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PubMed2005

A hybrid genetic algorithm and expectation maximization method for global gene trajectory clustering.

Clustering time-course gene expression data (gene trajectories) is an important step towards solving the complex problem of gene regulatory network modeling and discovery as it significantly reduces the dimensionality of the gene space required for analysis. Traditional clustering methods that perform hill-climbing from randomly initialized cluster centers are prone to produce inconsistent and sub-optimal cluster solutions over different runs. This paper introduces a novel method that hybridizes genetic algorithm (GA) and expectation maximization algorithms (EM) for clustering gene trajectories with the mixtures of multiple linear regression models (MLRs), with the objective of improving the global optimality and consistency of the clustering performance. The proposed method is applied to cluster the human fibroblasts and the yeast time-course gene expression data based on their trajectory similarities. It outperforms the standard EM method significantly in terms of both clustering accuracy and consistency. The biological implications of the improved clustering performance are demonstrated.

Algorithms↗
PubMed2000

Accuracy of haplotype frequency estimation for biallelic loci, via the expectation-maximization algorithm for unphased diploid genotype data.

Haplotype analyses have become increasingly common in genetic studies of human disease because of their ability to identify unique chromosomal segments likely to harbor disease-predisposing genes. The study of haplotypes is also used to investigate many population processes, such as migration and immigration rates, linkage-disequilibrium strength, and the relatedness of populations. Unfortunately, many haplotype-analysis methods require phase information that can be difficult to obtain from samples of nonhaploid species. There are, however, strategies for estimating haplotype frequencies from unphased diploid genotype data collected on a sample of individuals that make use of the expectation-maximization (EM) algorithm to overcome the missing phase information. The accuracy of such strategies, compared with other phase-determination methods, must be assessed before their use can be advocated. In this study, we consider and explore sources of error between EM-derived haplotype frequency estimates and their population parameters, noting that much of this error is due to sampling error, which is inherent in all studies, even when phase can be determined. In light of this, we focus on the additional error between haplotype frequencies within a sample data set and EM-derived haplotype frequency estimates incurred by the estimation procedure. We assess the accuracy of haplotype frequency estimation as a function of a number of factors, including sample size, number of loci studied, allele frequencies, and locus-specific allelic departures from Hardy-Weinberg and linkage equilibrium. We point out the relative impacts of sampling error and estimation error, calling attention to the pronounced accuracy of EM estimates once sampling error has been accounted for. We also suggest that many factors that may influence accuracy can be assessed empirically within a data set-a fact that can be used to create "diagnostics" that a user can turn to for assessing potential inaccuracies in estimation.

Algorithms↗
PubMed1998

Application of distance-dependent resolution compensation and post-reconstruction filtering for myocardial SPECT.

Compensation for distance-dependent resolution can be directly incorporated in maximum likelihood reconstruction. Our objective was to examine the effectiveness of this compensation using either the standard expectation maximization (EM) algorithm or an accelerated algorithm based on use of ordered subsets (OSEM). We also investigated the application of post-reconstruction filtering in combination with resolution compensation. Using the MCAT phantom, projections were simulated for 360 degrees data, including attenuation and distance-dependent resolution. Projection data were reconstructed using conventional EM and OSEM with subset size 2 and 4, with/without 3D compensation for detector response (CDR). Also post-reconstruction filtering (PRF) was performed using a 3D Butterworth filter of order 5 with various cutoff frequencies (0.2-1.2 cycles cm(-1)). Image quality and reconstruction accuracy were improved when CDR was included. Image noise was lower with CDR for a given iteration number. PRF with cutoff frequency greater than 0.6 cycles cm(-1) improved noise with no reduction in recovery coefficient for myocardium but the effect was less when CDR was incorporated in the reconstruction. CDR alone provided better results than use of PRF without CDR. Results suggest that using CDR without PRF, and stopping at a small number of iterations, may provide sufficiently good results for myocardial SPECT. Similar behaviour was demonstrated for OSEM.

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PubMed1999

Local EM estimation of the hazard function for interval-censored data.

