We provide global convergence guarantees for the expectation-maximization (EM) algorithm applied to mixtures of two Gaussians with known covariance matrices. We show that EM converges geometrically to the correct mean vectors, and provide simple, closed-form expressions for the convergence rate. As a simple illustration, we show that in one dimension ten steps of the EM algorithm initialized at...

Expectation Maximization (EM) [4, 3, 6] is a numerical algorithm for the maximization of functions of several variables. There are several tutorial introductions to EM, including [8, 5, 2, 7]. These are excellent references for greater generality about EM, several good intuitions, and useful explanations. The purpose of this document is to explain in a more self-contained way how EM can solve a...

The current literature on MRI segmentation methods is reviewed. Particular emphasis is placed on the relative merits of single image versus multispectral segmentation, and supervised versus unsupervised segmentation methods. Image preprocessing and registration are discussed, as well as methods of validation. In this paper, we present a new multiresolution algorithm that extends the wellknown E...

background: in this study, quantitative 32p bremsstrahlung planar and spect imaging and consequent dose assessment were carried out as a comprehensive phantom study to define an appropriate method for accurate dosimetry in clinical practice. materials and methods: ct, planar and spect bremsstrahlung images of jaszczak phantom containing a known activity of 32p were acquired. in addition, phanto...

We propose an Expectation-Maximization (EM) algorithm which works on binary decision diagrams (BDDs). The proposed algorithm, BDD-EM algorithm, opens a way to apply BDDs to statistical learning. The BDD-EM algorithm makes it possible to learn probabilities in statistical models described by Boolean formulas, and the time complexity is proportional to the size of BDDs representing them. We apply...

We perform sequence estimation for CPM signals transmitted in a time varying multipath channel. The EM (Expectation-Maximization) algorithm, an iterative proce dure for producing maximum likelihood estimates, is applied to handle the unknown channel. In order to enable implementation of the EM algorithm in this system, a simplification of this algorithm is derived. Channel estimates derived fro...

The Expectation-Maximization (EM) algorithm is a general algorithm for maximum-likelihood estimation where the data are “incomplete” or the likelihood function involves latent variables. Note that the notion of “incomplete data” and “latent variables” are related: when we have a latent variable, we may regard our data as being incomplete since we do not observe values of the latent variables; s...

A new approach for fitting statistical models to time-resolved laser-induced fluorescence spectroscopy (TRLFS) spectra is presented. Such spectra result from counting emitted photons in defined intervals. Any photon can be described by emission time and wavelength as observable attributes and by component and peak affiliation as hidden ones. Understanding the attribute values of the emitted pho...