Une approche fondamentale pour la résolution de problémes de contrôle optimal est basée sur le principe de programmation dynamique. Ce principe conduit aux équations d'Hamilton-Jacobi, qui peuvent être résolues numériquement par des méthodes classiques comme la méthode des différences finies, les méthodes semi-lagrangiennes, ou les schémas antidiffusifs. À cause de la discrétisation de l'espace d'état, la dimension des problèmes de contrôle pouvant être abordés par ces méthodes classiques est souvent limitée à 3 ou 4. Ce phénomène est appellé malédiction de la dimension. Cette thèse porte sur les méthodes numériques max-plus en contôle optimal deterministe et ses analyses de convergence. Nous étudions et developpons des méthodes numériques destinées à attenuer la malédiction de la dimension, pour lesquelles nous obtenons des estimations théoriques de complexité. Les preuves reposent sur des résultats de théorie de Perron-Frobenius non linéaire. En particulier, nous étudions les propriétés de contraction des opérateurs monotones et non expansifs, pour différentes métriques de Finsler sur un cône (métrique de Thompson, métrique projective d'Hilbert). Nous donnons par ailleurs une généralisation du "coefficient d'ergodicité de Dobrushin" à des opérateurs de Markov sur un cône général. Nous appliquons ces résultats aux systèmes de consensus ainsi qu'aux équations de Riccati généralisées apparaissant en contrôle stochastique.

Daugelis praktiškai reikšmingu sistemu mokymo uždaviniu reikalauja gebeti panaudoti didelio matavimo, strukturizuotus, netiesinius duomenis. Vaizdu, teksto, socialiniu bei verslo ryšiu analize, ivairus bioinformatikos uždaviniai galetu buti tokiu uždaviniu pavyzdžiais. Todel požymiu išskyrimas dažnai yra pirmasis žingsnis, kuriuo pradedama duomenu analize ir nuo kurio priklauso galutinio rezultato sekme. Šio disertacinio darbo tyrimo objektas yra požymiu išskyrimo algoritmai, besiremiantys priklausomumo savoka. Darbe nagrinejamas priklausomumas, nusakytas kovariacinio operatoriaus Hilberto-Šmidto normos (HSIC mato) branduoliniu ivertiniu. Pasiulyti šiuo ivertiniu besiremiantys HBFE ir HSCA algoritmai leidžia dirbti su bet kokios strukturos duomenimis, bei yra formuluojami tikriniu vektoriu terminais (tai leidžia optimizavimui naudoti standartinius paketus), bei taikytini ne tik prižiurimo, bet ir dalinai prižiurimo mokymo imtims. Pastaruoju atveju HBFE ir HSCA modifikacijos remiasi Laplaso reguliarizacija. Eksperimentais su klasifikavimo bei daugiažymio klasifikavimo duomenimis parodyta, jog pasiulyti algoritmai leidžia pagerinti klasifikavimo efektyvuma lyginant su PCA ar LDA. / In many important real world applications the initial representation of the data is inconvenient, or even prohibitive for further analysis. For example, in image analysis, text analysis and computational genetics high-dimensional, massive, structural, incomplete, and noisy data sets are common. Therefore, feature extraction, or revelation of informative features from the raw data is one of fundamental machine learning problems. Efficient feature extraction helps to understand data and the process that generates it, reduce costs for future measurements and data analysis. The representation of the structured data as a compact set of informative numeric features allows applying well studied machine learning techniques instead of developing new ones.. The dissertation focuses on supervised and semi-supervised feature extraction methods, which optimize the dependence structure of features. The dependence is measured using the kernel estimator of Hilbert-Schmidt norm of covariance operator (HSIC measure). Two dependence structures are investigated: in the first case we seek features which maximize the dependence on the dependent variable, and in the second one, we additionally minimize the mutual dependence of features. Linear and kernel formulations of HBFE and HSCA are provided. Using Laplacian regularization framework we construct semi-supervised variants of HBFE and HSCA. Suggested algorithms were investigated experimentally using conventional and multilabel classification data... [to full text]

