Call number: LD2668 .T4 1984 S335 / Master of Music / Music, Theatre, and Dance

Thesis (PhD (Statistics and Actuarial Science))—University of Stellenbosch, 2008. / The problem of variable selection in binary kernel classification is addressed in this thesis. Kernel methods are fairly recent additions to the statistical toolbox, having originated approximately two decades ago in machine learning and artificial intelligence. These methods are growing in popularity and are already frequently applied in regression and classification problems. Variable selection is an important step in many statistical applications. Thereby a better understanding of the problem being investigated is achieved, and subsequent analyses of the data frequently yield more accurate results if irrelevant variables have been eliminated. It is therefore obviously important to investigate aspects of variable selection for kernel methods. Chapter 2 of the thesis is an introduction to the main part presented in Chapters 3 to 6. In Chapter 2 some general background material on kernel methods is firstly provided, along with an introduction to variable selection. Empirical evidence is presented substantiating the claim that variable selection is a worthwhile enterprise in kernel classification problems. Several aspects which complicate variable selection in kernel methods are discussed. An important property of kernel methods is that the original data are effectively transformed before a classification algorithm is applied to it. The space in which the original data reside is called input space, while the transformed data occupy part of a feature space. In Chapter 3 we investigate whether variable selection should be performed in input space or rather in feature space. A new approach to selection, so-called feature-toinput space selection, is also proposed. This approach has the attractive property of combining information generated in feature space with easy interpretation in input space. An empirical study reveals that effective variable selection requires utilisation of at least some information from feature space. Having confirmed in Chapter 3 that variable selection should preferably be done in feature space, the focus in Chapter 4 is on two classes of selecion criteria operating in feature space: criteria which are independent of the specific kernel classification algorithm and criteria which depend on this algorithm. In this regard we concentrate on two kernel classifiers, viz. support vector machines and kernel Fisher discriminant analysis, both of which are described in some detail in Chapter 4. The chapter closes with a simulation study showing that two of the algorithm-independent criteria are very competitive with the more sophisticated algorithm-dependent ones. In Chapter 5 we incorporate a specific strategy for searching through the space of variable subsets into our investigation. Evidence in the literature strongly suggests that backward elimination is preferable to forward selection in this regard, and we therefore focus on recursive feature elimination. Zero- and first-order forms of the new selection criteria proposed earlier in the thesis are presented for use in recursive feature elimination and their properties are investigated in a numerical study. It is found that some of the simpler zeroorder criteria perform better than the more complicated first-order ones. Up to the end of Chapter 5 it is assumed that the number of variables to select is known. We do away with this restriction in Chapter 6 and propose a simple criterion which uses the data to identify this number when a support vector machine is used. The proposed criterion is investigated in a simulation study and compared to cross-validation, which can also be used for this purpose. We find that the proposed criterion performs well. The thesis concludes in Chapter 7 with a summary and several discussions for further research.

Thesis (PhD (Statistics and Actuarial Science))—Stellenbosch University, 2008. / Kernel Fisher discriminant analysis (KFDA) is a kernel-based technique that can be used to classify observations of unknown origin into predefined groups. Basically, KFDA can be viewed as a non-linear extension of Fisher’s linear discriminant analysis (FLDA). In this thesis we give a detailed explanation how FLDA is generalized to obtain KFDA. We also discuss two methods that are related to KFDA. Our focus is on binary classification. The influence of atypical cases in discriminant analysis has been investigated by many researchers. In this thesis we investigate the influence of atypical cases on certain aspects of KFDA. One important aspect of interest is the generalization performance of the KFD classifier. Several other aspects are also investigated with the aim of developing criteria that can be used to identify cases that are detrimental to the KFD generalization performance. The investigation is done via a Monte Carlo simulation study. The output of KFDA can also be used to obtain the posterior probabilities of belonging to the two classes. In this thesis we discuss two approaches to estimate posterior probabilities in KFDA. Two new KFD classifiers are also derived which use these probabilities to classify observations, and their performance is compared to that of the original KFD classifier. The main objective of this thesis is to develop criteria which can be used to identify cases that are detrimental to the KFD generalization performance. Nine such criteria are proposed and their merit investigated in a Monte Carlo simulation study as well as on real-world data sets. Evaluating the criteria on a leave-one-out basis poses a computational challenge, especially for large data sets. In this thesis we also propose using the smallest enclosing hypersphere as a filter, to reduce the amount of computations. The effectiveness of the filter is tested in a Monte Carlo simulation study as well as on real-world data sets.