We propose a smooth hazard estimator for interval-censored survival data using the method of local likelihood. The model is fit using a local EM algorithm. The estimator is more descriptive than traditional empirical estimates in regions of concentrated information and takes on a parametric flavor in regions of sparse information. We derive two different standard error estimates for the smooth curve, one based on asymptotic theory and the other on the bootstrap. We illustrate the local EM method for times to breast cosmesis deterioration (Finkelstein, 1986, Biometrics 42, 845-854) and for times to HIV-1 infection for individuals with hemophilia (Kroner et al., 1994, Journal of AIDS 7, 279-286). Our hazard estimates for each of these data sets show interesting structures that would not be found using a standard parametric hazard model or empirical survivorship estimates.

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PubMed2002

An expectation-maximisation algorithm for the deconvolution of the intrinsic distribution of single molecule's parameters.

Values obtained from single molecule techniques exhibit distinct distributions comprising an uncertainty due to random noise convoluted with the intrinsic distribution of the molecule's properties. In the fields of single molecule light microscopy and spectroscopy, force microscopy and spectroscopy as well as other techniques like electrophysiology, sophisticated data analysis algorithms are available which extract the interesting parameters and their uncertainties from the noisy data set. The intrinsic distributions of these parameters contain valuable information about the molecules' physical and chemical properties, that need to be deconvoluted from the data. Here, we present an expectation-maximisation (EM-) algorithm that estimates the intrinsic distribution in single molecule experiments. The performance is tested by using computer simulations and the application of the method is demonstrated for data from single molecule force spectroscopy.

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PubMed2006

SNiPer-HD: improved genotype calling accuracy by an expectation-maximization algorithm for high-density SNP arrays.

MOTIVATION: The technology to genotype single nucleotide polymorphisms (SNPs) at extremely high densities provides for hypothesis-free genome-wide scans for common polymorphisms associated with complex disease. However, we find that some errors introduced by commonly employed genotyping algorithms may lead to inflation of false associations between markers and phenotype. RESULTS: We have developed a novel SNP genotype calling program, SNiPer-High Density (SNiPer-HD), for highly accurate genotype calling across hundreds of thousands of SNPs. The program employs an expectation-maximization (EM) algorithm with parameters based on a training sample set. The algorithm choice allows for highly accurate genotyping for most SNPs. Also, we introduce a quality control metric for each assayed SNP, such that poor-behaving SNPs can be filtered using a metric correlating to genotype class separation in the calling algorithm. SNiPer-HD is superior to the standard dynamic modeling algorithm and is complementary and non-redundant to other algorithms, such as BRLMM. Implementing multiple algorithms together may provide highly accurate genotyping calls, without inflation of false positives due to systematically miss-called SNPs. A reliable and accurate set of SNP genotypes for increasingly dense panels will eliminate some false association signals and false negative signals, allowing for rapid identification of disease susceptibility loci for complex traits. AVAILABILITY: SNiPer-HD is available at TGen's website: http://www.tgen.org/neurogenomics/data.

Algorithms↗
PubMed2005

Fine mapping functional sites or regions from case-control data using haplotypes of multiple linked SNPs.

Previously, we reported an algorithm for scanning a large number of tightly linked single nucleotide polymorphisms (SNPs) for LD mapping of functional sites or regions from a family-based association design. In the present study, we extend our method to a case-control design. We first use the expectation maximization (EM) algorithm to estimate haplotype frequencies of multiple linked SNPs, and follow this by constructing a contingency table statistic S for LD analysis, based on the estimated haplotype frequencies. An empirical p-value is obtained based on the null distribution of the maximum of S (S*) from a large number (e.g., 1,000 or more) of randomized permutations. The proposed algorithm has been implemented in a computer program in which window searching for functional SNP sites can cover any number of loci without limitation, except that of computer storage. Unlike other programs for a case-control design that always conduct tests at a fix window width, in our program after setting a maximum size of haplotype window width, for a given maximum window width all possible widths of haplotypes are utilized to find the maximum statistic S * for each locus under investigation. The sensitivity of the proposed algorithm has been examined with simulated and real genotyping datasets. Association analyses indicate that our program is powerful enough to detect most, if not all, functional SNPs simulated in the original model or identified in the original report. Moreover, the program is very flexible and can be used in either regional or genome-wide scanning for association analysis with SNP markers.

