1. Chapter 12: Cluster analysis and segmentation of customers

2. Commercial applications
A chain of radio-stores uses cluster analysis for identifying three different customer types with varying needs.
An insurance company is using cluster analysis for classifying customers into segments like the “self confident customer”, “the price conscious customer” etc.
A producer of copying machines succeeds in classifying industrial customers into “satisfied” and “non-satisfied or quarrelling” customers.

3. Input-data 1 Output-data 2 3 4 Cluster: X1 X2 … Xn Obs. 1 Obs. 2
Obs. i
Obs, m
Cluster 1
Cluster 2
Classify
rows
Factor 1
Factor 2
Factor:
X1 X2 X3… Xj…Xn
Obs. 1
Obs. 2 …
Obs. m 3 4
Classify
columns
Figure Relatedness of multivariate methods: cluster analysis and factor analysis

4. Dependence and Independence methods
Dependence Methods: We assume that a variable (i.e. Y) depends on (are caused or determined by) other variables (X1, X2 etc.)
Examples: Regression, ANOVA, Discriminant Analysis
Independence Methods: We do not assume that any variable(s) is (are) caused by or determined by others. Basically, we only have X1, X2 ….Xn (but no Y)
Examples: Cluster Analysis, Factor Analysis etc.

5. Dependence and Independence methods
Dependence Methods: The model is defined apriori (prior to survey and/or estimation)
Examples: Regression, ANOVA, Discriminant Analysis
Independence Methods: The model is defined aposteriori (after the survey and/or estimation has been carried out)
Examples: Cluster Analysis, Factor Analysis etc.
When using independence methods we let the data speak for themselves!

6. Dependence method: Multiple regression
Y (Sales)
X1 (Price)
X2 (Price Competitor)
X3 (Adverting)
Obs1
Obs2
Obs3
Obs4
Obs5
Obs6
Obs7
Obs8
Obs9
Obs10 . 95 90 80 85 ..
100 75
The primary focus is on the variables!

7. Independence method: Cluster analysisX1 X2 X3
Obs1
Obs2
Obs3
Obs4
Obs5
Obs6
Obs7
Obs8
Obs9
Obs10 5 3 2 . 4 1
Cluster 1
Cluster 2
Cluster 3
The primary focus is on the observations!

8. Cluster analysis output: A new cluster-variable with a cluster-number on each respondentX1 X2 X3
Cluster
Obs1
Obs2
Obs3
Obs4
Obs5
Obs6
Obs7
Obs8
Obs9
Obs10 5 3 2 . 4 .. 1

9. Cluster analysis: A cross-tab between the cluster- variable and background + opinions is established
Age
%-Females
Household size
Opinion 1
Opinion 2
Opinion 3 32 31
1.4
3.2
2.1
2.2 44 54
2.9
4.0
3.4
3.3 56 46
2.6
3.0
“Younger male nerds”
Core-families with
Traditional values
“Senior-relaxers”

10. Cluster profiling: (hypothetical)
“Ecological shopper”
Cluster 2:
“Traditional shopper”
Buy ecological food
Advertisements funny
Low price important
1 = Totally Agree
Note: Finally the clusters’ respective media-behaviour needs to be uncovered

11. A small example of cluster analysis
Friendly (X02)
Stagnant (X08)
 distances
Cluster
John
Bob
Cathy
John-Bob
John-Cathy
Bob-Cathy 5 1 4 3 2 8 6 A B

12. Governing principle Maximization of homogeneity within clusters
and simultaneously
Maximization of heterogeneity across clusters

13. Partitioning/k-means
Non-overlapping
(Exclusive) Methods
Overlapping Methods
Non-hierarchical
Hierarchical
Non-hierarchical/
Partitioning/k-means
- Overlapping k-centroids
Overlapping k-means
Latent class techniques
- Fuzzy clustering
- Q-type Factor analysis (9)
Agglomerative
Divisive
- Sequential threshold
- Parallel threshold
- Neural Networks
- Optimized partitioning (8)
Linkage
Methods
Centroid
Variance
Name in SPSS 1 2 3 4 5 6 7 8 9
Between-groups linkage
Within-groups linkage
Nearest neighbour
Furthest neighbour
Centroid clustering
Median clustering
Ward’s method
K-means cluster
(Factor)
- Centroid (5)
- Median (6)
- Average
- Between (1)
- Within (2)
- Weighted
- Single
- Ordinary (3)
- Density
- Two stage Density
- Complete (4)
- Ward (7)
Note: Methods in italics are available
In SPSS. Neural networks necessitate
SPSS’ data mining tool Clementine
Figure Overview of clustering methods

14. 2 Non overlapping Overlapping Single Linkage: Minimum distance *
Complete Linkage:
Maximum distance *
Hierarchical
Non-hierarchical
Average Linkage:
Average distance *
Centroid method:
Distance between centres * 1a 1b 1c
1b1
1b2 2
Agglomerative
Divisive
Wards method:
Minimization of
within-cluster variance *
Figure Illustration of important clustering issues in Figure 12.1

15. Euclidean distance (Default in SPSS):Y
(x1, y1)
(x2, y2)
y2-y1
x2-x1 B * A * X
d = (x2-x1)2 + (y2-y1)2
Other distances available in SPSS: City-Block uses  of absolute differences instead of squared differences of coordinates. Moreover: Minkowski distance, Cosine distance, Chebychev distance, Pearson Correlation.