Single view reconstruction is fundamentally an under-constrained problem. We aim to develop new approaches to model human face and motion with model priors that restrict the space of possible solutions. First, we develop a novel approach to recover the 3D shape from a single view image under challenging conditions, such as large variations in illumination and pose. The problem is addressed by employing the techniques of non-linear manifold embedding and alignment. Specifically, the local image models for each patch of facial images and the local surface models for each patch of 3D shape are learned using a non-linear dimensionality reduction technique, and the correspondences between these local models are then learned by a manifold alignment method. Local models successfully remove the dependency of large training databases for human face modeling. By combining the local shapes, the global shape of a face can be reconstructed directly from a single linear system of equations via least square. Unfortunately, this learning-based approach cannot be successfully applied to the problem of human motion modeling due to the internal and external variations in single view video-based marker-less motion capture. Therefore, we introduce a new model-based approach for capturing human motion using a stream of depth images from a single depth sensor. While a depth sensor provides metric 3D information, using a single sensor, instead of a camera array, results in a view-dependent and incomplete measurement of object motion. We develop a novel two-stage template fitting algorithm that is invariant to subject size and view-point variations, and robust to occlusions. Starting from a known pose, our algorithm first estimates a body configuration through temporal registration, which is used to search the template motion database for a best match. The best match body configuration as well as its corresponding surface mesh model are deformed to fit the input depth map, filling in the part that is occluded from the input and compensating for differences in pose and body-size between the input image and the template. Our approach does not require any makers, user-interaction, or appearance-based tracking. Experiments show that our approaches can achieve good modeling results for human face and motion, and are capable of dealing with variety of challenges in single view reconstruction, e.g., occlusion.

In many real-world applications of supervised learning, only a limited number of labeled examples are available because the cost of obtaining high-quality examples is high. Even with a relatively large number of labeled examples, the learning problem may still suffer from limited supervision as the complexity of the prediction function increases. Therefore, learning with limited supervision presents a major challenge to machine learning. With the goal of supervision reduction, this thesis studies the representation, discovery and incorporation of extra input and output information in learning. Information about the input space can be encoded by regularization. We first design a semi-supervised learning method for text classification that encodes the correlation of words inferred from seemingly irrelevant unlabeled text. We then propose a multi-task learning framework with a matrix-normal penalty, which compactly encodes the covariance structure of the joint input space of multiple tasks. To capture structure information that is more general than covariance and correlation, we study a class of regularization penalties on model compressibility. Then we design the projection penalty, which encodes the structure information from a dimension reduction while controlling the risk of information loss. Information about the output space can be exploited by error correcting output codes. Using the composite likelihood view, we propose an improved pairwise coding for multi-label classification, which encodes pairwise label density (as opposed to label comparisons) and decodes using variational methods. We then investigate problemdependent codes, where the encoding is learned from data instead of being predefined. We first propose a multi-label output code using canonical correlation analysis, where predictability of the code is optimized. We then argue that both discriminability and predictability are critical for output coding, and propose a max-margin formulation that promotes both discriminative and predictable codes. We empirically study our methods in a wide spectrum of applications, including document categorization, landmine detection, face recognition, brain signal classification, handwritten digit recognition, house price forecasting, music emotion prediction, medical decision, email analysis, gene function classification, outdoor scene recognition, and so forth. In all these applications, our proposed methods for encoding input and output information lead to significantly improved prediction performance.

Thesis (M.A. (Industrial Psychology))--North-West University, Potchefstroom Campus, 2008.

In this dissertation we developed theoretical models to analyse Gaussian and multinomial distributions. The analysis is focused on classification in high dimensional feature spaces and provides a basis for dealing with issues such as data sparsity and feature selection (for Gaussian and multinomial distributions, two frequently used models for high dimensional applications). A Naïve Bayesian philosophy is followed to deal with issues associated with the curse of dimensionality. The core treatment on Gaussian and multinomial models consists of finding analytical expressions for classification error performances. Exact analytical expressions were found for calculating error rates of binary class systems with Gaussian features of arbitrary dimensionality and using any type of quadratic decision boundary (except for degenerate paraboloidal boundaries). Similarly, computationally inexpensive (and approximate) analytical error rate expressions were derived for classifiers with multinomial models. Additional issues with regards to the curse of dimensionality that are specific to multinomial models (feature sparsity) were dealt with and tested on a text-based language identification problem for all eleven official languages of South Africa. / Thesis (M.Ing. (Computer Engineering))--North-West University, Potchefstroom Campus, 2009.

