International Telemetering Conference Proceedings / October 22-25, 2001 / Riviera Hotel and Convention Center, Las Vegas, Nevada / The expectation-maximization (EM) algorithm is well established as a computationally efficient method for separable signal parameter estimation. Here, a new geometric derivation and interpretation of the EM algorithm is given that facilitates the understanding of its convergence properties. Geometric considerations then lead to an alternative separable signal parameter estimator based on successive cancellation. The new Generalized Successive Interference Cancellation (GSIC) algorithm may offer better performance than EM in the presence of large signal power disparities. Finally, application of the GSIC algorithm to CDMA-based radiolocation is discussed, and simulation results are presented.

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Thesis (Ph. D.)--University of Hong Kong, 2006.

Characterizing the genetic contributors to complex disease traits will inevitably require consideration of haplotypic phase, the specific alignment of alleles on a single homologous chromosome. In population based studies, however, phase is generally unobservable as standard genotyping techniques provide investigators only with data on unphased genotypes. Several statistical methods have been described for estimating haplotype frequencies and their association with a trait in the context of phase ambiguity. These methods are limited, however, to diploid populations in which individuals have exactly two homologous chromosomes each and are thus not suitable for more general infectious disease settings. Specifically, in the context of Malaria and HIV, the number of infections is also unknown. In addition, for both diploid and non-diploid settings, the challenge of high-dimensionality and an unknown model of association remains. Our research includes: (1) extending the expectation-maximization approach of Excoffier and Slatkin to address the challenges of unobservable phase and the unknown numbers of infections; (2) extending the method of Lake et al. to estimate simultaneously both haplotype frequencies and the haplotype-trait associations in the non-diploid settings; and (3) application of two Bayesian approaches to the mixed modeling framework with unobservable cluster (haploype) identifiers, to address the challenges associated with high-dimensional data. Simulation studies are presented as well as applications to data arising from a cohort of children multiply infected with Malaria and a cohort of HIV infected individuals at risk for anti-retroviral associated dyslipidemia. This research is joint work with Drs. S.M. Rich, R.M. Yucel, J. Staudenmayer and A.S. Foulkes.

The expectation-maximization (EM) algorithm is a widely utilized approach to max- imum likelihood estimation in the presence of missing data, this thesis focuses on its application within the model-based clustering framework. The performance of the EM algorithm can be highly dependent on how the algorithm is initialized. Several ways of initializing the EM algorithm have been proposed, however, the best method to use for initialization remains a somewhat controversial topic. From an attempt to obtain a superior method of initializing the EM algorithm, comes the concept of using multiple existing methods together in what will be called a `voting' procedure. This procedure will use several common initialization methods to cluster the data, then a nal starting ^zig matrix will be obtained in two ways. The hard `voting' method follows a majority rule, whereas the soft `voting' method takes an average of the multiple group memberships. The nal ^zig matrix obtained from both methods will dictate the starting values of ^ g; ^ g; and ^ g used to initialize the EM algorithm.

Microarray data clustering represents a basic exploratory tool to find groups of genes exhibiting similar expression patterns or to detect relevant classes of molecular subtypes. Among a wide range of clustering approaches proposed and applied in the gene expression community to analyze microarray data, mixture model-based clustering has received much attention to its sound statistical framework and its flexibility in data modeling. However, clustering algorithms following the model-based framework suffer from two serious drawbacks. The first drawback is that the performance of these algorithms critically depends on the starting values for their iterative clustering procedures. Additionally, they are not capable of working directly with very high dimensional data sets in the sample clustering problem where the dimension of the data is up to hundreds or thousands. The thesis focuses on the two challenges and includes the following contributions: First, the thesis introduces the statistical model of our proposed normalized Expectation Maximization (EM) algorithm followed by its clustering performance analysis on a number of real microarray data sets. The normalized EM is stable even with random initializations for its EM iterative procedure. The stability of the normalized EM is demonstrated through its performance comparison with other related clustering algorithms. Furthermore, the normalized EM is the first mixture model-based clustering approach to be capable of working directly with very high dimensional microarray data sets in the sample clustering problem, where the number of genes is much larger than the number of samples. This advantage of the normalized EM is illustrated through the comparison with the unnormalized EM (The conventional EM algorithm for Gaussian mixture model-based clustering). Besides, for experimental microarray data sets with the availability of class labels of data points, an interesting property of the convergence speed of the normalized EM with respect to the radius of the hypersphere in its corresponding statistical model is uncovered. Second, to support the performance comparison of different clusterings a new internal index is derived using fundamental concepts from information theory. This index allows the comparison of clustering approaches in which the closeness between data points is evaluated by their cosine similarity. The method for deriving this internal index can be utilized to design other new indexes for comparing clustering approaches which employ a common similarity measure.

Thesis (Ph.D.)--McMaster University, 2004. / Supervisor: N. Balakrishnan. Includes bibliographical references (p. 186-191).

Thesis (Ph.D.) -- University of Adelaide, School of Agriculture, Food and Wine, Discipline of Biometrics SA, 2008. / "October 2008" Includes bibliography (p. 283-290) Also available in print form.

Thesis (Ph. D.)--University of Hong Kong, 2006. / Also available in print.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2009. / Title from title screen (site viewed February 25, 2010). PDF text: ii, 93 p. : ill. ; 1 Mb. UMI publication number: AAT 3386580. Includes bibliographical references. Also available in microfilm and microfiche formats.