Thesis (MComm) -- Stellenbosch University, 2002. / ENGLISH ABSTRACT: Consider a data set with a categorical response variable and a set of explanatory variables. The response variable can have two or more categories and the explanatory variables can be numerical or categorical. This is a typical setup for a classification analysis, where we want to model the response based on the explanatory variables. Traditional statistical methods have been developed under certain assumptions such as: the explanatory variables are numeric only and! or the data follow a multivariate normal distribution. hl practice such assumptions are not always met. Different research fields generate data that have a mixed structure (categorical and numeric) and researchers are often interested using all these data in the analysis. hl recent years robust methods such as classification trees have become the substitute for traditional statistical methods when the above assumptions are violated. Classification trees are not only an effective classification method, but offer many other advantages. The aim of this thesis is to highlight the advantages of classification trees. hl the chapters that follow, the theory of and further developments on classification trees are discussed. This forms the foundation for the CART software which is discussed in Chapter 5, as well as other software in which classification tree modeling is possible. We will compare classification trees to parametric-, kernel- and k-nearest-neighbour discriminant analyses. A neural network is also compared to classification trees and finally we draw some conclusions on classification trees and its comparisons with other methods. / AFRIKAANSE OPSOMMING: Beskou 'n datastel met 'n kategoriese respons veranderlike en 'n stel verklarende veranderlikes. Die respons veranderlike kan twee of meer kategorieë hê en die verklarende veranderlikes kan numeries of kategories wees. Hierdie is 'n tipiese opset vir 'n klassifikasie analise, waar ons die respons wil modelleer deur gebruik te maak van die verklarende veranderlikes. Tradisionele statistiese metodes is ontwikkelonder sekere aannames soos: die verklarende veranderlikes is slegs numeries en! of dat die data 'n meerveranderlike normaal verdeling het. In die praktyk word daar nie altyd voldoen aan hierdie aannames nie. Verskillende navorsingsvelde genereer data wat 'n gemengde struktuur het (kategories en numeries) en navorsers wil soms al hierdie data gebruik in die analise. In die afgelope jare het robuuste metodes soos klassifikasie bome die alternatief geword vir tradisionele statistiese metodes as daar nie aan bogenoemde aannames voldoen word nie. Klassifikasie bome is nie net 'n effektiewe klassifikasie metode nie, maar bied baie meer voordele. Die doel van hierdie werkstuk is om die voordele van klassifikasie bome uit te wys. In die hoofstukke wat volg word die teorie en verdere ontwikkelinge van klassifikasie bome bespreek. Hierdie vorm die fondament vir die CART sagteware wat bespreek word in Hoofstuk 5, asook ander sagteware waarin klassifikasie boom modelering moontlik is. Ons sal klassifikasie bome vergelyk met parametriese-, "kernel"- en "k-nearest-neighbour" diskriminant analise. 'n Neurale netwerk word ook vergelyk met klassifikasie bome en ten slote word daar gevolgtrekkings gemaak oor klassifikasie bome en hoe dit vergelyk met ander metodes.

published_or_final_version / Management Studies / Master / Master of Business Administration

In the Canadian Cordillera, Mesozoic calcalkaline and alkaline intrusive igneous rocks that are prospective for hosting porphyry Cu-Au mineralization may be overlain by thick glacial overburden. Previous studies have shown that magnetite from ore deposits has a unique trace element signature that differs from magnetite in common igneous or metamorphic rocks. This study investigated if the composition of ore-related magnetite in till could provide a unique exploration tool to locate porphyry deposits in glaciated terrain. Bulk till samples were collected over an area of ~700 km2 surrounding the Mount Polley porphyry Cu-Au deposit, south-central British Columbia. Twenty elements were measured by LA-ICP-MS in ~50 detrital magnetite grains in each of 20 till samples. Previously proposed discrimination diagrams are proven to be of limited use in correctly identifying ore-related magnetite. Therefore, linear discriminant analysis (LDA) was performed on a compiled dataset of magnetite compositions from various porphyry deposits and intrusive igneous rocks in order to rigorously redefine the chemical signature of hydrothermal magnetite from porphyry systems. Application of the LDA models to magnetite in till found that the dispersal of hydrothermal grains from Mount Polley is coincident with the deposit and the interpreted ice-flow history. Anomalous concentrations of hydrothermal magnetite grains in till are detected up to 2.5 km west-southwest and 4 km northwest of the deposit, indicating that magnetite has a strong potential to be an effective indicator in mineral exploration for porphyry systems. / Graduate

This research examines certain modifications of the mathematical programming models to improve their classificatory performance. These modifications involve the inclusion of second-order terms and secondary goals in mathematical programming models. A Monte Carlo simulation study is conducted to investigate the performance of two standard parametric models and various mathematical programming models, including the MSD (minimize sum of deviations) model, the MIP (mixed integer programming) model and the hybrid linear programming model.

