1. Cluster analysis Presented by Dr.Chayada Bhadrakom
Agricultural and Resource Economics, Kasetsart University

2. Lecture / Tutorial outline
Cluster analysis
Lecture / Tutorial outline
Cluster analysis
Example of cluster analysis
Work on SPSS

3. Introduction
Example
Marketing research: Customer survey on brand awareness

4. Question Is there a linear relation between brand awareness and yearly income? Hypothesis: The higher a person's income, the higher his/her brand awareness.

5. Question Is there structure in the brand awareness dataset
Question Is there structure in the brand awareness dataset? Are there clusters for the combination of yearly income and brand awareness?

6. Cluster Analysis
It is a class of techniques used to classify cases into groups that are relatively homogeneous within themselves and heterogeneous between each other, on the basis of a defined set of variables. These groups are called clusters.

8. Cluster Analysis and marketing research
Market segmentation. E.g. clustering of consumers according to their attribute preferences
Understanding buyers behaviours. Consumers with similar behaviours/characteristics are clustered
Identifying new product opportunities. Clusters of similar brands/products can help identifying competitors / market opportunities
Reducing data. E.g. in preference mapping

9. Steps to conduct a Cluster Analysis
Formulate the problem
Select a distance measure
Select a clustering algorithm
Determine the number of clusters
Validate the analysis

11. Problem Formulation
Perhaps the most important part of formulating the clustering problem is selecting the variables on which the clustering is based
Basically, the set of variables selected should describe the similarity between objects in terms that are relevant to the marketing research problem
The variables should be selected based on past research, theory, or a consideration of the hypotheses being tested. In exploratory research, the researcher should exercise judgment and intuition

12. Defining distance Most common Euclidean
Dij distance between cases i and j
xki value of variable Xk for case j
The Euclidean distance is the square root of the sum of
the squared differences in values for each variable.

13. Choosing a clustering procedure
Clustering Procedures
Nonhierarchical
Hierarchical
Agglomerative
Divisive
Sequential
Threshold
Parallel
Optimizing
Partitioning
Ward’s Method
Linkage
Methods
Variance
Centroid
Single
Complete
Average

14. Clustering procedures
Hierarchical procedures
Agglomerative (start from n clusters, to get to 1 cluster)
Divisive (start from 1 cluster, to get to n cluster)
Non hierarchical procedures
K-means clustering

15. Agglomerative clustering

16. Agglomerative clustering
Linkage methods
Single linkage (minimum distance)
Complete linkage (maximum distance)
Average linkage
Ward’s method
Compute sum of squared distances within clusters
Aggregate clusters with the minimum increase in the overall sum of squares
Centroid method
The distance between two clusters is defined as the difference between the centroids (cluster averages)

17. Linkage Methods of Clustering
Single Linkage or
Nearest neighbor
Minimum Distance
Cluster 1
Cluster 2
Complete Linkage or
Furthest Neighbor
Maximum Distance
Cluster 1
Cluster 2
Average Linkage
Between-groups Linkage
Average Distance
Cluster 1
Cluster 2

18. Other Agglomerative Clustering Methods
Ward’s Procedure
Centroid Method

19. Example of hierarchical method: Single linkage

20. Example of hierarchical method: Complete linkage

21. K-means clustering The number k of cluster is fixed
An initial set of k “seeds” (aggregation centres) is provided
First k elements
Other seeds
Given a certain treshold, all units are assigned to the nearest cluster seed
New seeds are computed
Go back to step 3 until no reclassification is necessary
Units can be reassigned in successive steps (optimising partioning)

22. Hierarchical vs Non hierarchical methods
Hierarchical clustering
No decision about the number of clusters
Problems when data contain a high level of error
Can be very slow
Initial decision are more influential (one-step only)
Non hierarchical clustering
Faster, more reliable
Need to specify the number of clusters (arbitrary)
Need to set the initial seeds (arbitrary)

23. Suggested approach
First perform a hierarchical method to define the number of clusters
Then use the k-means procedure to actually form the clusters

24. Defining the number of clusters: elbow rule (1)

25. Elbow rule (2): the scree diagram

26. Validating the analysis
Impact of initial seeds / order of cases
Impact of the selected method
Consider the relevance of the chosen set of variables

27. SPSS Example

29. Number of clusters: 10 – 6 = 4

31. Open the dataset Cluster_small.sav

41. Open the dataset supermarkets_update.sav

42. The supermarkets.sav dataset

43. Cluster analysis: basic steps
Apply Ward’s methods
Check the agglomeration schedule
Decide the number of clusters
Apply the k-means method

44. Analyse / Classify

45. Select the component scores

46. Select Ward’s algorithm

47. Output: Agglomeration schedule

48. Number of clusters
Identify the step where the “distance coefficients” makes a bigger jump

49. The scree diagram (Excel needed)

50. Number of clusters Number of cases 150 N Step of ‘elbow’ 145 S
__________________________________
Number of clusters N-S

51. Now repeat the analysis
Choose the k-means technique
Set 5 as the number of clusters
Save cluster number for each case
Run the analysis

52. K-means

53. K-means dialog box

54. Save cluster membership

55. Cluster membership

56. Interpret