# A novel regularized approach for functional data clustering: An application to milking kinetics in dairy goats

## TL;DR

This paper introduces a new regularized clustering method for functional data, specifically applied to analyze milking kinetics in dairy goats, enhancing phenotypic trait characterization in precision livestock farming.

## Contribution

It presents a novel piecewise linear estimation technique with regularized change-point detection combined with k-means clustering for functional data analysis.

## Key findings

- Improved clustering performance demonstrated through numerical experiments.
- Effective characterization of inter-animal variability in milk emission kinetics.
- Enhanced understanding of lactation process in dairy goats.

## Abstract

Motivated by an application to the clustering of milking kinetics of dairy goats, we propose in this paper a novel approach for functional data clustering. This issue is of growing interest in precision livestock farming that has been largely based on the development of data acquisition automation and on the development of interpretative tools to capitalize on high-throughput raw data and to generate benchmarks for phenotypic traits. The method that we propose in this paper falls in this context. Our methodology relies on a piecewise linear estimation of curves based on a novel regularized change-point estimation method and on the k-means algorithm applied to a vector of coefficients summarizing the curves. The statistical performance of our method is assessed through numerical experiments and is thoroughly compared with existing ones. Our technique is finally applied to milk emission kinetics data with the aim of a better characterization of inter-animal variability and toward a better understanding of the lactation process.