论文信息 - On the Convergence of the Fuzzy Clustering Algorithm “Fuzzy ISODATA”

On the Convergence of the Fuzzy Clustering Algorithm “Fuzzy ISODATA”

In der vorliegenden Arbeit wird fur den unscharfen Partitionierungsalgorithmus “Fuzzy ISODATA” gezeigt, das ausgehend von beliebigem Startpunkt jeder Haufungspunkt der generierten Folge ein stationarer Punkt des erweiterten, Quadratischen-Fehlersummen-Funktionals ist, welches als Partitionierungskriterium dient. Weiterhin liefert jeder dieser Haufungspunkte den gleichen Zielfunktionswert. Der Algorithmus “Fuzzy ISODATA” produziert keine Zyklen. In this paper it is shown for the Fuzzy ISODATA algorithm that starting from an arbitrary initial point every accumulation point of the sequence generated is a stationary point of the extended within-group sum of squared errors (WGSS) functional taken as partitioning criterion. Further every accumulation point yields the same value of the objective functional. The Fuzzy ISODATA algorithm doesn't produce cycles.

G. Trzebiatowski | B. Bank

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