# Piecewise regression mixture for simultaneous functional data clustering and optimal segmentation

arXiv: https://arxiv.org/abs/1312.6974 · HTML: https://mlsanity.com/paper/1312.6974/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2013.

## Built on by (most cited first, 4 of 4)

- [Review of Clustering Methods for Functional Data](https://mlsanity.com/paper/2210.00847/) (2022)
- [Mixture of segmentation for heterogeneous functional data](https://mlsanity.com/paper/2303.10712/) (2023)
- [A Regression Mixture Model to understand the effect of the Covid-19 pandemic on Public Transport Ridership](https://mlsanity.com/paper/2402.12392/) (2024)
- [Mixture of partially linear experts](https://mlsanity.com/paper/2405.02905/) (2024)

## Abstract (arXiv)

This paper introduces a novel mixture model-based approach for simultaneous clustering and optimal segmentation of functional data which are curves presenting regime changes. The proposed model consists in a finite mixture of piecewise polynomial regression models. Each piecewise polynomial regression model is associated with a cluster, and within each cluster, each piecewise polynomial component is associated with a regime (i.e., a segment). We derive two approaches for learning the model parameters. The former is an estimation approach and consists in maximizing the observed-data likelihood via a dedicated expectation-maximization (EM) algorithm. A fuzzy partition of the curves in K clusters is then obtained at convergence by maximizing the posterior cluster probabilities. The latter however is a classification approach and optimizes a specific classification likelihood criterion through a dedicated classification expectation-maximization (CEM) algorithm. The optimal curve segmentation is performed by using dynamic programming. In the classification approach, both the curve clustering and the optimal segmentation are performed simultaneously as the CEM learning proceeds. We show that the classification approach is the probabilistic version that generalizes the deterministic K-means-like algorithm proposed in H'ebrail et al. (2010). The proposed approach is evaluated using simulated curves and real-world curves. Comparisons with alternatives including regression mixture models and the K-means like algorithm for piecewise regression demonstrate the effectiveness of the proposed approach.