In this thesis, 2D Local Discriminant Bases (LDB) algorithm is used to 2D search structure to classify remotely sensed data. 2D Linear Discriminant Analysis (LDA) method is converted into an M-ary classifier by combining majority voting principle and linear distance parameters. The feature extraction algorithm extracts the relevant features by removing the irrelevant ones and/or combining the ones which do not represent supplemental information on their own. The algorithm is implemented on a remotely sensed airborne data set from Tippecanoe County, Indiana to evaluate its performance. The spectral and spatial-frequency features are extracted from the multispectral data and used for classifying vegetative species like corn, soybeans, red clover, wheat and oat in the data set.

Orientador: Trajano Pires da Nóbrega Neto / Banca: José Othon Dantas Lopes / Banca: Clotilzio Moreira dos Santos / Resumo: Dado um número inteiro positivo d, encontrar um corpo de grau d que tenha, em valor absoluto, o menor discriminante é um problema clássico e poucos resultados se tem até hoje no sentido de se resolver tal desafio. O principal interesse deste trabalho consiste em estudar o problema acima sobre os corpos de números Abelianos, particularmente aqueles de grau primo. Para tanto será preciso dominar algumas técnicas referentes ao cálculo do discriminante de corpos de números, em especial, dos corpos Abelianos. / Abstract: Given a positive interger d, finding a field of degree d which has, to absolute value, the smallest discriminant it is a classical problem and few results has been got until at present time, to solve this challenge. The main purpose of this paper it is to study the problem above on Abelian numbers fields in special that ones of prime degree. However, it is necessary to know any techniques for calculating the numbers fiel discriminant, specially, to Abelian fields. / Mestre

Magister Artium (Psychology) - MA(Psych) / The purpose of the present study was to gather further external validity evidence towards the validity argument for an instrument designed to measure individual and contextual factors associated with adolescent substance use in low socio-economic status communities in the Western Cape, South Africa. The South African Substance Use Contextual Risk Instrument (SASUCRI) measures adolescents’ subjective experiences of their own psycho-social and their communities’ functioning. The present study uses secondary data analysis in order to further evaluate its external validity. Both content and structural evidence for the instrument has been gathered in the larger study in which the present study is located. Validity theory was used as the theoretical framework for the gathering of the different types of evidence in support of the validity argument for this instrument. The study employed non-probability purposive sampling to select schools from three education districts from which twenty-six schools were selected where the sample total was N=1959. English and Afrikaans versions of the instrument were administered to English- and Afrikaans home language, school-going adolescents, aged 12 to 21 years. All ethical standards were maintained throughout the research process. External evidence procedures were conducted using Discriminant Function Analysis (DFA) to evaluate the extent to which the instrument could discriminate between substance using and non-using adolescents. The DFA revealed that nine SASUCRI sub-scales totals can act as significant predictors to substance use among adolescents based on the predictive validity of sub-scales.

This thesis covers misclassification probabilities via an Edgeworth-type expansion of the maximum likelihood based discriminant function. When deriving misclassification errors, first the expectation and variance in the population are assumed to be known where the variance is the same across populations and thereafter we consider the case where those parameters are unknown. Cumulants of the discriminant function for discriminating between two multivariate normal populations are derived. Approximate probabilities of the misclassification errors are established via an Edgeworth-type expansion using a standard normal distribution.

Evaluating classifiers in controlled settings is essential for empirical applications, as extensive knowledge on model-behaviour is needed for accurate predictions. This thesis investigates robustness against non-normality of two prominent classifiers, LDA and QDA. Through simulation, errors in leave-one-out cross-validation are compared for data generated by different multivariate distributions, also controlling for covariance structures, class separation and sample sizes. Unexpectedly, the classifiers perform better on data generated by heavy-tailed symmetrical distributions than by the normal distribution. Possible explanations are proposed, but the cause remains unknown. There is need for further studies, investigating more settings as well as mathematical properties to verify and understand these results.

No description available.