Algorithms↗
PubMed2005

Haplotype reconstruction for diploid populations.

The inference of haplotype pairs directly from unphased genotype data is a key step in the analysis of genetic variation in relation to disease and pharmacogenetically relevant traits. Most popular methods such as Phase and PL do require either the coalescence assumption or the assumption of linkage between the single-nucleotide polymorphisms (SNPs). We have now developed novel approaches that are independent of these assumptions. First, we introduce a new optimization criterion in combination with a block-wise evolutionary Monte Carlo algorithm. Based on this criterion, the 'haplotype likelihood', we develop two kinds of estimators, the maximum haplotype-likelihood (MHL) estimator and its empirical Bayesian (EB) version. Using both real and simulated data sets, we demonstrate that our proposed estimators allow substantial improvements over both the expectation-maximization (EM) algorithm and Clark's procedure in terms of capacity/scalability and error rate. Thus, hundreds and more ambiguous loci and potentially very large sample sizes can be processed. Moreover, applying our proposed EB estimator can result in significant reductions of error rate in the case of unlinked or only weakly linked SNPs.

Algorithms↗
PubMedDate not supplied

Time series for modelling counts from a relapsing-remitting disease: application to modelling disease activity in multiple sclerosis.

Many chronic diseases are relapsing-remitting diseases, in which subjects alternate between periods with increasing and decreasing disease activity; relapsing-remitting multiple sclerosis is an example. This paper proposes two classes of models for sequences of counts observed from a relapsing-remitting disease. In the first, the relapsing-remitting nature of the data is modelled by a Poisson time series with a periodic trend in the mean. In this approach, the mean is expressed as a function of a sinusoidal trend and past observations of the time series. An algorithm that uses GLIM is developed, and it results in maximum-likelihood estimation for the amplitude, frequency and autoregressive effects. In the second class of models, the relapsing-remitting behaviour is described by a Poisson time series in which changes in the mean follow a latent Markov chain. An EM algorithm is developed for maximum-likelihood estimation for this model. The two models are illustrated and compared with data from a study evaluating the use of serial magnetic resonance imaging as a measure of disease activity in relapsing-remitting multiple sclerosis.

Algorithms↗
PubMed2003

Finding subtle motifs by branching from sample strings.

UNLABELLED: Many motif finding algorithms apply local search techniques to a set of seeds. For example, GibbsDNA (Lawrence et al. 1993, Science, 262, 208-214) applies Gibbs sampling to random seeds, and MEME (Bailey and Elkan, 1994, Proceedings of the Second International Conference on Intelligent Systems for Molecular Biology (ISMB-94), 28-36) applies the EM algorithm to selected sample strings, i.e. substrings of the sample. In the case of subtle motifs, recent benchmarking efforts show that both random seeds and selected sample strings may never get close to the globally optimal motif. We propose a new approach which searches motif space by branching from sample strings, and implement this idea in both pattern-based and profile-based settings. Our PatternBranching and ProfileBranching algorithms achieve favorable results relative to other motif finding algorithms. AVAILABILITY: http://www-cse.ucsd.edu/groups/bioinformatics/software.html

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PubMed2003

Expectation maximization strategies for multi-atlas multi-label segmentation.

It is well-known in the pattern recognition community that the accuracy of classifications obtained by combining decisions made by independent classifiers can be substantially higher that the accuracy of the individual classifiers. In order to combine multiple segmentations we introduce two extensions to an expectation maximization (EM) algorithm for ground truth estimation based on multiple experts (Warfield et al., MICCAI 2002). The first method repeatedly applies the Warfield algorithm with a subsequent integration step. The second method is a multi-label extension of the Warfield algorithm. Both extensions integrate multiple segmentations into one that is closer to the unknown ground truth than the individual segmentations. In atlas-based image segmentation, multiple classifiers arise naturally by applying different registration methods to the same atlas, or the same registration method to different atlases, or both. We perform a validation study designed to quantify the success of classifier combination methods in atlas-based segmentation. By applying random deformations, a given ground truth atlas is transformed into multiple segmentations that could result from imperfect registrations of an image to multiple atlas images. We demonstrate that a segmentation produced by combining multiple individual registration-based segmentations is more accurate for the two EM methods we propose than for simple label averaging.

