Thesis (Ph. D. in Mathematics)--Vanderbilt University, Aug. 2006. / Title from title screen. Includes bibliographical references.

Thesis (MSc)--University of Stellenbosch, 2002. / ENGLISH ABSTRACT: In this thesis, we present a technique for the automatic detection of image orientation using Support Vector Machines (SVMs). SVMs are able to handle feature spaces of high dimension and automatically choose the most discriminative features for classification. We investigate the use of various kernels, including heavy tailed RBF kernels. We compare the classification performance of SVMs with the performance of multilayer perceptrons and a Bayesian classifier. Our results show that SVMs out perform both of these methods in the classification of individual images. We also implement an application for the classification of film rolls in a photographic workflow environment with 100% classification accuracy. / AFRIKAANSE OPSOMMING: In hierdie tesis, gebruik ons 'n tegniek vir die automatiese klassifisering van beeldoriëntasie deur middel van Support Vector Machines (SVM's). SVM's kan kenmerkruimtes van 'n hoë dimensie hanteer en kan automaties die mees belangrike kenmerke vir klassifikasie kies. Ons vors die gebruik van verskeie kerne, insluitende RBF-kerne, na. Ons vergelyk die klassifiseringsresultate van SVM's met die van multilaagperseptrone en 'n Bayes-klassifiseerder. Ons bewys dat SVM's beter resultate gee as beide van hierdie metodes vir die klassifikasie van individuele beelde. Ons implementeer ook a toepassing vir die klassifisering van rolle film in a fotografiese werkvloei-omgewing met 100% klassifikasie akuraatheid.

A presente dissertação propõe novas abordagens para seleção de variáveis com vistas à formação de grupos representativos de observações. Para tanto, sugere um novo índice de importância das variáveis apoiado nos parâmetros oriundos da Análise de Componentes Principais (APC), o qual é integrado a uma sistemática do tipo forward para seleção de variáveis. A qualidade dos agrupamentos formados é medida através do Silhouette Index. Um estudo de simulação é projetado para avaliar a robustez e o desempenho da sistemática proposta em dados com diferentes níveis de correlação, ruído e número de observações a serem clusterizadas. Na sequência, é apresentada uma versão modificada da sistemática original, a qual utiliza funções kernel para remapeamento dos dados com vistas ao incremento da qualidade de clusterização e redução das variáveis retidas para formação dos agrupamentos. A versão modificada é aplicada em 3 bancos de dados da indústria química, aumentando a qualidade da clusterização medida pelo SI médio em 150% e utilizando em torno de 6% das variáveis originais. / This thesis proposes new approaches for variable selection aimed at forming representative groups of observations. For that matter, we suggest a new variable importance index based on parameters derived from the Principal Component Analysis (PCA), which is integrated to a forward procedure for variable selection. The quality of clustering procedure is assessed by the Silhouette Index. A simulation study is designed to evaluate the robustness of the proposed method on different levels of variable correlation, noise and number of observations to be clustered. Next, we modify the original method by remapping observations through kernel functions tailored to improving the clustering quality and reducing the retained variables. The modified version is applied to 3 databases related to chemical processes, increasing the quality of clustering measured by SI on average 150%, while using around 6% of the original variables.

