Orthogonalization of data via Gromov-Wasserstein type feedback for clustering and visualization

TL;DR

This paper introduces an adaptive orthogonalization method for clustering and visualization that leverages a Gromov-Wasserstein inspired feedback mechanism within the diffusion map framework, improving cluster separation and robustness.

Contribution

The paper presents a novel adaptive orthogonalization approach using Gromov-Wasserstein feedback for enhanced clustering and visualization, with proven convergence and application to biological data.

Findings

Method achieves high specificity in clustering

Robust to noise and data variations

Produces biologically meaningful clusters

Abstract

In this paper we propose an adaptive approach for clustering and visualization of data by an orthogonalization process. Starting with the data points being represented by a Markov process using the diffusion map framework, the method adaptively increase the orthogonality of the clusters by applying a feedback mechanism inspired by the Gromov-Wasserstein distance. This mechanism iteratively increases the spectral gap and refines the orthogonality of the data to achieve a clustering with high specificity. By using the diffusion map framework and representing the relation between data points using transition probabilities, the method is robust with respect to both the underlying distance, noise in the data and random initialization. We prove that the method converges globally to a unique fixpoint for certain parameter values. We also propose a related approach where the transition probabilities in the Markov process are required to be doubly stochastic, in which case the method generates a minimizer to a nonconvex optimization problem. We apply the method on cryo-electron microscopy image data from biopharmaceutical manufacturing where we can confirm biologically relevant insights related to therapeutic efficacy. We consider an example with morphological variations of gene packaging and confirm that the method produces biologically meaningful clustering results consistent with human expert classification.