Diversity Clustering: A Soft Clustering Model Inspired by Ecological Diversity

We propose diversity clustering, a novel soft clustering model inspired by functional diversity measures from ecology. Motivated by the view of species as overlapping groups defined by functional similarity, the model represents clusters as normalized fuzzy sets with symmetric, similarity-based memberships while retaining a unique focal cluster for each instance. We study different formalizations of diversity clustering, and characterize it within the landscape of soft clustering models. Beyond the theoretical characterization, we study the problem of inducing diversity clusterings from data. We introduce a convex optimization formulation, which enforces the axioms of diversity clustering while balancing data-driven similarity and cluster granularity. We analyze the resulting optimization problem and its computational properties, and present gradient-based algorithms, together with complexity guarantees.Our contribution provides a bridge between ecological diversity theory and soft clustering, offering a new framework for modeling overlap, redundancy, and functional similarity in data.