Agglomerative Hierarchical Clustering (AHC)

Agglomerative Hierarchical Clustering (AHC) is part of:
  • Pro Core statistical software

  • System configuration

    • Windows:
      • Versions: 9x/Me/NT/2000/XP/Vista/Win 7/Win 8
      • Excel: 97 and later
      • Processor: 32 or 64 bits
      • Hard disk: 150 Mb
    • Mac OS X:
      • OS: OS X
      • Excel: X, 2004 and 2011
      • Hard disk: 150Mb.


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Advantages of Agglomerative Hierarchical Clustering

Agglomerative Hierarchical Clustering (AHC) is a classification method which has the following advantages:

Principle of Agglomerative Hierarchical Clustering

Agglomerative Hierarchical Clustering (AHC) is an iterative classification method whose principle is simple.

  1. The process starts by calculating the dissimilarity between the N objects.
  2. Then two objects which when clustered together minimize a given agglomeration criterion, are clustered together thus creating a class comprising these two objects.
  3. Then the dissimilarity between this class and the N-2 other objects is calculated using the agglomeration criterion. The two objects or classes of objects whose clustering together minimizes the agglomeration criterion are then clustered together.

This process continues until all the objects have been clustered.

These successive clustering operations produce a binary clustering tree (dendrogram), whose root is the class that contains all the observations. This dendrogram represents a hierarchy of partitions. It is then possible to choose a partition by truncating the tree at a given level, the level depending upon either user-defined constraints (the user knows how many classes are to be obtained) or more objective criteria.

Agglomerative Hierarchical Clustering aggregation methods

XLSTAT proposes several aggregation methods:

Proximities used in Agglomerative Hierarchical Clustering

The proximity between two objects is measured by measuring at what point they are similar (similarity) or dissimilar (dissimilarity). If the user chooses a similarity, XLSTAT converts it into a dissimilarity as the AHC algorithm uses dissimilarities. The conversion for each object pair consists in taking the maximum similarity for all pairs and subtracting from this the similarity of the pair in question.

XLSTAT proposes several similarities/dissimilarities that are suitable for a particular type of data:

  Similarity Dissimilarity
Quantitative data Pearson's coefficient of correlation Spearman's coefficient of rank correlation Kendall's coefficient of rank correlation Inertia Covariance (n) Covariance (n-1) Percent agreement Euclidean distance Chi-square distance Manhattan distance Pearson's dissimilarity Spearman's dissimilarity Kendall's dissimilarity Percent disagreement
Binary data (0/1) Jaccards coefficient Dice coefficient Sokal & Sneath coefficient (2) Rogers & Tanimoto coefficient Simple matching coefficient Indice de Sokal & Sneath coefficient (1) Phi coefficient Ochiais coefficient Kulczinskis coefficient Percent agreement Jaccards coefficient Dice coefficient Sokal & Sneath coefficient (2) Rogers & Tanimoto coefficient Simple matching coefficient Indice de Sokal & Sneath coefficient (1) Phi coefficient Ochiais coefficient Kulczinskis coefficient Percent agreement

Note: For non-binary categorical variables, it is preferable to first perform a Multiple Correspondence Analysis (MCA) and to consider the coordinates of the observations on the factorial axes as new variables.

Results provided by XLSTAT for Agglomerative Hierarchical Clustering