The EM algorithm is a popular method for computing maximum likelihood estimates or posterior modes in models that can be formulated in terms of missing data or latent structure. Although easy implementation and stable convergence help to explain the popularity of the algorithm, its convergence is sometimes notoriously slow. In recent years, however, various adaptations have significantly improv...

We present a noise-injected version of the Expectation-Maximization (EM) algorithm: the Noisy Expectation Maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that additive noise speeds up the average convergence of the EM algorithm to a local maximum of the likelihood surface if a positivity condition holds. Corollary...

This paper presents a new method based on the Expectation-Maximization (EM) algorithm that we apply for color image segmentation. Since this algorithm partitions the data based on an initial set of mixtures, the color segmentation provided by the EM algorithm is highly dependent on the starting condition (initialization stage). Usually the initialization procedure selects the color seeds random...

The expectation−maximization (EM) algorithm for maximum likelihood image recovery converges very slowly. Thus, the ordered subsets EM (OS−EM) algorithm has been widely used in image reconstruction for tomography due to an order−of−magnitude acceleration over the EM algorithm [1]. However, OS− EM is not guaranteed to converge. The recently proposed ordered subsets, separable paraboloidal surroga...

In this article, an on-line EM algorithm is derived for general Exponential Family models with Hidden variables (EFH models). It is proven that the on-line EM algorithm is equivalent to a stochastic gradient method with the inverse of the Fisher information matrix as a coeecient matrix. As a result, the stochastic approximation theory guarantees the convergence to a local maximum of the likelih...

Mixture models have been widely used in cluster analysis. Traditional mixture densities-based clustering algorithms usually predefine the number of clusters via random selection or contend based knowledge. An improper pre-selection of the number of clusters may easily lead to bad clustering outcome. Expectation-maximization (EM) algorithm is a common approach to estimate the parameters of mixtu...

Mixture models implemented via the expectation-maximization (EM) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the EM algorithm requires considerable computational time in its application to huge data sets such as a three-dimensional magnetic resonance (MR) image of over 10 million voxels. Recently, it was shown tha...

In the field of statistical data mining, the Expectation Maximization (EM) algorithm is one of the most popular methods used for solving parameter estimation problems in the maximum likelihood (ML) framework. Compared to traditional methods such as steepest descent, conjugate gradient, or Newton-Raphson, which are often too complicated to use in solving these problems, EM has become a popular m...

The expectation maximisation (EM) algorithm has proven to be e ective for a range of identi cation problems. Unfortunately, the way in which the EM algorithm has previously been applied has proven unsuitable for the commonly employed innovations form model structure. This paper addresses this problem, and presents a previously unexamined method of EM algorithm employment. The results are pro le...

The EM (expectation-maximization) algorithm is a broadly applicable method for calculating maximum likelihood estimates given incomplete data [1]. EM algorithms have received considerable attention due to their computation feasibility in tomographic image reconstruction [2~4], symbol detection [5] and parameter estimation [6]. However, it is less recognized that EM algorithms can be equally app...