Functional Magnetic Resonance Imaging (fMRI) is one of the best techniques for neuroimaging and has revolutionized the way to understand the brain functions. It measures the changes in the blood oxygen level-dependent (BOLD) signal which is related to the neuronal activity. Complexity of the data, presence of different types of noises and the massive amount of data makes the fMRI data analysis a challenging one. It demands efficient signal processing and statistical analysis methods.  The inference of the analysis is used by the physicians, neurologists and researchers for better understanding of the brain functions.      The purpose of this study is to design a toolbox for fMRI data analysis. It includes methods to detect the brain activity maps, estimation of the hemodynamic response (HDR) and the connectivity of the brain structures. This toolbox provides methods for detection of activated brain regions measured with Bayesian estimator. Results are compared with the conventional methods such as t-test, ordinary least squares (OLS) and weighted least squares (WLS). Brain activation and HDR are estimated with linear adaptive model and nonlinear method based on radial basis function (RBF) neural network. Nonlinear autoregressive with exogenous inputs (NARX) neural network is developed to model the dynamics of the fMRI data.  This toolbox also provides methods to brain connectivity such as functional connectivity and effective connectivity.  These methods are examined on simulated and real fMRI datasets.

Many types of radial basis functions, such as multiquadrics, contain a free parameter called shape factor, which controls the flatness of RBFs. In the 1-D problems, Fornberg et al. [2] proved that with simple conditions on the increasingly flat radial basis function, the solutions converge to the Lagrange interpolating. In this report, we study and extend it to the 1-D Poisson equation RBFs direct solver, and observed that the interpolants converge to the Spectral Collocation Method using Polynomial. In 2-D, however, Fornberg et al. [2] observed that limit of interpolants fails to exist in cases of highly regular grid layouts. We also test this in the PDEs solver and found the error behavior is different from interpolating problem.

Thesis (MSc (Applied Mathematics))--Stellenbosch University, 2008. / A popular method for interpolating multidimensional scattered data is using radial basis functions. In this thesis we present the basic theory of radial basis function interpolation and also regard the solvability and stability of the method. Solving the interpolant directly has a high computational cost for large datasets, hence using numerical methods to approximate the interpolant is necessary. We consider some recent numerical algorithms. Software to implement radial basis function interpolation and to display the 3D interpolants obtained, is developed. We present results obtained from using our implementation for radial basis functions on GIS and 3D face data as well as an image warping application.

Den stora mängden tillgänglig data på internet kan användas för att förbättra förutsägelser genom maskininlärning. Problemet är att sådan data ofta är i ett obehandlat format och kräver att någon manuellt bestämmer etiketter på den insamlade datan innan den kan användas av algoritmen. Semi-supervised learning (SSL) är en teknik där algoritmen använder ett fåtal förbehandlade exempel och därefter automatiskt bestämmer etiketter för resterande data. Ett tillvägagångssätt inom SSL är att representera datan i en graf, vilket kallas för graf-baserad semi-supervised learning (GSSL), och sedan hitta likheter mellan noderna i grafen för att automatiskt bestämma etiketter.Vårt mål i denna uppsatsen är att förenkla de avancerade processerna och stegen för att implementera en GSSL-algoritm. Vi kommer att gå igen grundläggande steg som hur utvecklingsmiljön ska installeras men även mer avancerade steg som data pre-processering och feature extraction. Feature extraction metoderna som uppsatsen använder sig av är bag-of-words (BOW) och term frequency-inverse document frequency (TF-IDF). Slutgiltligen presenterar vi klassificering av dokument med Label Propagation (LP) och Multinomial Naive Bayes (MNB) samt en detaljerad beskrivning över hur GSSL fungerar.Vi presenterar även prestanda för klassificering-algoritmerna genom att klassificera 20 Newsgroup datasetet med LP och MNB. Resultaten dokumenteras genom två olika utvärderingspoäng vilka är F1-score och accuracy. Vi gör även en jämförelse mellan MNB och LP med två olika typer av kärnor, KNN och RBF, på olika mängder av förbehandlade träningsdokument. Resultaten ifrån klassificering-algoritmerna visar att MNB är bättre på att klassificera datasetet än LP. / The large amount of available data on the web can be used to improve the predictions made by machine learning algorithms. The problem is that such data is often in a raw format and needs to be manually labeled by a human before it can be used by a machine learning algorithm. Semi-supervised learning (SSL) is a technique where the algorithm uses a few prepared samples to automatically prepare the rest of the data. One approach to SSL is to represent the data in a graph, also called graph-based semi-supervised learning (GSSL), and find similarities between the nodes for automatic labeling.Our goal in this thesis is to simplify the advanced processes and steps to implement a GSSL-algorithm. We will cover basic tasks such as setup of the developing environment and more advanced steps such as data preprocessing and feature extraction. The feature extraction techniques covered are bag-of-words (BOW) and term frequency-inverse document frequency (TF-IDF). Lastly, we present how to classify documents using Label Propagation (LP) and Multinomial Naive Bayes (MNB) with a detailed explanation of the inner workings of GSSL. We showcased the classification performance by classifying documents from the 20 Newsgroup dataset using LP and MNB. The results are documented using two different evaluation scores called F1-score and accuracy. A comparison between MNB and the LP-algorithm using two different types of kernels, KNN and RBF, was made on different amount of labeled documents. The results from the classification algorithms shows that MNB is better at classifying the data than LP.