Thesis (MBA)--Stellenbosch University, 2000. / ENGLISH ABSTRACT: The assumption underlying this study is that the regime of the economy imparts certain characteristics to the business cycle indicators and that by using a discriminant analysis it would be possible to gain information from the various indicators as to the state of activity in the economy. A discriminant analysis was developed on an Excel spreadsheet. The Schwartz Information Criterion, SIC, was calculated for the models. This value compares how closely the model follows the true data generating process. The discriminant analysis was performed using all the variables or indicators applicable to the model in question. Using a linear programming algorithm the variables were removed from the model in order to maximise the SIC value for the model. The result was a variable set that maximised the information about the regime of the economy available from the various economic indicators. The models' performance was evaluated for post sample performance in a test data set. Five models were developed. They were: • the coincident logistic model; • the one period ahead logistic CLI (composite leading indicator) model; • the one period ahead logistic component model; • the three period ahead logistic CLI model; and • the three period ahead logistic component model. All the models produced meaningful results in the estimation data set for the United States economy. In the test data set only the coincident logistic model was found to give a clear signal of the regime switch. All models applied to the US data showed activity around all the regime switches. Two of the models did not produce useful results when applied to South African economic data. For this reason the one and two period ahead logistic component models were not used. The remaining three models gave clear signals of regime switches for all regime switches in the estimation and the test data set. The best overall model as far as SIC value was the one period ahead logistic CLI model applied to the South African data. The highest SIC for a model applied to the United States data is the logistic coincident model. The models were also evaluated on the number of wrong classifications. The best model in this regard is the coincident logistic model and one period ahead logistic CLI model applied to the United States data. The most accurate model for the South African data was the one-month ahead logistic CLI model in the estimation data set and the logistic coincident model in the test data set. The models were more decisive in the South African data than in the United States data set having a much lower region of uncertainty. Taking into consideration the greater decisiveness in conjunction with accuracy the models performed better with the South African data. The discriminant analysis generates a probability of expansion, which is used in conjunction with a classification rule based on observed frequencies in the estimation data set. A plot of the probability of expansion calculated by the models versus the true data generating process reveals that the models provide meaningful information as to the regime of the economy. The models tend to lag the true data generating process but do show activity around the regime switches. The models when applied to the United States data show good correlation with the true data generating process over the estimation data set but not as good over the test data set. The models perform better when applied to South African data when evaluated graphically. The models when applied to the South African data give good clear signals over all regime switches in all data sets. Indications of regime switches in the estimation data set were clearer than in the test data set. The use of a discriminant analysis for regime classification has been proven to be effective. This method should be used in conjunction with other methods to evaluate business cycle regimes. Useful information is extracted as regards the state of the economy from the various economic indicators. For this reason discriminant analysis of business cycles can be used as an additional tool for the evaluation of business cycle regimes. / AFRIKAANSE OPSOMMING: Die onderliggende aanname van hierdie studie is dat die ekonomiese stelsel sekere eienskappe aan die sakesiklus verleen, en dat 'n diskriminant ontleding dit moontlik maak om inligting te verkry uit die verskeie aanwysers oor die stand van ekonomiese aktiwiteite. 