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Cluster analysis
- 1. CLUSTER ANALYSIS Wei-Jiun, Shen Ph. D.
- 2. When you were still young and naïve… Classification
- 3. You may classify them by Shape
- 4. You may classify them by Color
- 5. You may classify them by Sum of internal angles
- 6. Classification Shape Color Sum of internal angles Similarity of characteristics
- 7. Purpose of cluster analysis Grouping objects based on the similarity of characteristics they possess. Homogeneity Heterogeneity Geometrically, the objects within clusters will be close together, while the distance between clusters will be farther apart.
- 8. Major role that cluster analysis can play Data reduction Classify large number of observation into manageable groups Taxonomy description Exploratory Confirmatory Examining the influence of cluster on dependent variables Whether different motivational constructs are differentially associated with effort and enjoyment
- 9. How does cluster analysis work? The primary objective of cluster analysis is to define the structure of the data by placing the most similar observations into groups. What clustering variables can be used? How do we measure similarity? How do we form clusters? How many clusters do we form?
- 10. Selecting clustering variables Statistically, Any quantitative variable Theoretically, conceptually, practically, Theoretical fundament corresponding to research Q
- 11. Measuring similarity Similarity The degree of correspondence among objects across all of the characteristics. Correlational measures Distance measures
- 12. Similarity measure Correlation measure Grouping cases base on respondent pattern Distance measure Grouping cases base on distance 0 1 2 3 4 5 X1 X2 X3 X4 case1 case2 case3
- 13. Distance measures Euclidean distance Squared Euclidean distance City-block (Manhattan) distance Chebychev distance Mahalanobis D 2(standardization/variance-covariance)
- 14. Illustration
- 15. Forming clusters Similarity Method Hierarchical Agglomerative / divisive non-hierarchical (quick)
- 16. Number of clusters Theoretical specified Statistical stopping rule Measures of heterogeneity change
- 17. Example N=7 2 variables (scale range from 0-10 ) Hierarchical cluster analysis with agglomerative method
- 19. Example - measure similarity Euclidean distance
- 20. Example - similarity & number of clusters Procedure 0.778 -0.048 0.090 0.662 0.524 （｜E-F ｜+｜E-G ｜+｜F-G ｜）/ 3（｜E-F ｜+｜E-G ｜+｜F-G ｜）+ ｜F-G ｜/ 4
- 21. Example – graphing Graphical portrayal
- 23. Standardizing the data Clustering variables that have scales using widely differing numbers of scale points or that exhibit large differences in standard deviations should be standardized. Z-score Standardized distance (e.g., Mahalanobis distance)
- 24. Deriving clusters Hierarchical cluster analysis Hierarchical Non-hierarchical cluster analysis K-means Combination of both methods Two Step
- 26. Hierarchical cluster analysis (HCA) The stepwise procedure Agglomerate or divide group step by step Agglomerative (SPSS selected) Aggregate object with object / cluster with cluster N clusters to 1 cluster Divisive Separate cluster to object 1 cluster to n clusters
- 27. Dendogram / tree graph
- 28. Agglomerative aglorithms Single linkage Complete linkage Average linkage Centroid method Ward’s method Mahalanobis diatance
- 29. Agglomerative aglorithms Single linkage / neighbor method Defines similarity between clusters as the shortest distance from any object in one cluster to any object in the other. Pics: Retrieved from: http://ppt.cc/uKm0
- 30. Agglomerative aglorithms Complete linkage / Farthest – neighbor method Defines two clusters based on the maximum distance between any two members in the two clusters.
- 31. Agglomerative aglorithms Centroid method Cluster centroids Are the mean values of the observation on the variables of the cluster The distance between the two clusters equals the distance between the two centroids
- 32. Agglomerative aglorithms Average linkage The distance between two clusters is defined as the average distance between all pairs of the two clusters’ members.
- 33. Agglomerative aglorithms Ward’s method The similarity between two clusters is the sum of squares within the clusters summed over all variables. Least variance within cluster
- 34. Number of clusters Theoretical specified Statistical stopping rule Measures of heterogeneity change
- 35. Hierarchical cluster analysis The hierarchical cluster analysis provides an excellent framework with which to compare any set of cluster solutions. This method helps in judging how many clusters should be retained or considered.
- 37. Non-hierarchical cluster analysis (non-HCA) Non-hierarchical cluster analysis assign objects into clusters once the number of clusters is specified. Two steps in non-HCA Specify cluster seed: identify starting points Assignment-assign each observation to one of the cluster seeds.
- 38. Non-hierarchical cluster analysis-algorithm Aims to partition n observation into k clusters in which each observation belongs to the cluster with the nearest mean. Cluster seed assignment Sequential (1 by 1) Parallel (simultaneously) Optimization K-means method 0 1 2 3 4 5 6 0 1 2 3 4 5 scattrplot case
- 39. Pros and Cons of HCA Advantage Comprehensive information A wide range of alternative clustering solution Disadvantage Outliers Large samples / large numbers of variable
- 40. Pros and Cons of non-HCA Advantage Less susceptible to outliers Extremely large data sets Disadvantage Less information Susceptible to initial seed point
- 41. Combination of each method Two step Hierarchical technique is used to select the number of clusters and profile clusters centers that serve as initial cluster seeds in the nonhierarchical procedure. A nonhierarchical method then clusters all observations using the seed points to provide more accurate cluster memberships.
- 42. Interpretation of clusters Mean profile of cluster Name the clusters
- 43. Validation of clusters Cross validation Two sub-sample Confirmatory Discriminant analysis Predictive validity Differences on variables Profile analysis (M)Analysis of variance
- 44. Assumptions of cluster analysis Inferential statistics? Representativeness Multicollinearity Factor analysis Cluster analysis
- 45. Compare to other multivariate analyses Cluster analysis (CA) vs. Factor analysis (FA) CA: grouping cases based on distance (proximity) FA: grouping observations based on pattern of variations (correlation) Cluster analysis vs. Discriminant analysis (DA) CA: group is NOT given (exploratory) DA: group is given (confirmatory)
- 46. Summary Research question Assumption confirmation Multicollinearity Cluster analysis Selecting clustering variables Conducting analysis Interpreting clusters Validating clusters Main analysis It is just a beginning…