Beyond Local Centers toward Prototypes: Joint Learning of Self-Representation and Adaptive Clustering

Abstract

In this paper, we propose a prototype-learning framework that addresses a common limitation of proximity-based methods: the need to specify proximity weights in advance. Rather than relying on a fixed proximity matrix computed from raw observations, the proposed method jointly learns the prototype representation and the proximity structure. We implement this idea by extending the convex-clustering framework, replacing the pre-specified proximity input with a self-representation matrix learned from the prototype-level representation. The resulting adaptive proximity matrix captures intrinsic relationships among prototypes, yielding prototypes that better reflect the underlying data geometry rather than merely serving as cluster centers. We solve the resulting nonconvex optimization problem using an optimization algorithm based on multiaffine ADMM. Experiments on synthetic non-Euclidean datasets and real benchmark datasets show that the proposed method learns prototypes that better cover the underlying data geometry than standard convex clustering, while removing the need to manually specify proximity weights.