The postsecondary enrollment of student veterans has increased with the troop draw down in Iraq and Afghanistan as well as the generous amendments made to the Post 9/11 GI Bill. Acquired disabilities remain a reality for this population as they transition into the civilian world; consequently, previous literature cites the role of disabilities amongst student veterans. Also, prior research often aggregates these two groups without a thorough understanding of the ways in which they differ. This study compared student veterans with disabilities to student veterans without disabilities in order to understand the enrollment and demographic factors on which they differed, if any. Using a secondary data analysis of the 2007-2008 National Postsecondary Student Aid Survey, univariate tests of significance, a logistic regression, and a discriminant function analysis examined the relationship between disability status and seven predictor variables: age, gender, GPA, major, risk index, degree program type, and whether or not a student was exclusively a distance learner. These seven variables as a whole were not significant predictors of disability status; however, the models provided valuable insight into the similarities and characteristics shared within this population. Univariate tests of significance revealed that students with disabilities had a significantly lower mean GPA, were more often male, tended to favor certain academic majors over others, more often enrolled in bachelor’s degree versus associate and certificate programs, and had a lower risk of attrition based on their index of risk. Major, degree program type, and risk index proved to be the most significant predictors of disability status in LR and DFA. A student veteran’s age and whether they were a distance learner had no significant bearing on disability status indicating that student veterans enroll in distance learning or campus-based programs without influence from an orthopedic or mobility impairment, the most common type of disability amongst student veterans. This study offers a full description of student veterans with disabilities including the specific types of disabilities with which this population enters higher education.

I Role of Behavioral Finance in Portfolio Investment Decisions: Evidence from India Abstract Extreme volatility has plagued financial markets worldwide since the 2008 Global Crisis. Investor sentiment has been one of the key determinants of market movements. In this context, studying the role played by emotions like fear, greed and anticipation, in shaping up investment decisions seemed important. Behavioral Finance is an evolving field that studies how psychological factors affect decision making under uncertainty. This thesis seeks to find the influence of certain identified behavioral finance concepts (or biases), namely, Overconfidence, Representativeness, Herding, Anchoring, Cognitive Dissonance, Regret Aversion, Gamblers' Fallacy, Mental Accounting, and Hindsight Bias, on the decision making process of individual investors in the Indian Stock Market. Primary data for analysis was gathered by distributing a structured questionnaire among investors who were categorized as (i) young, and (ii) experienced. Results obtained by analyzing a sample of 92 respondents, out of which 53 admitted to having suffered a loss of at least 30% because of the crisis, revealed that the degree of exposure to the biases separated the behavioral pattern of young and experienced investors. Gamblers' Fallacy, Anchoring and...

The study of facial expressions in humans dates back to the 19th century and the study of the emotions that these facial expressions portray dates back even further. It is a natural part of non-verbal communication for humans to pass across messages using facial expressions either consciously or subconsciously, it is also routine for other humans to recognize these facial expressions and understand or deduce the underlying emotions which they represent. Over two decades ago and following technological advances, particularly in the area of image processing, research began into the use of machines for the recognition of facial expressions from images with the aim of inferring the corresponding emotion. Given a previously unknown test sample, the supervised learning problem is to accurately determine the facial expression class to which the test sample belongs using the knowledge of the known class memberships of each image from a set of training images. The solution to this problem building an effective classifier to recognize the facial expression is hinged on the availability of representative training data. To date, much of the research in the area of Facial Expression Recognition (FER) is still based on posed (acted) facial expression databases, which are often exaggerated and therefore not representative of real life affective displays, as such there is a need for more publically accessible spontaneous databases that are well labelled. This thesis therefore reports on the development of the newly collected Loughborough University Spontaneous Expression Database (LUSED); designed to bolster the development of new recognition systems and to provide a benchmark for researchers to compare results with more natural expression classes than most existing databases. To collect the database, an experiment was set up where volunteers were discretely videotaped while they watched a selection of emotion inducing video clips. The utility of the new LUSED dataset is validated using both traditional and more recent pattern recognition techniques; (1) baseline results are presented using the combination of Principal Component Analysis (PCA), Fisher Linear Discriminant Analysis (FLDA) and their kernel variants Kernel Principal Component Analysis (KPCA), Kernel Fisher Discriminant Analysis (KFDA) with a Nearest Neighbour-based classifier. These results are compared to the performance of an existing natural expression database Natural Visible and Infrared Expression (NVIE) database. A scheme for the recognition of encrypted facial expression images is also presented. (2) Benchmark results are presented by combining PCA, FLDA, KPCA and KFDA with a Sparse Representation-based Classifier (SRC). A maximum accuracy of 68% was obtained recognizing five expression classes, which is comparatively better than the known maximum for a natural database; around 70% (from recognizing only three classes) obtained from NVIE.