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Table of Contents Multivariate Data Modeling Classification and Discrimination Cluster Analysis Agglomerative Clustering | |
See also: cluster analysis, minimal spanning tree |
d_{qi}' = s d_{pi} + t d_{qi} + u d_{pq} + v |d_{pi}-d_{qp}|
with
s,t,u, and v being the system parameters,
d_{pi}, d_{qi}, d_{pq} the distances between the clusters (or objects), and
d_{qi}' being the new distance between the new cluster q and all other objects i. d_{qi}' replaces d_{qi} during the merging process.
Listed below are the parameters of the most commonly used clustering
techniques.
type of clustering | s | t | u | v | comment |
single linkage | 0.5 | 0.5 | 0 | -0.5 | contracting |
complete linkage | 0.5 | 0.5 | 0 | 0.5 | dilating |
average linkage | 0.5 | 0.5 | 0 | 0 | compromise |
median | 0.5 | 0.5 | -0.25 | 0 | not monotonous |
centroid | n_{p}/n | n_{q}/n | -n_{p}n_{q}/n^{2} | 0 | not monotonous |
Ward | (n_{p}+n_{i})/(n-n_{i}) | (n_{q}+n_{i})/(n-n_{i}) | -n_{i}/(n-n_{i}) | 0 | "best" approach |
flexible strategy | a | a | 1-2a | 0 | parameter a determines behavior |
n ... number of objects
n_{p} ... number of objects in cluster p n_{q} ... number of objects in cluster q n_{i} ... number of objects in cluster i |
Last Update: 2006-Jän-17