1. Clustering
based on book chapter Cluster Analysis in Multivariate Analysis by Hair, Anderson, Tatham, and Black

2. Cluster analysis
What?
we group objects based on characteristics they posses
also called as numerical taxonomy or typology construction
often atheoretical: no statistical basis, lots of heuristics

3. Intuitive basis
Ach, ja: Gestaltlagen

4. Clustering methods: nonhierarchical hierarchical fuzzy
vector quantization
hierarchical
agglomerative
divisive
fuzzy
probabilistic mixture models?

5. Obectives exploratory/confirmatory taxonomy description (e.g. biology)
data simplification (e.g. segmentation)

6. Select the variables
abracadabra, explicit theories, past research, suppositions, hopes, deadlines,

7. Research design detect and remove outliers choose a similarity measure
Householder norm (usually Euclid)
Mahalanobis
correlation
standardize the data
by variable
within case

8. Similarity measures

9. Research design representativeness of the sample (cf. outliers)
multicollinearity?

10. How is this done?
abracadabra, explicit theories, past research, suppositions, hopes, deadlines,

11. Clustering procedure single linkage complete linkage average linkage
centroid method
Ward’s method

12. Single linkage
results easily in snake-like clusters even if they don’t exist

13. Complete linkage
eliminates the snake formation, otherwise a big question mark

14. Average linkage joins clusters with smallest average distances
not so outlier sensitive
tends to form cluster with small within-cluster variation
biased to form clusters with approximately the same variance
etc.

15. Centroid method

16. Centroid method most outlier robust
confusing situations: intercentroid distances may become smaller than distances between already joined pairs: messes up the dendorgram

17. Ward’s method distance between two clusters is something squared
tends to combine clusters with small number of objects
biased toward clusters with approximately equal number of objects

18. Nonhierachical
heuristical methods: sequential treshold/parallel treshold
objective function based: VQ:s, e.g., K-means procedure
Hierachical: O(N2), K-means O(KN)

19. How many clusters open question
practical limits (it would be nice to have 3-6 clusters)
dendrogram based (large increase in cluster distances

20. Validation exogeneous variables indexes, e.g. Davies-Bouldin measure
age:15
age:20
age:14
doesn’t like DD
likes Donald Duck

21. Key issues similarity or dissimilarity measure
...and data standardization