A Projection Transform for Non-Euclidean Relational Clustering

The duality theory for the relational c-means algorithms relational Gaussian mixture model, etc. requires that a distance matrix R correspond to a set of vector object data whose squared A-norm distances (or less generally, squared Euclidean distances) match the elements of R. For most datasets, this is unrealistic constraint. As such, this paper proposes an alternating projection-based transform for converting non-Euclidean distance matrices into Euclidean distance matrices. Two synthetic and six real-world non-Euclidean datasets are used to illustrate that this method preserves cluster structure well.