'n Diskriminant ontleding is op 'n Excel-sigblad ontwerp. Die Schwartz Informasie Kriterium (SIK) is vir die modelle bereken. Hierdie waarde dui aan hoe getrou die model die ware datagenereringsproses volg. Die diskriminant ontleding is gedoen deur gebruik te maak van al die veranderlikes of aanwysers wat van toepassing is op die betrokke model. Die veranderlikes is uit die model verwyder deur die gebruik van 'n lineêre programmerings algoritme, ten einde die SIK-waarde van die model te maksimaliseer. Die resultaat was 'n stel veranderlikes wat inligting via die verskeie ekonomiese aanwysers oor die beskikbare ekonomiese stelsel maksimaliseer het. Die model is vir buite-steekproef prestasie in 'n toetsdatastel evalueer. Die volgende vyf modelle is ontwikkel: • samevallende logistiese model • een periode vooruit logistiese saamgestelde leidende aanwysers (SLA)- model • een periode vooruit logistiese komponentmodel • drie periode vooruit logistiese SLA-model • drie periode vooruit logistiese komponentmodel. Al die modelle het betekenisvolle resultate in die steekproefdata vir die ekonomie van die VSA gelewer. In die toetsdatastel het slegs die samevallende logistiese model 'n duidelike aanduiding van regime-verandering gegee. Alle modelle wat op die VSA data toegepas is, het aktiwiteite rondom al die regime-veranderings aangetoon. Twee van die modelle wat op Suid-Afrikaanse data toegepas is, het nie bruikbare resultate opgelewer nie, en om hierdie rede is die een en twee periodes vooruit logistiese komponentmodelle nie gebruik nie. Die oorblywende drie modelle het duidelike aanduidings van regime-veranderings vir alle regime-veranderings aangetoon in die steekproefdata en die toetsdatastel. Die beste oorkoepelende model in terme van SIK-waarde was die een periode vooruit logistiese SLA-model wat op Suid-Afrikaanse data toegepas is. Die grootste SIK-waarde vir 'n model wat op VSA-data toegepas is, is vir die samevallende logistiese model. Modelle is ook evalueer in terme van die foutiewe klassifikasies. Die beste model in hierdie verband is die samevallende logistiese model en die een periode vooruit logistiese SLA-model wat op VSA-data toegepas is. Die mees akkurate model vir Suid-Afrikaanse data was die een maand vooruit logistiese SLA-model in die steekproef datastel en die samevallende logistiese model in die toetsdatastel. Die modelle was meer beslissend in die Suid-Afrikaanse data as in die VSA-datastel, omdat die Suid-Afrikaanse data 'n baie kleiner onsekerheidsgebied openbaar het. Gegewe die groter beslistheid tesame met akkuraatheid, het die modelle beter presteer met Suid-Afrikaanse data. Die diskriminant ontleding skep 'n opswaaiwaarskynlikheid, wat saam met 'n klassifikasiereël, gebaseer op die waargenome frekwensies in die steekproefdata, gebruik word. 'n Stip van die opswaaiwaarskynlikhede, bereken volgens die modelle versus die ware datagenereringsproses, dui daarop dat die modelle betekenisvolle inligting oor die ekonomiese stelsel bied. Die modelle neig om die ware datagenereringsproses te volg, maar toon tog beweging rondom regime-veranderings. Die modelle het goeie korrelasie met die ware datagenereringsproses oor die steekproefdatastel getoon op die VSA-data, maar nie juis goeie korrelasie oor die toetsdatastel nie. Die modelle presteer beter wanneer dit op Suid-Afrikaanse data toegepas word, en gee goeie, duidelike tekens oor alle regime-veranderings in alle datastelle. Aanduidings van regime-veranderings in die steekproefdatastel was duideliker as in die toetsdatastel. 'n Diskriminant ontleding vir stelselklassifikasie het effektief geblyk te wees. Hierdie metode behoort saam met ander metodes gebruik te word om sakesiklusstelsels te evalueer. Nuttige inligting word uit die verskillende ekonomiese aanwysers verkry oor die stand van die ekonomie. Juis om hierdie rede kan 'n diskriminant ontleding van sakesiklusse as bykomende instrument gebruik word om sakesiklusse te evalueer.

