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Cluster analysis

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Page 1: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Cluster analysis

Page 2: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

• Partition MethodsDivide data into disjoint clusters

• Hierarchical Methods

Build a hierarchy of the observations and deduce the clusters from it.

Page 3: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

K-means

Page 4: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Criteria

Page 5: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Same criteria with multivariate data:

Page 6: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Justifying the criteria• Anova: decomposition of the variance.

Univariate:

SST=SSW+SSB

Multivariate:

Minimizing the withing clusters variance is equivalent to maximize the between clusters variance (the difference between clusters).

Page 7: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

K-means algorithm

Page 8: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Number of clusters

Page 9: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Consequences of standardization

Page 10: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Ruspini example

Page 11: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 12: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 13: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 14: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 15: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Problems of k-means

• Very sensitive to outliers

• Euclidean distances not appropriate for eliptical clusters

• It does not give the number of clusters.

Page 16: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Hierarchical Algoritms

Page 17: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Agglomerative algorithms

Page 18: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Nearest neighbour distance

Page 19: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Farthest neighbour distance

Page 20: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Average distance

Page 21: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Centroid method distance

Page 22: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Ward’s method distance

Page 23: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Dendograms

Page 24: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Example

Page 25: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 26: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 27: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 28: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 29: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 30: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 31: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 32: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Problems of hierarchical cluster

• If n is large, slow. Each time n(n-1)/2 comparisons.

• Euclidean distances not always appropriate

• If n is large, dendogram difficult to interpret

Page 33: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Clustering by variables

Page 34: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 35: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Distances between quantitative variables

Page 36: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Distances between qualitative variables

Page 37: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Similarity between attributes

Page 38: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

Page 39: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters

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