Expectation–maximization algorithm

About: Expectation–maximization algorithm is a research topic. Over the lifetime, 11823 publications have been published within this topic receiving 528693 citations. The topic is also known as: EM algorithm & Expectation Maximization.

Protein bioinformatics and mixtures of bivariate von Mises distributions for angular data.

Abstract: Summary A fundamental problem in bioinformatics is to characterize the secondary structure of a protein, which has traditionally been carried out by examining a scatterplot (Ramachandran plot) of the conformational angles. We examine two natural bivariate von Mises distributions—referred to as Sine and Cosine models—which have five parameters and, for concentrated data, tend to a bivariate normal distribution. These are analyzed and their main properties derived. Conditions on the parameters are established which result in bimodal behavior for the joint density and the marginal distribution, and we note an interesting situation in which the joint density is bimodal but the marginal distributions are unimodal. We carry out comparisons of the two models, and it is seen that the Cosine model may be preferred. Mixture distributions of the Cosine model are fitted to two representative protein datasets using the expectation maximization algorithm, which results in an objective partition of the scatterplot into a number of components. Our results are consistent with empirical observations; new insights are discussed.

Modeling and incorporation of system response functions in 3-D whole body PET

Abstract: Appropriate application of spatially variant system models can correct for degraded resolution response and mispositioning errors. This paper explores the detector blurring component of the system model for a whole body positron emission tomography (PET) system and extends this factor into a more general system response function to account for other system effects including the influence of Fourier rebinning (FORE). We model the system response function as a three-dimensional (3-D) function that blurs in the radial and axial dimension and is spatially variant in radial location. This function is derived from Monte Carlo simulations and incorporates inter-crystal scatter, crystal penetration, and the blurring due to the FORE algorithm. The improved system model is applied in a modified ordered subsets expectation maximization (OSEM) algorithm to reconstruct images from rebinned, fully 3-D PET data. The proposed method effectively removes the spatial variance in the resolution response, as shown in simulations of point sources. Furthermore, simulation and measured studies show the proposed method improves quantitative accuracy with a reduction in tumor bias compared to conventional OSEM on the order of 10%-30% depending on tumor size and smoothing parameter

Estimating Flight Departure Delay Distributions —A Statistical Approach With Long-term Trend and Short-term Pattern

Abstract: In this article we develop a model for estimating flight departure delay distributions required by air traffic congestion prediction models. We identify and study major factors that influence flight departure delays, and develop a strategic departure delay prediction model. This model employs nonparametric methods for daily and seasonal trends. In addition, the model uses a mixture distribution to estimate the residual errors. To overcome problems with local optima in the mixture distribution, we develop a global optimization version of the expectation–maximization algorithm, borrowing ideas from genetic algorithms. The model demonstrates reasonable goodness of fit, robustness to the choice of the model parameters, and good predictive capabilities. We use flight data from United Airlines and Denver International Airport from the years 2000/2001 to train and validate our model.