Standardize • INCOME • MIN(1,INCOME/200000) • AGE OF CAR • IF({AGE OF CAR})<12 months,1, • ELSE[MIN{(8-Years)/7},1]

8. Sort Data by Outcome

9. Standardized Training Data

10. Identify Cluster Means(could use median, mode)

11. New Case #1 • From new data (could be test set or new observations to classify) squared distance to each centroid Michelin: 0.840 Goodyear 0.025 Opie’s tires 0.047 • So minimum distance to Goodyear

12. New Case #2 • Squared distance to each centroid Michelin: 0.634 Goodyear 0.255 Opie’s tires 0.057 • So minimum distance to Opie’s

13. Software Methods • Hierarchical clustering • Number of clusters unspecified a priori • Two-step a form of hierarchical clustering • K-means clustering • Self-organizing maps • Neural network • Hybrids combine methods

14. Application: Credit Cards • Credit scoring critical • Use past applicants; develop model to predict payback • Look for indicators providing early warning of trouble

15. British Credit Card Company • Monthly account status – over 90 thousand customers, one year operations • Outcome variable STATE: cumulative months of missed payments (integer) • Some errors & missing data (eliminated observations) • Biased sample of 10 thousand observations • Required initial STATE of 0

16. British Credit Card Company • Compared clustering approaches with pattern detection method • Used medians rather than centroids • More stable • Partitioned data • Clustering useful for general profile behavior • Pattern search method sought local clusters • Unable to partition entire data set • Identified a few groups with unusual behavior

17. Insurance Claim Application • Large data warehouse of financial transactions & claims • Customer retention very important • Recent heavy growth in policies • Decreased profitability • Used clustering to analyze claim patterns • Wanted hidden trends & patterns

18. Insurance Claim Mining • Undirected knowledge discovery • Cluster analysis to identify risk categories • Data for 1996-1998 • Quarterly data • Claims for prior 12 months • Contribution to profit of each policy • Over 100,000 samples • Heavy growth in young people with expensive automobiles • Transformed data to normalize, remove outliers

19. Insurance Claim Mining • Number of clusters • Too few – no discrimination – best here was 50 • Used k-means algorithm to minimize least squared error • Identified a few cluster with high claims frequency, unprofitability • Compared 1998 data with 1996 data to find trends • Developed model to predict new policy holder performance • Used for pricing

20. Computational Constraints • Each cluster should have adequate sample size • Since cluster averages are used, cluster analysis not as sensitive to disproportional cluster sizes relative to matching • The more variables you have, the greater the computational complexity • The curse of dimensionality • (it won’t run in a reasonable time if you have too many variables)