The paper gives a brief review of the expectation-maximization algorithm (Dempster, Laird, and Rubin 1977) in the comprehensible framework of discrete mathematics. In Section 2, two prominent estimation methods, the relative-frequency estimation and the maximum-likelihood estimation are presented. Section 3 is dedicated to the expectation-maximization algorithm and a simpler variant, the genera...

Factor graphs allow large probability distributions to be stored efficiently and facilitate fast computation of marginal probabilities, but the difficulty of training them has limited their use. Given a large set of data points, the training process should yield factors for which the observed data has a high likelihood. We present a factor graph learning algorithm which on each iteration merges...

This paper explores the problem of feature subset selection for unsupervised learning within the wrapper framework. In particular, we examine feature subset selection wrapped around expectation-maximization (EM) clustering with order identiication (identifying the number of clusters in the data). We investigate two diierent performance criteria for evaluating candidate feature subsets: scatter ...

We discuss the evaluation of subsets of variables for the discriminative evidence they provide in multivariate mixture modeling for classification. Novel development of Bayesian classification analysis uses a natural measure of concordance between mixture component densities, and defines an effective and computationally feasible method for assessing and prioritizing subsets of variables accordi...

The famous Expectation Maximization technique suffers two major drawbacks. First, the number of components has to be specified apriori. Also, the Expectation Maximization is sensitive to initialization. In this paper, we present a new stochastic technique for estimating the mixture parameters. Parzen Window is used to estimate a discrete estimate of the PDF of the given data. Stochastic Learnin...

The expectation maximization (EM) algorithm computes maximum likelihood estimates of unknown parameters in probabilistic models involving latent variables. More pragmatically speaking, the EM algorithm is an iterative method that alternates between computing a conditional expectation and solving a maximization problem, hence the name expectation maximization. We will in this work derive the EM ...

We present the CEM (Conditional Expectation Maximization) algorithm as an extension of the EM (Expectation Maximization) algorithm to conditional density estimation under missing data. A bounding and maximization process is given to speciically optimize conditional likelihood instead of the usual joint likelihood. We apply the method to conditioned mixture models and use bounding techniques to ...

Fishburn, P.C. and W.T. Trotter, Linear extensions of semiorders: A maximization problem, Discrete Mathematics 103 (1992) 25-40. We consider the problem of determining which partially ordered sets on n points with k pairs in their ordering relations have the greatest number of linear extensions. The posets that maximize the number of linear extensions for each hxed (n, k), 0 G k G (;), are semi...

objective(s): the aim of this study was to determine the optimal reconstruction parameters for iterative reconstruction in different devices and collimators for dopamine transporter (dat) single-photon emission computed tomography (spect). the results were compared between filtered back projection (fbp) and different attenuation correction (ac) methods.methods: an anthropomorphic striatal phant...