Cluster analysis
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Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters from it. K-means. Criteria. Same criteria with multivariate data:. Justifying the criteria. Anova: decomposition of the variance.

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  • Partition Methods

    Divide data into disjoint clusters

  • Hierarchical Methods

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





Justifying the criteria
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).






Problems of k means
Problems of k-means

  • Very sensitive to outliers

  • Euclidean distances not appropriate for eliptical clusters

  • It does not give the number of clusters.











Problems of hierarchical cluster
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






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