Interpretable Image Clustering via Diffeomorphism-Aware K-Means

TL;DR

This paper introduces an interpretable image clustering method that accounts for nonlinear deformations in image manifolds by integrating diffeomorphism invariance into a K-means framework, improving clustering robustness.

Contribution

It proposes a novel diffeomorphism-aware similarity measure and uses Thin-Plate Spline interpolation to effectively learn deformations, enhancing clustering performance on complex image data.

Findings

Competitively performs against state-of-the-art methods

Effectively handles nonlinear image deformations

Provides an interpretable clustering framework

Abstract

We design an interpretable clustering algorithm aware of the nonlinear structure of image manifolds. Our approach leverages the interpretability of $K$-means applied in the image space while addressing its clustering performance issues. Specifically, we develop a measure of similarity between images and centroids that encompasses a general class of deformations: diffeomorphisms, rendering the clustering invariant to them. Our work leverages the Thin-Plate Spline interpolation technique to efficiently learn diffeomorphisms best characterizing the image manifolds. Extensive numerical simulations show that our approach competes with state-of-the-art methods on various datasets.