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Register a new userUnsupervised learning of regression mixture models with unknown number of components
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Authors
Faicel Chamroukhi
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Regression mixture models are widely studied in statistics, machine learning and data analysis. Fitting regression mixtures is challenging and is usually performed by maximum likelihood by using the expectation-maximization (EM) algorithm. However, it is well-known that the initialization is crucial for EM. If the initialization is inappropriately performed, the EM algorithm may lead to unsatisfactory results. The EM algorithm also requires the number of clusters to be given a priori; the problem of selecting the number of mixture components requires using model selection criteria to choose one from a set of pre-estimated candidate models. We propose a new fully unsupervised algorithm to learn regression mixture models with unknown number of components. The developed unsupervised learning approach consists in a penalized maximum likelihood estimation carried out by a robust expectation-maximization (EM) algorithm for fitting polynomial, spline and B-spline regressions mixtures. The proposed learning approach is fully unsupervised: 1) it simultaneously infers the model parameters and the optimal number of the regression mixture components from the data as the learning proceeds, rather than in a two-fold scheme as in standard model-based clustering using afterward model selection criteria, and 2) it does not require accurate initialization unlike the standard EM for regression mixtures. The developed approach is applied to curve clustering problems. Numerical experiments on simulated data show that the proposed robust EM algorithm performs well and provides accurate results in terms of robustness with regard initialization and retrieving the optimal partition with the actual number of clusters. An application to real data in the framework of functional data clustering, confirms the benefit of the proposed approach for practical applications.
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We consider an equivariant approach imposing data-driven bounds for the variances to avoid singular and spurious solutions in maximum likelihood (ML) estimation of clusterwise linear regression models. We investigate its use in the choice of the number of components and we propose a computational shortcut, which significantly reduces the computational time needed to tune the bounds on the data. In the simulation study and the two real-data applications, we show that the proposed methods guarantee a reliable assessment of the number of components compared to standard unconstrained methods, together with accurate model parameters estimation and cluster recovery.
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