Hierarchical algorithms

The algorithms of hierarchical clustering are used for grouping patterns of internal organization which they have, ie there is no knowledge about etiquette class to which they belong is unknown. These algorithms work by joining or dividing the most similar pair of groups in each step or iteration.

Summary

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  • 1 How they work
  • 2 Classification
    • 1 Division hierarchical algorithms
    • 2 Agglomerative hierarchical algorithms
  • 3 Stopping criteria
  • 4 Operation example
  • 5 See also
  • 6 Sources

How do they work

Hierarchical algorithms produce a nested sequence of partitions of the set of objects, that is, groups are organized hierarchically and each group (cluster) can be seen as the union of other groups (clusters), thus obtaining different levels of group hierarchy . This hierarchical organization is traditionally represented by a tree called a dendrogram , which provides a taxonomy or hierarchical index of the processed information.

Classification

These algorithms, depending on the way they create the hierarchy, are subdivided, in turn, into divisive or agglomerative .

Division hierarchical algorithms

Hierarchical divisive algorithms start by considering the set of objects as a group and in each iteration divide a group in two until as many groups remain as there are individual objects in the collection or until a certain stopping criterion is met .

Agglomerative hierarchical algorithms

On the other hand, hierarchical agglomerative algorithms based on distances start by considering each object as unit groups and in each iteration the two closest groups are joined until a single group is obtained or until a certain stopping criterion is met. Agglomerative hierarchical algorithms differ from each other in the way they calculate the distance between groups. Two of the main representatives of this type of algorithm are Single Link and CURE .

Stopping criteria

The most used stopping criteria in hierarchical agglomerative strategies are: when c groups are obtained or when the distance between the closest pair of groups is greater than a given threshold.

Operation example

The upper image represents a dendrogram in which the grouping process of nine objects is shown using agglomerative algorithms, since it is based on the idea of ​​considering each object as a unitary group and then uniting the most similar groups. until you get a single group.

 

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