Cluster validation in linear fuzzy clustering of relational data from multi-cluster principal coordinate analysis view point

This paper considers a new approach to cluster validation in linear fuzzy clustering of relational data. Considering the close connection between linear fuzzy clustering and local PCA, the relational clustering model can be regarded as a multi-cluster MDS model. In the new cluster validation approach, the quality of fuzzy partitions is measured from the multi-cluster principal coordinate analysis view point, in which the reconstructed low dimensional substructure in each cluster is compared with the result of principal coordinate analysis considering fuzzy membership degrees to the cluster.