Thesis (PhD)--Stellenbosch University, 1997. / One copy microfiche. / ENGLISH ABSTRACT: Discriminani analysis and logistic regression are techniques that can be used to classify entities of unknown origin into one of a number of groups. However, the underlying models and assumptions for application of the two techniques differ. In this study, the two techniques are compared with respect to classification of entities. Firstly, the two techniques were compared in situations where no data dependent variable selection took place. Several underlying distributions were studied: the normal distribution, the double exponential distribution and the lognormal distribution. The number of variables, sample sizes from the different groups and the correlation structure between the variables were varied to' obtain a large number of different configurations. .The cases of two and three groups were studied. The most important conclusions are: "for normal and double' exponential data linear discriminant analysis outperforms logistic regression, especially in cases where the ratio of the number of variables to the total sample size is large. For lognormal data, logistic regression should be preferred, except in cases where the ratio of the number of variables to the total sample size is large. " Variable selection is frequently the first step in statistical analyses. A large number of potenti8.Ily important variables are observed, and an optimal subset has to be selected for use in further analyses. Despite the fact that variable selection is often used, the influence of a selection step on further analyses of the same data, is often completely ignored. An important aim of this study was to develop new selection techniques for use in discriminant analysis and logistic regression. New estimators of the postselection error rate were also developed. A new selection technique, cross model validation (CMV) that can be applied both in discriminant analysis and logistic regression, was developed. ."This technique combines the selection of variables and the estimation of the post-selection error rate. It provides a method to determine the optimal model dimension, to select the variables for the final model and to estimate the post-selection error rate of the discriminant rule. An extensive Monte Carlo simulation study comparing the CMV technique to existing procedures in the literature, was undertaken. In general, this technique outperformed the other methods, especially with respect to the accuracy of estimating the post-selection error rate. Finally, pre-test type variable selection was considered. A pre-test estimation procedure was adapted for use as selection technique in linear discriminant analysis. In a simulation study, this technique was compared to CMV, and was found to perform well, especially with respect to correct selection. However, this technique is only valid for uncorrelated normal variables, and its applicability is therefore limited. A numerically intensive approach was used throughout the study, since the problems that were investigated are not amenable to an analytical approach. / AFRIKAANSE OPSOMMING: Lineere diskriminantanaliseen logistiese regressie is tegnieke wat gebruik kan word vir die Idassifikasie van items van onbekende oorsprong in een van 'n aantal groepe. Die agterliggende modelle en aannames vir die gebruik van die twee tegnieke is egter verskillend. In die studie is die twee tegnieke vergelyk ten opsigte van k1assifikasievan items. Eerstens is die twee tegnieke vergelyk in 'n apset waar daar geen data-afhanklike seleksie van veranderlikes plaasvind me. Verskeie onderliggende verdelings is bestudeer: die normaalverdeling, die dubbeleksponensiaal-verdeling,en die lognormaal verdeling. Die aantal veranderlikes, steekproefgroottes uit die onderskeie groepe en die korrelasiestruktuur tussen die veranderlikes is gevarieer om 'n groot aantal konfigurasies te verkry. Die geval van twee en drie groepe is bestudeer. Die belangrikste gevolgtrekkings wat op grond van die studie gemaak kan word is: vir normaal en dubbeleksponensiaal data vaar lineere diskriminantanalise beter as logistiese regressie, veral in gevalle waar die. verhouding van die aantal veranderlikes tot die totale steekproefgrootte groot is. In die geval van data uit 'n lognormaalverdeling, hehoort logistiese regressie die metode van keuse te wees, tensy die verhouding van die aantal veranderlikes tot die totale steekproefgrootte groot is. Veranderlike seleksie is dikwels die eerste stap in statistiese ontledings. 'n Groot aantal potensieel belangrike veranderlikes word waargeneem, en 'n subversamelingwat optimaal is, word gekies om in die verdere ontledings te gebruik. Ten spyte van die feit dat veranderlike seleksie dikwels gebruik word, word die invloed wat 'n seleksie-stap op verdere ontledings van dieselfde data. het, dikwels heeltemal geYgnoreer.'n Belangrike doelwit van die studie was om nuwe seleksietegniekete ontwikkel wat gebruik kan word in diskriminantanalise en logistiese regressie. Verder is ook aandag gegee aan ontwikkeling van beramers van die foutkoers van 'n diskriminantfunksie wat met geselekteerde veranderlikes gevorm word. 'n Nuwe seleksietegniek, kruis-model validasie (KMV) wat gebruik kan word vir die seleksie van veranderlikes in beide diskriminantanalise en logistiese regressie is ontwikkel. Hierdie tegniek hanteer die seleksie van veranderlikes en die beraming van die na-seleksie foutkoers in een stap, en verskaf 'n metode om die optimale modeldimensiete bepaal, die veranderlikes wat in die model bevat moet word te kies, en ook die na-seleksie foutkoers van die diskriminantfunksie te beraam. 'n Uitgebreide simulasiestudie waarin die voorgestelde KMV-tegniek met ander prosedures in die Iiteratuur. vergelyk is, is vir beide diskriminantanaliseen logistiese regressie ondemeem. In die algemeen het hierdie tegniek beter gevaar as die ander metodes wat beskou is, veral ten opsigte van die akkuraatheid waarmee die na-seleksie foutkoers beraam word. Ten slotte is daar ook aandag gegee aan voor-toets tipeseleksie. 'n Tegniek is ontwikkel wat gebruik maak van 'nvoor-toets berarningsmetode om veranderlikes vir insluiting in 'n lineere diskriminantfunksie te selekteer. Die tegniek ISin 'n simulasiestudie met die KMV-tegniek vergelyk, en vaar baie goed, veral t.o.v. korrekte seleksie. Hierdie tegniek is egter slegs geldig vir ongekorreleerde normaalveranderlikes, wat die gebruik darvan beperk. 'n Numeries intensiewe benadering is deurgaans in die studie gebruik. Dit is genoodsaak deur die feit dat die probleme wat ondersoek is, nie deur middel van 'n analitiese benadering hanteer kan word nie.

