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 a MR image segmentation algorithm based on the conventional Expectation Maximization (EM) algorithm and the multiresolution analysis of images. Although the EM algorithm was used in MRI brain segmentation, as well as, image segmentation in general, it fails to utilize the strong spatial correlation between neighboring pixels. The multiresolution-based image segmentation techniques, w...

The EM algorithm is used for many applications including Boltzmann machine, stochastic Perceptron and HMM. This algorithm gives an iterating procedure for calculating the MLE of stochastic models which have hidden random variables. It is simple, but the convergence is slow. We also have “Fisher’s scoring method”. Its convergence is faster, but the calculation is heavy. We show that by using the...

The expectation-maximization (EM) algorithm aims to nd the maximum of a log-likelihood function, by alternating between conditional expectation (E) step and maximization (M) step. This survey rst introduces the general structure of the EM algorithm and the convergence guarantee. Then Gaussian Mixture Model (GMM) are employed to demonstrate how EM algorithm could be applied under Maximum-Likelih...

The Fisher-EM algorithm has been recently proposed in [4] for the simultaneous visualization and clustering of high-dimensional data. It is based on a latent mixture model which fits the data into a latent discriminative subspace with a low intrinsic dimension. Although the Fisher-EM algorithm is based on the EM algorithm, it does not respect at a first glance all conditions of the EM convergen...

The application of the Bayesian Structural EM algorithm to learn Bayesian networks for clustering implies a search over the space of Bayesian network structures alternating between two steps: an optimization of the Bayesian network parameters (usually by means of the EM algorithm) and a structural search for model selection. In this paper, we propose to perform the optimization of the Bayesian ...

PURPOSE To develop an intensity inhomogeneity algorithm for breast sonograms in order to assist visual identification and automatic delineation of lesion boundaries. METHODS The proposed algorithm was composed of two essential ideas. One was decomposing the region of interest (ROI) into foreground and background regions by a cell-based segmentation algorithm, called constrained fuzzy cell-bas...

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...

Wepropose a new approach to EM learning of PCFGs. We completely separate the process of EM learning from that of parsing, and for the former, we introduce a new EM algorithm called the graphical EM algorithm that runs on a new data structure called support graphs extracted from WFSTs (well formed substring tables) of various parsers. Learning experiments with PCFGs using two Japanese corpora in...

We study unsupervised classification of text documents into a taxonomy of concepts annotated by only a few keywords. Our central claim is that the structure of the taxonomy encapsulates background knowledge that can be exploited to improve classification accuracy. Under our hierarchical Dirichlet generative model for the document corpus, we show that the unsupervised classification algorithm pr...