Adaptive Probabilistic Distance Clustering on the Simplex

Probabilistic Distance Clustering relies critically on the choice of distance metric, which becomes particularly challenging for compositional data due to the geometry of the simplex. While log-ratio transformations are commonly used to address this issue, recent work suggests that more flexible, data-driven representations, such as the -transformation, may offer improved performance. In this paper, we propose an adaptive extension of cluster-size-adjusted Probabilistic Distance Clustering for compositional data, termed PDQ, which embeds the -transformation within the clustering algorithm. The transformation parameter is estimated in an unsupervised manner by minimizing the PDQ objective, allowing the geometry of the data space to adapt to the underlying cluster structure. A preliminary simulation study illustrates the robustness of the proposed approach across different data-generating mechanisms.