We present Glimmer, a new multilevel visualization algorithm for multidimensional scaling designed to exploit modern graphics processing unit (GPU) hard-ware. We also present GPU-SF, a parallel, force-based subsystem used by Glimmer. Glimmer organizes input into a hierarchy of levels and recursively applies GPU-SF to combine and refine the levels. The multilevel nature of the algorithm helps avoid local minima while the GPU parallelism improves speed of computation. We propose a robust termination condition for GPU-SF based on a filtered approximation of the normalized stress function. We demonstrate the benefits of Glimmer in terms of speed, normalized stress, and visual quality against several previous algorithms for a range of synthetic and real benchmark datasets. We show that the performance of Glimmer on GPUs is substantially faster than a CPU implementation of the same algorithm. We also propose a novel texture paging strategy called distance paging for working with precomputed distance matrices too large to fit in texture memory. / Science, Faculty of / Computer Science, Department of / Graduate

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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