Cluster analysis is used to detect underlying group structure in data. Model-based clustering is the process of performing cluster analysis which involves the fitting of finite mixture models. However, parameter estimation in mixture model-based approaches to clustering is notoriously difficult. To this end, this thesis focuses on the development of evolutionary computation as an alternative technique for parameter estimation in mixture models. An evolutionary algorithm is proposed and illustrated on the well-established Gaussian mixture model with missing values. Next, the family of Gaussian parsimonious clustering models is considered, and an evolutionary algorithm is developed to estimate the parameters. Next, an evolutionary algorithm is developed for latent Gaussian mixture models and to facilitate the flexible clustering of high-dimensional data. For all models and families of models considered in this thesis, the proposed algorithms used for model-fitting and parameter estimation are presented and the performance illustrated using real and simulated data sets to assess the clustering ability of all models. This thesis concludes with a discussion and suggestions for future work. / Dissertation / Doctor of Philosophy (PhD)

在計算矩陣的特徵值(eigenvalues)中,QR演算法是一種常見的技巧. 尤其如果使用適當的移位,將可以較快得到特徵值. 在本文中提出一種新的移位策略, 我們證明這各方法是可行的,而且可適用於任何矩陣. 換句說, 本篇論文主旨即是提出有關新的移位QR演算法的收斂. / The QR algorithm is a popular method for computing all the eigenvalues of a dense matrix. If we use a proper shift, we can accelerate convergence of the iterative process. Hence, we design a new shift strategy which includes an eigenvalue of the trailing principal 3-by-3 submatrix of the tridiagonal matrix. We prove the global convergence of the new strategy. In other words, the purpose of this thesis is to propose a theory of the convergence of a new shifted QR algorithm.

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This thesis investigates extending the dynamically-typed, functional programming language Scheme, with simulated overloading in order to permit the binding of multiple, distributed defnitions to function names. Overloading facilitates the use of an incremental style of programming in which functions can be defined with a base behaviour and then extended with additional behaviour as it becomes necessary to support new data types. A technique is demonstrated that allows existing functions to be extended, without modifcation, therefore improving code reuse. Using the primitives provided by Scheme, it is possible to write functions that perform like the generic routines (functions) of the programming language EL1. These functions use the type of their arguments to determine, at run-time, the computation to perform. It is shown that by gathering the definitions for an overloaded function and building a generic routine, the language appears to provide overloading. A language extension that adds the syntax necessary to instruct the system to gather the distributed set of definitions for an overloaded function and incrementally build an equivalently applicable generic function is described. A simple type inference algorithm, necessary to support the construction of generic functions, is presented and detailed. Type inference is required to determine the domain of an overloaded function in order to generate the code needed to perform run-time overload resolution. Some limitations and possible extensions of the algorithm are discussed.