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

2026-05-14

AI Summary

This work proposes the K-Models framework, which explicitly incorporates ordinal constraints into functional clustering to address the limited interpretability of traditional methods that often overlook the underlying generative mechanisms of function-valued data with inherent ordering structures. By jointly estimating latent key components responsible for generating observed curves during clustering, the approach integrates functional data analysis, ordinal-constrained optimization, and stochastic process modeling. The method achieves clustering performance comparable to state-of-the-art techniques while substantially enhancing interpretability and scientific insight, as demonstrated on both simulated data and real-world region-of-interest (ROI) curves characterizing antigen–antibody interactions.

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.

Problem

• ordinal clustering
• functional data
• interpretability
• antigen-antibody interaction
• clustering

Innovation

• ordinal clustering
• functional data
• interpretability
• K-Models
• structural constraints