While the study of emotions is of universal interest because of its central role in the social sciences and humanities, emotions are of special interest for South Africa for both theoretical and applied reasons. South Africa, with its eleven official languages, is a true multicultural society with extreme differences in terms of culture, acculturation, and socio-economic status. Cultural frameworks differ substantially between ethno-cultural groups, and clarification of the differences between cultural frameworks can counter interpretation biases that could result in daily frictions and major conflicts. Additional fundamental cross-cultural research on emotional differences between cultural groups, together with the generation of a mutual understanding of the different cultural frameworks, makes these frameworks explicit and facilitates the incorporation of these frameworks into daily communication and interaction processes. The objectives of this research were to determine what the emotion structure of the Sepedi, Xitsonga and Tshivenda languages groups within a sample of Sepedi-, Xitsonga- and Tshivenda-speaking participants is, and how it compares with the European Emotion Structure. Furthermore this research aimed to establish the emotion structure and the relevant and representative features for each emotion component (such as appraisals, action tendencies, and subjective experiences) that have been encoded in a sample of Sepedi-, Xitsonga- and Tshivenda-speaking participants. Like\vise it was deemed necessary to verify (a) the extent to which the emotion words refer to specific positions on each of the emotion features of these language groups and (b) the extent of similarity or dissimilarity between emotion experiences of the Sepedi, Xitsonga and Tshivenda groups in the SAPS, as well as to compare the meaning structure between a "bottom-up" and a "top-down" (as conducted in Nicholls' research in 2008) approach between Sepedi-, Xitsonga- and Tshivenda-speaking participants. A survey design with convenience sampling was used to achieve the research objectives. The study population (n=390) consisted of Sepedi-, Xitsonga- and Tshivenda-speaking entry-level police applicants from the South African Police Service (SAPS). The Sepedi, Xitsonga and Tshivenda GRlD questionnaires were administered. Statistical methods and procedures (multidimensional scaling and descriptive statistics) were used and Cronbachrs alpha coefficients were determined to analyse the results. Results of this study on the Sepedi, Xitsonga and Tshivenda cultural groups indicated the extraction of a two-factor model within the Sepedi group. Due to the extremely low reliability analyses of the Xitsonga and Tshivenda language groups' data, a reliable scale analysis and the meaning structures of these two groups could not be determined. The low reliabilities could be attributed to the direct language translation of the questionnaire and the assessment may not have captured the full understanding of the items in the GRlD instrument. Results of this study for the Sepedi language group corresponded well with the results found in the study for the Sepedi group conducted by Nicholls (2008) on the emotion lexicon on the Sepedi, Xitsonga and Tshivenda language groups in South Africa. The Nicholls study (2008) indicated the extraction of a three-dimensional structure (evaluation, arousal, dominance) and a four-factor loading (positive emotion, sadness, fear, anger) for the Sepedi-speaking language group. In comparison, this research presented the extraction of a two-dimensional structure (evaluation and arousal) and a two-factor loading (positive emotion and sadness). Emotion concepts of the Sepedi group indicated that basic emotion concepts (love, joy, anger, sadness, fear, and surprise) readily came to mind in both Nicholls' (2008) and this study. Emotion concepts listed by the Sepedi group could be interpreted as emotion words associated with social, personality or environmental aspects and may be related to negative evaluation, dominance and/or aggression. Recommendations for future research were made. / Thesis (M.Com. (Industrial Psychology)--North-West University, Potchefstroom Campus, 2010.