Algorithms↗
PubMed2002

Efficient algorithms for quantitative trait loci mapping problems.

Rapid advances in molecular genetics push the need for efficient data analysis. Advanced algorithms are necessary for extracting all possible information from large experimental data sets. We present a general linear algebra framework for quantitative trait loci (QTL) mapping, using both linear regression and maximum likelihood estimation. The formulation simplifies future comparisons between and theoretical analyses of the methods. We show how the common structure of QTL analysis models can be used to improve the kernel algorithms, drastically reducing the computational effort while retaining the original analysis results. We have evaluated our new algorithms on data sets originating from two large F(2) populations of domestic animals. Using an updating approach, we show that 1-3 orders of magnitude reduction in computational demand can be achieved for matrix factorizations. For interval-mapping/composite-interval-mapping settings using a maximum likelihood model, we also show how to use the original EM algorithm instead of the ECM approximation, significantly improving the convergence and further reducing the computational time. The algorithmic improvements makes it feasible to perform analyses which have previously been deemed impractical or even impossible. For example, using the new algorithms, it is reasonable to perform permutation testing using exhaustive search on populations of 200 individuals using an epistatic two-QTL model.

Algorithms↗
PubMed1994

Accelerated EM reconstruction in total-body PET: potential for improving tumour detectability.

Total-body positron emission tomography (PET) is a useful diagnostic tool for evaluating malignant disease. However, tumour detection is limited by image artefacts due to the lack of attenuation correction and noise. Attenuation correction may be possible using transmission data acquired after or simultaneously with emission data. Despite the elimination of attenuation artefacts, however, tumour detection is still hampered by noise, which is amplified during image reconstruction by filtered backprojection (FBP). We have investigated, as an alternative to FBP, an accelerated expectation maximization (EM) algorithm for its potential to improve tumour detectability in total-body PET. Signal to noise ratio (SNR), calculated for a tumour with respect to the surrounding background, is used as a figure of merit. A software tumour phantom, with conditions typical of those encountered in a total-body PET study using simultaneous acquisition, is used to optimize and compare various reconstruction approaches. Accelerated EM reconstruction followed by two-dimensional filtering is shown to yield significantly higher SNR than FBP for a range of tumour sizes, concentrations and counting statistics (deltaSNR = 6.3 +/- 3.9, p < 0.001). The methods developed are illustrated by examples derived from physical phantom and patient data.

Algorithms↗
PubMed2002

Improved estimators for fractional Brownian motion via the expectation-maximization algorithm.

Fractional Brownian motion (FBM) provides a useful model for many physical and biological phenomena demonstrating long-term dependencies and 1/f-type spectral behavior. In this model, only one parameter is necessary to describe the complexity of the data, the Hurst exponent (H). The development of accurate estimators for H is a topic of interest in areas such as radiographic image processing and heart rate variability (HRV) analysis. The development of a 1D estimator utilizing the Expectation-Maximization (EM) algorithm is explained; the estimator is designed for a signal model consisting of FBM and additive white noise. The performance of this estimator is tested on simulated noisy FBM data sets, and found to provide more accurate estimates of H than a maximum likelihood estimator for FBM and the detrended fluctuation analysis (DFA) method.

Algorithms↗
PubMed2006

Reconstruction of 2D PET data with Monte Carlo generated system matrix for generalized natural pixels.

