  In this paper, we study the modeling and the classification of functional
data presenting regime changes over time. We propose a new model-based
functional mixture discriminant analysis approach based on a specific hidden
process regression model that governs the regime changes over time. Our
approach is particularly adapted to handle the problem of complex-shaped
classes of curves, where each class is potentially composed of several
sub-classes, and to deal with the regime changes within each homogeneous
sub-class. The proposed model explicitly integrates the heterogeneity of each
class of curves via a mixture model formulation, and the regime changes within
each sub-class through a hidden logistic process. Each class of complex-shaped
curves is modeled by a finite number of homogeneous clusters, each of them
being decomposed into several regimes. The model parameters of each class are
learned by maximizing the observed-data log-likelihood by using a dedicated
expectation-maximization (EM) algorithm. Comparisons are performed with
alternative curve classification approaches, including functional linear
discriminant analysis and functional mixture discriminant analysis with
polynomial regression mixtures and spline regression mixtures. Results obtained
on simulated data and real data show that the proposed approach outperforms the
alternative approaches in terms of discrimination, and significantly improves
the curves approximation.
