Abstract
The focus of the present paper is on clustering, namely the problem of finding distinct groups in a dataset so that each group consists of similar observations. We consider the finite mixtures of regression models, given their flexibility in modeling heterogeneous time series. Our study aims to implement a novel approach, which fits mixture models based on the spline and polynomial regression in the case of auto-correlated data, to cluster time series in an unsupervised machine learning framework. Given the assumption of auto-correlated data and the usage of exogenous variables in the mixture model, the usual approach of estimating the maximum likelihood parameters using the Expectation–Maximization (EM) algorithm is computationally prohibitive. Therefore, we provide a novel algorithm for model fitting combining auto-correlated observations with spline and polynomial regression. The case study of this paper consists of the task of clustering the time series of sales data influenced by promotional campaigns. We demonstrate the effectiveness of our method in a case study of 131 sales series data from a real-world company. Numerical outcomes demonstrate the efficacy of the proposed method for clustering auto-correlated time series. Despite the specific case study of this paper, the proposed method can be used in several real-world application fields.
Highlights
Clustering is the problem of finding distinct groups in a dataset so that each group consists of similar observations
We propose to fill the research gap by developing a finite mixture model through autoregressive mixtures combined with spline and polynomial regression for auto-correlated time series
We provide some necessary preliminaries about the methodology for finite mixture models for clustering
Summary
Clustering is the problem of finding distinct groups in a dataset so that each group consists of similar observations. Reference [1] provides a comprehensive review of standard procedures to clustering time series. A benchmark study on several methods for time series clustering is in the reference [2]. The approach focused in the present study consists of fitting the available data with a parametric model. This model uses an underlying mixture of statistical distributions, where each distribution represents a specific group of time series. Each time series is assigned to a mixture component (distribution) with the highest probability value. We consider the finite mixtures of regression models, given their flexibility in modeling heterogeneous time series
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