16. Euclidean distance Y B (3, 5) * 5-2 A * (1, 2) 3-1 X

17. Which two pairs of points are to be clustered first?G * A B * * F C * * D * E H * *

18. Maybe A/B and D/E (depending on algorithm!)* A B * * F C * * D * E H * *

19. Quo vadis, C? G * A B * * C * D * E H * *

20. Quo vadis, C? (Continued)G * A B * * C * D * E H * *

21. How does one decide which cluster a “newcoming” point is to join?
Measuring distances from point to clusters or points:
“Farthest neighbour” (complete linkage)
“Nearest neighbour” (single linkage)
“Neighbourhood centre” (average linkage)

22. Quo vadis, C? (Continued)G * A B * *
10,5
8,5
7,0
11,0 C *
8,5 D *
9,0
12,0
9,5 E H * *

23. Complete linkage G * A B * * 10,5 C * D * 9,5 E H * *
Minimize longest distance from cluster to point G * A B * *
10,5 C * D *
9,5 E H * *

24. Average linkage G * A B * * 8,5 C * D * 9,0 E H * *
Minimize average distance from cluster to point G * A B * *
8,5 C * D *
9,0 E H * *

25. Single linkage Minimize shortest distance from cluster to point G * AB * *
7,0 C *
8,5 D * E H * *

26. Single linkage: Pitfall*
A and C merge into the same cluster omitting B! *
Chaining or Snake-like clusters *
Cluster formation begins A C *
All the time the closest observation is put into the existing cluster(s) * B * * * * *

27. Single linkage: Advantage* * * * ** * *
Outliers * * * *
Entropy group * * * *
Good outlier detection and removal procedure in cases with “noisy” data sets

28. Cluster analysis Do our data at all permit the use of means?
More potential pitfalls & problems:
Do our data at all permit the use of means?
Some methods (i.e. Wards) are biased toward production of clusters with approximately the same number of observations.
Other methods (i. e. Centroid) require data as input that are metric scaled. So, strictly speaking it is not allowable to use this algorithm, when clustering data containing interval scales (Likert- or semantic differential scales).

29. Cluster analysis: Small artificial example1
0,68
0,92
0,42
0,58 3 2 6 4 5
Note: 6 points yield
15 possible pairwise
distances - [n*(n-1)]/2

30. Cluster analysis: Small artificial example1
0,68 3
0,42 2 6
0,92 4 5
0,58

31. Cluster analysis: Small artificial example1
0,68 3
0,42 2 6
0,92 4 5
0,58

32. Dendrogram * * * * * * 0,2 0,4 0,6 0,8 1,0 OBS 1 OBS 2 Step 0: OBS 3
Each observation
is treated as a
separate cluster
OBS 3 *
OBS 4 *
OBS 5 *
OBS 6 *
Distance Measure
0, , , , ,0

33. Dendrogram (Continued)
OBS 1 *
Cluster 1
OBS 2 *
Step 1:
Two observations
with smallest
pairwise distances
are clustered
OBS 3 *
OBS 4 *
OBS 5 *
OBS 6 *
0, , , , ,0

34. Dendrogram (Continued)
OBS 1 *
Cluster 1
OBS 2 *
Step 2:
Two other observations
with smallest distances
amongst remaining points/clusters
are clustered
OBS 3 *
OBS 4 *
OBS 5 *
Cluster 2
OBS 6 *
0, , , , ,0

35. Dendrogram (Continued)
OBS 1 *
Cluster 1
OBS 2 *
OBS 3 *
Step 3:
Observation 3 joins
with cluster 1
OBS 4 *
OBS 5 *
Cluster 2
OBS 6 *
0, , , , ,0

36. Dendrogram (Continued)
OBS 1 *
OBS 2 *
“Supercluster”
OBS 3 *
OBS 4 *
Step 4:
Cluster 1 and 2 - from
Step 3 joint into a
“Supercluster”
OBS 5 *
OBS 6 *
0, , , , ,0
A single observation
remains unclustered (Outlier)

37. Textbooks in Cluster Analysis
Brian S. Everitt
Cluster Analysis for Social Scientists, 1983
Maurice Lorr
Cluster Analysis for Researchers, 1984
Charles Romesburg
Cluster Analysis, 1984
Aldenderfer and Blashfield

38. Case: Clustering of beer brands
Brand profiles based om the 17 semantic differential scales
Purpose: to determine the market structure in terms of similar/different brands
Hypothesis: reflects the competitive structure among brands due to consumers bahaviour

39. Case: Clustering of beer brands

40. Case: Clustering of beer brands

41. Case: Clustering of beer brands

42. Case: Clustering of beer brands

43. Case: Clustering of beer brands

44. Case: Clustering of beer brands

45. Case: Clustering of beer brands