IFCS0621 Divisive clustering methoddescendant hierarchical algorithmclassical or symbolic data2 Application for clustering a set of categoriesexample of a set of species contaminated with mercuryco ID: 258194
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IFCS'061A divisive approach for clustering symbolic dataM. ChaventMathématiquesAppliquéesde Bordeaux (MAB), UniversitésBordeaux1 et 2 IFCS'0621. Divisive clustering methoddescendant hierarchical algorithmclassical or symbolic data2. Application for clustering a set of categoriesexample of a set of species contaminated with mercurycomparison of numerical and symbolic approach for clustering the species IFCS'064Introduction to di How to split a clusterComplete enumeration (Edward and Cavalli-Sforza, 1965)Heuristics (Mac-Naughton-Smith, 1964, ChidanandaGowdaet al. 1978)Criterion optimisation like split or diameter (Guénoche1991, Wang et al. 1996)Monothetic approachClustering : Williams & Lambert1959Classification :Breimanet al. 1984 (CART) or Quinlan 1986 (ID3) IFCS'066The proposed dissimilarity measure For a numerical symbolic(interval)data matrix :is the Hausdorffdistancebetween two intervalsIf all intervals are reduced to single points, itcorresponds to the Euclidean distanceThe normalized version of this distance : ),(1),('12'2jijipjHjiixxdvxxd== ),(1'12jijininiiHjxxdnv IFCS'068The extension of the within-clusterinertia thedistance matrixthe extension of the inertia of a cluster is :the extension of the within-clusters inertia of a partition in clusters is : 2''21)(iiCkkdnnCI)()(1==KkkCIPW IFCS'0610Binary question and symbolic data IFCS'0612The proposed divisive clustering method Choose at each step the cluster to be splitsuch that the new partition has minimum within inertia ?Stops after L iterations given as input by the user and the output is a hierarchyindexed by , which is isotonic )()()()(21kkkkCQCQCQC= IFCS'0614First numerical treatment Clusteringof the 67 fish:Ward hierarchical clfish5 concentration variables Potamotrygonhystrix Platydorascostatus Semaprochilodusvarii85.7114.29 Pseudoancistrusbarbatus Leporinusfrederici66.6733.33 Leporinusfasciatus Dorasmicropoeus Hopliasaimara Cynodongibbus Ageneiosusbrevifili Cluster 4 Cluster3 IFCS'0616Second numerical treatment Clustering of the 10 species on a classical numerical data set DorasmicropoeusAgeneiosusbrevifiliLn(Stomach/Muscle)Ln(liver/Muscle) IFCS'0619 with the DIV method :Symbolic treatment