A presente dissertação propõe novas abordagens para seleção de variáveis com vistas à formação de grupos representativos de observações. Para tanto, sugere um novo índice de importância das variáveis apoiado nos parâmetros oriundos da Análise de Componentes Principais (APC), o qual é integrado a uma sistemática do tipo forward para seleção de variáveis. A qualidade dos agrupamentos formados é medida através do Silhouette Index. Um estudo de simulação é projetado para avaliar a robustez e o desempenho da sistemática proposta em dados com diferentes níveis de correlação, ruído e número de observações a serem clusterizadas. Na sequência, é apresentada uma versão modificada da sistemática original, a qual utiliza funções kernel para remapeamento dos dados com vistas ao incremento da qualidade de clusterização e redução das variáveis retidas para formação dos agrupamentos. A versão modificada é aplicada em 3 bancos de dados da indústria química, aumentando a qualidade da clusterização medida pelo SI médio em 150% e utilizando em torno de 6% das variáveis originais. / This thesis proposes new approaches for variable selection aimed at forming representative groups of observations. For that matter, we suggest a new variable importance index based on parameters derived from the Principal Component Analysis (PCA), which is integrated to a forward procedure for variable selection. The quality of clustering procedure is assessed by the Silhouette Index. A simulation study is designed to evaluate the robustness of the proposed method on different levels of variable correlation, noise and number of observations to be clustered. Next, we modify the original method by remapping observations through kernel functions tailored to improving the clustering quality and reducing the retained variables. The modified version is applied to 3 databases related to chemical processes, increasing the quality of clustering measured by SI on average 150%, while using around 6% of the original variables.

A presente dissertação propõe novas abordagens para seleção de variáveis com vistas à formação de grupos representativos de observações. Para tanto, sugere um novo índice de importância das variáveis apoiado nos parâmetros oriundos da Análise de Componentes Principais (APC), o qual é integrado a uma sistemática do tipo forward para seleção de variáveis. A qualidade dos agrupamentos formados é medida através do Silhouette Index. Um estudo de simulação é projetado para avaliar a robustez e o desempenho da sistemática proposta em dados com diferentes níveis de correlação, ruído e número de observações a serem clusterizadas. Na sequência, é apresentada uma versão modificada da sistemática original, a qual utiliza funções kernel para remapeamento dos dados com vistas ao incremento da qualidade de clusterização e redução das variáveis retidas para formação dos agrupamentos. A versão modificada é aplicada em 3 bancos de dados da indústria química, aumentando a qualidade da clusterização medida pelo SI médio em 150% e utilizando em torno de 6% das variáveis originais. / This thesis proposes new approaches for variable selection aimed at forming representative groups of observations. For that matter, we suggest a new variable importance index based on parameters derived from the Principal Component Analysis (PCA), which is integrated to a forward procedure for variable selection. The quality of clustering procedure is assessed by the Silhouette Index. A simulation study is designed to evaluate the robustness of the proposed method on different levels of variable correlation, noise and number of observations to be clustered. Next, we modify the original method by remapping observations through kernel functions tailored to improving the clustering quality and reducing the retained variables. The modified version is applied to 3 databases related to chemical processes, increasing the quality of clustering measured by SI on average 150%, while using around 6% of the original variables.

Yes / Metamodelling or surrogate modelling techniques are frequently used across the engineering disciplines in conjunction with expensive simulation models or physical experiments. With the proliferation of metamodeling techniques developed to provide enhanced performance for specific problems, and the wide availability of a diverse choice of tools in engineering software packages, the engineering task of selecting a robust metamodeling technique for practical problems is still a challenge. This research introduces a framework for describing the typology of engineering problems, in terms of dimensionality and complexity, and the modelling conditions, reflecting the noisiness of the signals and the affordability of sample sizes, and on this basis presents a systematic evaluation of the performance of frequently used metamodeling techniques. A set of metamodeling techniques, selected based on their reported use for engineering problems (i.e. Polynomial, Radial Basis Function, and Kriging), were systematically evaluated in terms of accuracy and robustness against a carefully assembled set of 18 test functions covering different types of problems, sampling conditions and noise conditions. A set of four real-world engineering case studies covering both computer simulation and physical experiments were also analysed as validation tests for the proposed guidelines. The main conclusions drawn from the study are that Kriging model with Matérn 5/2 correlation function performs consistently well across different problem types with smooth (i.e. not noisy) data, while Kriging model with Matérn 3/2 correlation function provides robust performance under noisy conditions, except for the very high noise conditions, where the Kriging model with nugget appears to provide better models. These results provide engineering practitioners with a guide for the choice of a metamodeling technique for problem types and modelling conditions represented in the study, whereas the evaluation framework and benchmarking problems set will be useful for researchers conducting similar studies.