In discrete detector PET, natural pixels are image basis functions calculated from the response of detector pairs. By using reconstruction with natural pixel basis functions, the discretization of the object into a predefined grid can be avoided. Here, we propose to use generalized natural pixel reconstruction. Using this approach, the basis functions are not the detector sensitivity functions as in the natural pixel case but uniform parallel strips. The backprojection of the strip coefficients results in the reconstructed image. This paper proposes an easy and efficient way to generate the matrix M directly by Monte Carlo simulation. Elements of the generalized natural pixel system matrix are formed by calculating the intersection of a parallel strip with the detector sensitivity function. These generalized natural pixels are easier to use than conventional natural pixels because the final step from solution to a square pixel representation is done by simple backprojection. Due to rotational symmetry in the PET scanner, the matrix M is block circulant and only the first blockrow needs to be stored. Data were generated using a fast Monte Carlo simulator using ray tracing. The proposed method was compared to a listmode MLEM algorithm, which used ray tracing for doing forward and backprojection. Comparison of the algorithms with different phantoms showed that an improved resolution can be obtained using generalized natural pixel reconstruction with accurate system modelling. In addition, it was noted that for the same resolution a lower noise level is present in this reconstruction. A numerical observer study showed the proposed method exhibited increased performance as compared to a standard listmode EM algorithm. In another study, more realistic data were generated using the GATE Monte Carlo simulator. For these data, a more uniform contrast recovery and a better contrast-to-noise performance were observed. It was observed that major improvements in contrast recovery were obtained with MLEM when the correct system matrix was used instead of simple ray tracing. The correct modelling was the major cause of improved contrast for the same background noise. Less important factors were the choice of the algorithm (MLEM performed better than ART) and the basis functions (generalized natural pixels gave better results than pixels).

Algorithms↗
PubMedDate not supplied

Probabilistic linkage of large public health data files.

Probabilistic linkage technology makes it feasible and efficient to link large public health databases in a statistically justifiable manner. The problem addressed by the methodology is that of matching two files of individual data under conditions of uncertainty. Each field is subject to error which is measured by the probability that the field agrees given a record pair matches (called the m probability) and probabilities of chance agreement of its value states (called the u probability). Fellegi and Sunter pioneered record linkage theory. Advances in methodology include use of an EM algorithm for parameter estimation, optimization of matches by means of a linear sum assignment program, and more recently, a probability model that addresses both m and u probabilities for all value states of a field. This provides a means for obtaining greater precision from non-uniformly distributed fields, without the theoretical complications arising from frequency-based matching alone. The model includes an iterative parameter estimation procedure that is more robust than pre-match estimation techniques. The methodology was originally developed and tested by the author at the U.S. Census Bureau for census undercount estimation. The more recent advances and a new generalized software system were tested and validated by linking highway crashes to Emergency Medical Service (EMS) reports and to hospital admission records for the National Highway Traffic Safety Administration (NHTSA).

Adult↗
PubMed2006

Joint estimation of dynamic PET images and temporal basis functions using fully 4D ML-EM.

A fully 4D joint-estimation approach to reconstruction of temporal sequences of 3D positron emission tomography (PET) images is proposed. The method estimates both a set of temporal basis functions and the corresponding coefficient for each basis function at each spatial location within the image. The joint estimation is performed through a fully 4D version of the maximum likelihood expectation maximization (ML-EM) algorithm in conjunction with two different models of the mean of the Poisson measured data. The first model regards the coefficients of the temporal basis functions as the unknown parameters to be estimated and the second model regards the temporal basis functions themselves as the unknown parameters. The fully 4D methodology is compared to the conventional frame-by-frame independent reconstruction approach (3D ML-EM) for varying levels of both spatial and temporal post-reconstruction smoothing. It is found that using a set of temporally extensive basis functions (estimated from the data by 4D ML-EM) significantly reduces the spatial noise when compared to the independent method for a given level of image resolution. In addition to spatial image quality advantages, for smaller regions of interest (where statistical quality is often limited) the reconstructed time-activity curves show a lower level of bias and a lower level of noise compared to the independent reconstruction approach. Finally, the method is demonstrated on clinical 4D PET data.

Algorithms↗
PubMed2006

Context-based segmentation of image sequences.

We describe an algorithm for context-based segmentation of visual data. New frames in an image sequence (video) are segmented based on the prior segmentation of earlier frames in the sequence. The segmentation is performed by adapting a probabilistic model learned on previous frames, according to the content of the new frame. We utilize the maximum a posteriori version of the EM algorithm to segment the new image. The Gaussian mixture distribution that is used to model the current frame is transformed into a conjugate-prior distribution for the parametric model describing the segmentation of the new frame. This semisupervised method improves the segmentation quality and consistency and enables a propagation of segments along the segmented images. The performance of the proposed approach is illustrated on both simulated and real image data.

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