A performance study of a consensus clustering algorithm and properties of partition graph

By applying several clustering algorithms to a dataset E or the same algorithm with different parameters, we get several partitions of the dataset E. The problem of finding the best partition among these partitions is considered in this paper. The best partition, also called as consensus partition, minimizes the average number of disagreements between all the partitions. The first step consists of determining candidate consensus partitions. Then the distance between each candidate consensus partition and each of the given partitions is determined. A consensus partition is one whose total distance is minimum. Two distance criteria are used. These distances have interpretations as particular parameters of a graph called partition graph. Some properties of this graph are determined. A structurally simple graph called strong pattern graph is defined, which happens to be a perfect graph.