K-Models: a Flexible and Interpretable Method for Ordinal Clustering with Application to Antigen-Antibody Interaction Profiles

TL;DR

K-Models is a new clustering framework for functional data that incorporates ordinal constraints, enhancing interpretability and structure detection, demonstrated on antigen-antibody interaction profiles.

Contribution

It introduces K-Models, a novel method that integrates ordinal constraints into clustering, improving interpretability and underlying process estimation for functional data.

Findings

K-Models achieves comparable performance to state-of-the-art methods.

The method enhances interpretability of clustering results.

Applied to biomolecular interaction data, it successfully identifies intrinsic signal patterns.

Abstract

Existing clustering methods for functional data often prioritize partitioning accuracy over interpretability, making it challenging to extract meaningful insights when the data-generating process follows a specific underlying structure and an ordinal relationship among clusters is suspected. This work introduces K-Models, a novel framework that integrates ordinal constraints and estimates key underlying elements of the random process generating the observed functional profiles, improving both interpretability and structure identification. The proposed method is evaluated through simulations and real-world applications. In particular, it is tested on Region of Interest (ROI) curves, which represent reaction profiles from a reflectometric sensor monitoring biomolecular interactions, such as antigen-antibody binding. These curves represent changes in reflected light intensity over time at multiple measurement spots with immobilized antigens during analyte exposure, capturing the binding dynamics of the system. The goal is to identify intrinsic signal patterns solely from the observed dynamics, making this dataset an ideal benchmark for assessing the added interpretability of the proposed approach. By incorporating structural assumptions into the clustering process, K-Models enhances interpretability while maintaining performance comparable to state-of-the-art techniques, providing a valuable tool for analyzing functional data with an underlying ordinal structure.