Hierarchical Cluster Analysis and Dendrogram

The method implemented in Aabel is called the weighted pair-group with arithmetic averaging. When objects/observations are defined by a set of numeric variables, each object (worksheet row) is positioned in a multi-dimensional space of a dimension proportional to the number of variables (worksheet columns) used to define the object.

• Hierarchical clustering first calculates an n * n matrix of similarities between all objects, and merges the object pairs with the largest similarities. In the next iteration the similarities are recomputed by comparing the averaged similarities of merged objects relative to each other and to other objects. The iteration continues until the similarity matrix is reduced to 2 x 2. The end results are represented as a dendrogram, which is the most common way of displaying the cluster analysis results.
• The similarity measures in Aabel are based on one of the following options:
  • The correlation coefficient (Pearson's product moment correlation coefficient)
  • Euclidean distance similarity (straight line)
  • Standardized Euclidian distance coefficient
  • Manhattan distance similarity measure

  The dendrogram displayed below was generated using the geochemical data (from the Sudbury Structure) published by Naldrett, A.J., Hewins, R.H., Dressler, B.O., and Rao, B.V. (1984).