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...

P(X|θ) is the (observable) data likelihood. The parameter θ is omitted sometimes for simple notation. MLE is normally done by taking the derivative of the data likelihood P(X) with respect to the model parameter θ and solving the equation. However, in some cases where we have hidden (unobserved) variables in the model, the derivative w.r.t. the model parameter does not have a close form solutio...

texture image analysis is one of the most important working realms of image processing in medical sciences and industry. up to present, different approaches have been proposed for segmentation of texture images. in this paper, we offered unsupervised texture image segmentation based on markov random field (mrf) model. first, we used gabor filter with different parameters’ (frequency, orientatio...

In a previous class, we discussed an algorithm for learning a probabilistic matrix model which describes a fixed-length motif in a set of sequences S : : : S over an alphabet A. This algorithm is one of a class of methods collectively known as expectation maximization, or EM. We will describe the general EM algorithm, then derive the motif-finding algorithm by applying EM to learn a specific pr...

SUMMARY The Expectation-Maximization (EM) algorithm is a powerful computational technique for locating maxima of functions. It is widely used in statistics for maximum likelihood or maximum a posteriori estimation in incomplete data models. In certain situations however, this method is not applicable because the expectation step cannot be performed in closed{form. To deal with these problems, a...

In this paper we present a new algorithm for seg-mentation of noisy or textured images using the expectation -maximization (EM) algorithm for estimating parameters of the probability mass function of the pixel class labels and the maximization of the posterior marginals (MPM) criterion for the segmentation operation. A Markov random eld (MRF) model is used for the pixel class labels. We present...

This paper introduces variational expectation-maximization (VEM) algorithm for training Gaussian networks. Hyperparameters model distributions of parameters characterizing Gaussian mixture densities. The proposed algorithm employs a hierarchical learning strategy for estimating a set of hyperparameters and the number of Gaussian mixture components. A dual EM algorithm is employed as the initial...

The Expectation-Maximization (EM) algorithm is an iterative optimization technique that seeks to find the maximum likelihood parameter estimates in problems where some of the data is missing or hidden, or in problems that can be posed in a similar form, such as mixture model parameter estimation. The EM algorithm can be viewed in many different ways, one of the most insightful being in terms of...

We consider the design of iterative multiuser detectors based on the Expectation-Maximization (EM) algorithm and Parallel Interference Cancellation (PIC) for spacetime block coded (STBC) WCDMA employing 16-QAM in multipath fading channels. We show that the EM-based and PIC receivers improve the receiver performance particularly when two receive antennas are employed. We see that EM receiver sho...

A new approach for signal parametrization, which consists of a specific regression model incorporating a discrete hidden logistic process, is proposed. The model parameters are estimated by the maximum likelihood method performed by a dedicated Expectation Maximization (EM) algorithm. The parameters of the hidden logistic process, in the inner loop of the EM algorithm, are estimated using a mul...