This thesis aims to contribute to the area of kernel methods, which are a class of machine learning methods known for their wide applicability and state-of-the-art performance, but which suffer from high training and evaluation complexity. The work in this thesis utilizes the notion of reduced-set models to alleviate the training and testing complexities of these methods in a unified manner. In the first part of the thesis, we use recent results in kernel smoothing and integral-operator learning to design a generic strategy to speed up various kernel methods. In Chapter 3, we present a method to speed up kernel PCA (KPCA), which is one of the fundamental kernel methods for manifold learning, by using reduced-set density estimates (RSDE) of the data. The proposed method induces an integral operator that is an approximation of the ideal integral operator associated to KPCA. It is shown that the error between the ideal and approximate integral operators is related to the error between the ideal and approximate kernel density estimates of the data. In Chapter 4, we derive similar approximation algorithms for Gaussian process regression, diffusion maps, and kernel embeddings of conditional distributions. In the second part of the thesis, we use reduced-set models for kernel methods to tackle online learning in model-reference adaptive control (MRAC). In Chapter 5, we relate the properties of the feature spaces induced by Mercer kernels to make a connection between persistency-of-excitation and the budgeted placement of kernels to minimize tracking and modeling error. In Chapter 6, we use a Gaussian process (GP) formulation of the modeling error to accommodate a larger class of errors, and design a reduced-set algorithm to learn a GP model of the modeling error. Proofs of stability for all the algorithms are presented, and simulation results on a challenging control problem validate the methods.

Worldwide computer systems continue to execute malicious software that degrades the systemsâ performance and consumes network capacity by generating high volumes of unwanted traffic. Network-based detectors can effectively identify machines participating in the ongoing attacks by monitoring the traffic to and from the systems. But, network detection alone is not enough; it does not improve the operation of the Internet or the health of other machines connected to the network. We must identify malicious code running on infected systems, participating in global attack networks. This dissertation describes a robust and secure approach that identifies malware present on infected systems based on its undesirable use of network. Our approach, using virtualization, attributes malicious traffic to host-level processes responsible for the traffic. The attribution identifies on-host processes, but malware instances often exhibit parasitic behaviors to subvert the execution of benign processes. We then augment the attribution software with a host-level monitor that detects parasitic behaviors occurring at the user- and kernel-level. User-level parasitic attack detection happens via the system-call interface because it is a non-bypassable interface for user-level processes. Due to the unavailability of one such interface inside the kernel for drivers, we create a new driver monitoring interface inside the kernel to detect parasitic attacks occurring through this interface. Our attribution software relies on a guest kernelâ s data to identify on-host processes. To allow secure attribution, we prevent illegal modifications of critical kernel data from kernel-level malware. Together, our contributions produce a unified research outcome --an improved malicious code identification system for user- and kernel-level malware.

This paper demonstrates the properties of a Hilbert structure. In order to have a Hilbert structure it is necessary to satisfy certain properties or axioms. The main body of the paper is centered on six questions that develop these ideas.

This Doctoral thesis gives an introduction to the concept of kernel functionsand their signicance in the theory of special functions. Of particularinterest is the use of kernel function methods for constructing exact solutionsof Schrodinger type equations, in one spatial dimension, with interactions governedby elliptic functions. The method is applicable to a large class of exactlysolvable systems of Calogero-Moser-Sutherland type, as well as integrable generalizationsthereof. It is known that the Schrodinger operators with ellipticpotentials have special limiting cases with exact eigenfunctions given by orthogonalpolynomials. These special cases are discussed in greater detail inorder to explain the kernel function methods with particular focus on the Jacobipolynomials and Jack polynomials. / <p>QC 20161003</p>