Clustering model input samples: linking K-Means to Sobol’ indices

¹ MISTEA, Univ Montpellier, INRAE, Institut Agro, Montpellier, France
² EMMAH, INRAE, Avignon Université, Avignon, France

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 30 September 2025
Accepted: 28 May 2026

Abstract

This work is devoted to the problem of clustering a set of samples according to the effect they have as one of the many varying inputs of a model. An example is the problem of clustering weather series according to the effect they have on the yield simulated with a crop model when also other inputs such as soil or plant parameters vary. We introduce both simple solutions based on the K-Means algorithms and the derivation of two possible formulations of the clustering problem in a sensitivity analysis framework. We show that these formulations coincide in the sense that their criteria are closely related to each other, leading to a possibility to use the K-Means algorithm with an improved expression of clustering performance through the use of Sobol’ indices.