Hierarchical mixtures of experts and the EM algorithm
Neural Computation
On the approximation of curves by line segments using dynamic programming
Communications of the ACM
A New Learning Method for Piecewise Linear Regression
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Sparse Multinomial Logistic Regression: Fast Algorithms and Generalization Bounds
IEEE Transactions on Pattern Analysis and Machine Intelligence
A regression model with a hidden logistic process for feature extraction from time series
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
A clustering technique for the identification of piecewise affine systems
Automatica (Journal of IFAC)
Learning Non-linear Multivariate Dynamics of Motion in Robotic Manipulators
International Journal of Robotics Research
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Time series are used in many domains including finance, engineering, economics and bioinformatics generally to represent the change of a measurement over time. Modeling techniques may then be used to give a synthetic representation of such data. A new approach for time series modeling is proposed in this paper. It consists of a regression model incorporating a discrete hidden logistic process allowing for activating smoothly or abruptly different polynomial regression models. The model parameters are estimated by the maximum likelihood method performed by a dedicated Expectation Maximization (EM) algorithm. The M step of the EM algorithm uses a multi-class Iterative Reweighted Least-Squares (IRLS) algorithm to estimate the hidden process parameters. To evaluate the proposed approach, an experimental study on simulated data and real world data was performed using two alternative approaches: a heteroskedastic piecewise regression model using a global optimization algorithm based on dynamic programming, and a Hidden Markov Regression Model whose parameters are estimated by the Baum-Welch algorithm. Finally, in the context of the remote monitoring of components of the French railway infrastructure, and more particularly the switch mechanism, the proposed approach has been applied to modeling and classifying time series representing the condition measurements acquired during switch operations.