Potts Clustering with Complete Shrinkage: a novel clustering methodology with its Software Package pottscompleteshrinkage in Python

Abstract

We have modified the Potts Model Swendsen-Wang algorithm to insert some clusters constraints by applying a modified agglomerative clustering approach (Kurita, 1991). We have called the induced Potts Model, the Potts Clustering with Complete Shrinkage (PCCS), under the Python package pottscompleteshrinkage deployed on PyPi Index under its current release. In this approach, we deal with the increasing number of small clusters generated in a given partition by merging all small clusters of size ≤ h with their closest cluster in terms of minimal distance respectively, where h is an integer greater or equal to 2. The algorithm uses a technique in which distances of all pairs of observations are stored. Then the nearest cluster (with size ≥ h) is given by the cluster with the closest node in terms of minimal distance to the cluster to be merged using complete linkage. This approach is truly effective as it helps to control the clusters size, and we have found empirical evidence of Chi-Square and Gamma density curves for the constrained cluster size distribution of PCCS, when applied to some datasets taken from the multiple-output benchmark datasets available in the Mulan project website (Tsoumakas et al., 2020). We add a last framework based on Frequency of frequency distribution (FoF) to find the conditional bonds distribution given the clusters size constraints which results in an intractable distribution for large datasets, but its computation framework is a land of rich mathematical developments.