Emotions play an important role in the lives of human beings and, without doubt, emotions form an inherent part of the workplace (Ashkanasy, Zerbe, Charmine & Hartel, 2002). Studying emotions within the South African context is relevant for applied psychology. South Africa comprises eleven official languages which are representative of the general population in the working environment. As a result, knowledge and understanding of emotions is useful since it forms part of social interaction at work. The understanding of one’s own as well as others’ emotions and the ability to deal with those emotions contribute to the productivity and cooperation among employees in the working environment. The objective of this research was to determine the conceptualization of emotion and culture according to the literature study, to determine the different and representative emotion words within the isiNdebele speaking group, to determine the relevant and representative prototypical emotion words that have been encoded in this group, to determine the cognitive emotion structure of this group and lastly, to determine the interrater reliability of the raters and reliability of the measurement instrument as well as the dimensions of emotion structure in the isiNdebele speaking group in Mpumalanga province. A survey design with convenience sample was used to achieve the research objectives in a series of three independent studies. The study population of the first phase (N=126) consisted of a convenience sample of the isiNdebele speaking group who have metric and are working in the South African Police Service in Mpumalanga province. The study population of the second phase consisted of a convenience sample of Language Experts with degrees and diplomas (N=51) in isiNdebele language from different occupations. The study population of the third phase consisted of a convenience sample of the experts (educators) in isiNdebele speaking group (N=183) from different schools in the former KwaNdebele homeland in Mpumalanga province. In this study, free listing, prototypicality and similarity rating questionnaires were administered by a qualified psychometrist. Statistical methods and procedures (Multidimensional Scaling and Descriptive Statistics) were used and Cronbach alpha coefficients were determined to analyse the results of the isiNdebele speaking group. The results of the free listing task indicated the words with the highest frequency as cry (lila), happy (thaba), laugh (hleka), angry (kwata), disappointed (swaba), confused (hlangahlangana), depressed (gandeleleka), pain (ubuhlungu), tired (dinwa), and abused (hlukumezeka). The results of this phase also indicated the basic emotion concepts of happiness (thaba) and angry (kwata) as the only emotion terms which mostly came to mind to the isiNdebele speaking group. The results of the prototypicality rating task indicated the emotion terms ranked as the ten (10) most prototypical emotion terms for the isiNdebele speaking group (N=51) were “ukuthaba khulu” (exhilaration), “itukuthelo/ ukukwata” (anger), “ithabo elikhulu” (euphoria), “ukuthaba” (cheerfulness), “ithabo” (happiness), “ukudana” (dejection), “ukutlhuwa/ ukudana”(glumness), “ukuthaba” (joviality), “ukulila/isililo” (cry), “ithabo” (joy). A multi– dimensional scaling was conducted to determine the cognitive structure of emotion concepts whereby a two– dimensional structure (evaluation and power) was identified to the isiNdebele speaking group. Recommendations for future research to the organisation as well as recommendations for future research were suggested. / http://hdl.handle.net/10394/7044 / http://hdl.handle.net/10394/7044 / Thesis (M.A. (Industrial Psychology))--North-West University, Potchefstroom Campus, 2012.

Thesis (M.A. (Industrial Psychology))--North-West University, Potchefstroom Campus, 2008.

In this dissertation we developed theoretical models to analyse Gaussian and multinomial distributions. The analysis is focused on classification in high dimensional feature spaces and provides a basis for dealing with issues such as data sparsity and feature selection (for Gaussian and multinomial distributions, two frequently used models for high dimensional applications). A Naïve Bayesian philosophy is followed to deal with issues associated with the curse of dimensionality. The core treatment on Gaussian and multinomial models consists of finding analytical expressions for classification error performances. Exact analytical expressions were found for calculating error rates of binary class systems with Gaussian features of arbitrary dimensionality and using any type of quadratic decision boundary (except for degenerate paraboloidal boundaries). Similarly, computationally inexpensive (and approximate) analytical error rate expressions were derived for classifiers with multinomial models. Additional issues with regards to the curse of dimensionality that are specific to multinomial models (feature sparsity) were dealt with and tested on a text-based language identification problem for all eleven official languages of South Africa. / Thesis (M.Ing. (Computer Engineering))--North-West University, Potchefstroom Campus, 2009.