1. Análisis de Cluster

4. Selección de variables:
Consideraciones teórico- conceptuales y prácticas.
La técnica de AC no puede determinar cuales variables son relevantes y cuales no
Las variables no apropiadas pueden afectar el análisis

5. What is clustering?
A grouping of data objects such that the objects within a group are similar (or related) to one another and different from (or unrelated to) the objects in other groups
Inter-cluster distances are maximized
Intra-cluster distances are minimized

6. Why do we cluster?
Clustering : given a collection of data objects group them so that
Similar to one another within the same cluster
Dissimilar to the objects in other clusters
Clustering results are used:
As a stand-alone tool to get insight into data distribution
Visualization of clusters may unveil important information
As a preprocessing step for other algorithms
Efficient indexing or compression often relies on clustering

7. Applications of clustering?
Image Processing
cluster images based on their visual content
Web
Cluster groups of users based on their access patterns on webpages
Cluster webpages based on their content
Bioinformatics
Cluster similar proteins together (similarity wrt chemical structure and/or functionality etc)
Many more…

8. The clustering task
Group observations into groups so that the observations belonging in the same group are similar, whereas observations in different groups are different
Basic questions:
What does “similar” mean
What is a good partition of the objects? I.e., how is the quality of a solution measured
How to find a good partition of the observations

9. Observations to cluster
Real-value attributes/variables
e.g., salary, height
Binary attributes
e.g., gender (M/F), has_cancer(T/F)
Nominal (categorical) attributes
e.g., religion (Christian, Muslim, Buddhist, Hindu, etc.)
Ordinal/Ranked attributes
e.g., military rank (soldier, sergeant, lutenant, captain, etc.)
Variables of mixed types
multiple attributes with various types

11. Algoritmos jerárquicos

12. Aglomerativos

13. vecino más proximo

14. Ejemplo

17. Hierarchical joining algorithms
Centroid
Single (nearest-neighbour): distance between two clusters = distance between two closest members of the two clusters.
Complete (furthest neighbour): distance between two clusters = distance between two most distant cluster members.
Centroid : distance between two clusters = distance between multivariate means of each cluster.
Cluster 1
Single
Cluster 2
Cluster 3
Complete
2001
Bio 8100s Applied Multivariate Biostatistics

18. Hierarchical joining algorithms (cont’d)
Cluster 1
Average: distance between two clusters = average distance between all members of the two clusters.
Median: distance between two clusters = median distance between all members of the two clusters.
Ward: distance between two clusters = average distance between all members of the two clusters with adjustment for covariances.
Cluster 2
Cluster 3
Mean/median/adjusted mean
of all pairwise distances
2001
Bio 8100s Applied Multivariate Biostatistics

19. Partitioned clustering: the procedureX1
Choose k “seed” cases which are spread apart from center of all objects as much as possible.
Assign all remaining objects to nearest seed.
Reassign objects so that within-group sum of squares is reduced…
…and continue to do so until SSwithin is minimized.
Seed 1
Seed 2
Seed 3 X2
Objects
Seeds
Object
center
Bio 8100s Applied Multivariate Biostatistics
2001