The current edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-IV-TR; American Psychiatric Association, 2000) defines personality disorders as categorical entities that are distinct from themselves and from normal personality traits. However, many scientists now believe that personality disorders can best be conceptualized using a dimensional model of traits that span normal and abnormal personality, such as the Five-Factor Model (FFM). Many research studies have indicated that the current personality disorder system can be adequately conceptualized using the FFM. However, if the FFM or any dimensional model is to be considered as a credible alternative to the current model, it must first demonstrate an increment in the validity of the assessment offered within a clinical setting. Thus, the current study extended previous research by comparing the convergent and discriminant validity of the current DSM-IV-TR model to the FFM across four assessment methodologies. Eighty-eight individuals that were currently receiving ongoing psychotherapy were assessed for the FFM and the DSM-IV-TR personality disorders using self-report, informant report, structured interview, and therapist ratings. The results indicated that the FFM had an appreciable advantage over the DSM-IV-TR in terms of discriminant validity and, at the domain level, convergent validity. Implications of the findings for future research are discussed.

In the last twelve years there has been considerable research interest in mathematical programming approaches to the statistical classification problem, primarily because they are not based on the assumptions of the parametric methods (Fisher's linear discriminant function, Smith's quadratic discriminant function) for optimality. This dissertation focuses on the development of mathematical programming models for the three-group classification problem and examines the computational efficiency and classificatory performance of proposed and existing models. The classificatory performance of these models is compared with that of Fisher's linear discriminant function and Smith's quadratic discriminant function. Additionally, this dissertation investigates theoretical characteristics of mathematical programming models for the classification problem with three or more groups. A computationally efficient model for the three-group classification problem is developed. This model minimizes directly the number of misclassifications in the training sample. Furthermore, the classificatory performance of the proposed model is enhanced by the introduction of a two-phase algorithm. The same algorithm can be used to improve the classificatory performance of any interval-based mathematical programming model for the classification problem with three or more groups. A modification to improve the computational efficiency of an existing model is also proposed. In addition, a multiple-group extension of a mathematical programming model for the two-group classification problem is introduced. A simulation study on classificatory performance reveals that the proposed models yield lower misclassification rates than Fisher's linear discriminant function and Smith's quadratic discriminant function under certain data configurations. Data configurations, where the parametric methods outperform the proposed models, are also identified. A number of theoretical characteristics of mathematical programming models for the classification problem are identified. These include conditions for the existence of feasible solutions, as well as conditions for the avoidance of degenerate solutions. Additionally, conditions are identified that guarantee the classificatory non-inferiority of one model over another in the training sample.