SMIXS: Novel efficient algorithm for non-parametric mixture regression-based clustering

TL;DR

SMIXS is an improved non-parametric clustering algorithm combining splines and GMMs, offering better stability and efficiency for longitudinal data analysis, with demonstrated superior performance and practical weather regime clustering.

Contribution

The paper introduces SMIXS, a novel algorithm that enhances non-parametric mixture regression clustering by reducing computational complexity and improving stability.

Findings

SMIXS outperforms GMM in synthetic data clustering and regression.

The algorithm achieves significant computational speed-ups.

SMIXS effectively clusters atmospheric data into weather regimes.

Abstract

We investigate a novel non-parametric regression-based clustering algorithm for longitudinal data analysis. Combining natural cubic splines with Gaussian mixture models (GMM), the algorithm can produce smooth cluster means that describe the underlying data well. However, there are some shortcomings in the algorithm: high computational complexity in the parameter estimation procedure and a numerically unstable variance estimator. Therefore, to further increase the usability of the method, we incorporated approaches to reduce its computational complexity, we developed a new, more stable variance estimator, and we developed a new smoothing parameter estimation procedure. We show that the developed algorithm, SMIXS, performs better than GMM on a synthetic dataset in terms of clustering and regression performance. We demonstrate the impact of the computational speed-ups, which we formally prove in the new framework. Finally, we perform a case study by using SMIXS to cluster vertical atmospheric measurements to determine different weather regimes.