Model-based clustering is considered for Gaussian multivariate functional data as an extension of the univariate functional setting. Principal components analysis is introduced and used to define an approximation of the notion of density for multivariate functional data. An EM like algorithm is proposed to estimate the parameters of the reduced model. Application on climatology data illustrates...

The EM algorithm and its extensions are popular tools for modal estimation but are often criticised for their slow convergence. We propose a new method that can often make EM much faster. The intuitive idea is to use a 'covariance adjustment' to correct the analysis of the M step, capitalising on extra information captured in the imputed complete data. The way we accomplish this is by parameter...

We propose a gossip-based distributed algorithm for Gaussian mixture learning, Newscast EM. The algorithm operates on network topologies where each node observes a local quantity and can communicate with other nodes in an arbitrary point-to-point fashion. The main difference between Newscast EM and the standard EM algorithm is that the M-step in our case is implemented in a decentralized manner...

this paper addresses the vehicle routing problem with delivery time cost. this problem aims to find a set of routes of minimal total costs including the travelling cost and delivery time cost, starting and ending at the depot, in such a way that each customer is visited by one vehicle given the capacity of the vehicle to satisfy a specific demand. in this research, a hybrid metaheuristic approa...

In some situations, EM algorithm shows slow convergence problems. One possible reason is that standard procedures update the parameters simultaneously. In this paper we focus on nite mixture estimation. In this framework, we propose a component-wise EM, which updates the parameters sequentially. We give an interpretation of this procedure as a proximal point algorithm and use it to prove the co...

Expectation-maximization (EM) algorithm has been used to maximize the likelihood function or posterior when the model contains unobserved latent variables. One main important application of EM algorithm is to find the maximum likelihood estimator for mixture models. In this article, we propose an EM type algorithm to maximize a class of mixture type objective functions. In addition, we prove th...

We develop an algorithm for estimating parameters of a distribution sampled with contamination. We employ a statistical technique known as “expectation maximization” (EM). Given models for both member and contaminant populations, the EM algorithm iteratively evaluates the membership probability of each discrete data point, then uses those probabilities to update parameter estimates for member a...

Difference of convex functions (DC) programming is an important approach to nonconvex optimization problems because these structures can be encountered in several fields. Effective optimization methods, called DC algorithms, have been developed in deterministic optimization literature. In machine learning, a lot of important learning problems such as the Boltzmann machines (BMs) can be formulat...

An expectation maximization (EM) algorithm is derived to estimate the parameters of a phylogenetic model, a probabilistic model of molecular evolution that considers the phylogeny, or evolutionary tree, by which a set of present-day organisms are related. The EM algorithm is then extended for use with a combined phylogenetic and hidden Markov model. An efficient method is also shown for computi...

The EM algorithm is one of the most commonly used methods of maximum likelihood estimation. In many practical applications, it converges at a frustratingly slow linear rate. The current paper considers an acceleration of the EM algorithm based on classical quasi-Newton optimization techniques. This acceleration seeks to steer the EM algorithm gradually toward the Newton-Raphson algorithm, which...