[pt] Tendo como objetivo a construção de uma metodologia para a estimação do agregado do Consumo Pessoal para as Contas Nacionais do Brasil, o presente trabalho contém a definição de uma modificação sobre o Estimador de Regressão de Nadaraya-Watson (NWRE), que objetiva o uso de uma rede neural tipo RBF sobre dados provenientes de duas pesquisas dotadas de planos amostrais amplamente diferenciados, quais sejam: POF e PNAD. A partir da aplicação de tal modelo, são obtidos dados e calculados erros estimados, além de outras estatísticas que se mostram úteis na validação das estimativas. / [en] It is the objective of this dissertation to produce a methodological framework to the estimation of the Family Comsumption agregate in the brasilian National Accounts. In order to perform this task, a modification in the Nadaraya-Watson Regression Estimator (NWRE) has been developed, intended to allow the use of an RBF neural network in the context of data originated in two surveys which significantly differ in sample design, which are POF and PNAD. From the application of the developed methodology, groups of data are presented, providing results, estimated errors and other statistics useful for the comprehension and validation of the model. / [es] El objetivo de este trabajo es establecer una metodologia para la estimación del agregado del Consumo familiar para las Cuentas Nacionales del Brasil. Para ello, se define una modificación sobre el Estimador de Regresión de Nadaraya- Watson (NWRE), que tiene como objetivo el uso de una red neural tipo RBF sobre datos provenientes de dos investigaciones dotadas de planos muestrales ampliamente diferenciados: POF y PNAD. A partir de la aplicación de tal modelo, se obtienen los datos y se calculan los erros estimados, además de otras estadísticas útiles en la evaluación de las estimativas.

The power industry has undergone significant restructuring throughout the world since the 1990s. In particular, its traditional, vertically monopolistic structures have been reformed into competitive markets in pursuit of increased efficiency in electricity production and utilization. However, along with market deregulation, power systems presently face severe challenges. One is power system stability, a problem that has attracted widespread concern because of severe blackouts experienced in the USA, the UK, Italy, and other countries. Another is that electricity market operation warrants more effective planning, management, and direction techniques due to the ever expanding large-scale interconnection of power grids. Moreover, many exterior constraints, such as environmental protection influences and associated government regulations, now need to be taken into consideration. All these have made existing challenges even more complex. One consequence is that more advanced power system data analysis methods are required in the deregulated, market-oriented environment. At the same time, the computational power of modern computers and the application of databases have facilitated the effective employment of new data analysis techniques. In this thesis, the reported research is directed at developing computational intelligence based techniques to solve several power system problems that emerge in deregulated electricity markets. Four major contributions are included in the thesis: a newly proposed quantum-inspired particle swarm optimization and self-adaptive learning scheme for radial basis function neural networks; online wavelet denoising techniques; electricity regional reference price forecasting methods in the electricity market; and power system security assessment approaches for deregulated markets, including fault analysis, voltage profile prediction under contingencies, and machine learning based load shedding scheme for voltage stability enhancement. Evolutionary algorithms (EAs) inspired by biological evolution mechanisms have had great success in power system stability analysis and operation planning. Here, a new quantum-inspired particle swarm optimization (QPSO) is proposed. Its inspiration stems from quantum computation theory, whose mechanism is totally different from those of original EAs. The benchmark data sets and economic load dispatch research results show that the QPSO improves on other versions of evolutionary algorithms in terms of both speed and accuracy. Compared to the original PSO, it greatly enhances the searching ability and efficiently manages system constraints. Then, fuzzy C-means (FCM) and QPSO are applied to train radial basis function (RBF) neural networks with the capacity to auto-configure the network structures and obtain the model parameters. The benchmark data sets test results suggest that the proposed training algorithms ensure good performance on data clustering, also improve training and generalization capabilities of RBF neural networks. Wavelet analysis has been widely used in signal estimation, classification, and compression. Denoising with traditional wavelet transforms always exhibits visual artefacts because of translation-variant. Furthermore, in most cases, wavelet denoising of real-time signals is actualized via offline processing which limits the efficacy of such real-time applications. In the present context, an online wavelet denoising method using a moving window technique is proposed. Problems that may occur in real-time wavelet denoising, such as border distortion and pseudo-Gibbs phenomena, are effectively solved by using window extension and window circle spinning methods. This provides an effective data pre-processing technique for the online application of other data analysis approaches. In a competitive electricity market, price forecasting is one of the essential functions required of a generation company and the system operator. It provides critical information for building up effective risk management plans by market participants, especially those companies that generate and retail electrical power. Here, an RBF neural network is adopted as a predictor of the electricity market regional reference price in the Australian national electricity market (NEM). Furthermore, the wavelet denoising technique is adopted to pre-process the historical price data. The promising network prediction performance with respect to price data demonstrates the efficiency of the proposed method, with real-time wavelet denoising making feasible the online application of the proposed price prediction method. Along with market deregulation, power system security assessment has attracted great concern from both academic and industry analysts, especially after several devastating blackouts in the USA, the UK, and Russia. This thesis goes on to propose an efficient composite method for cascading failure prevention comprising three major stages. Firstly, a hybrid method based on principal component analysis (PCA) and specific statistic measures is used to detect system faults. Secondly, the RBF neural network is then used for power network bus voltage profile prediction. Tests are carried out by means of the “N-1” and “N-1-1” methods applied in the New England power system through PSS/E dynamic simulations. Results show that system faults can be reliably detected and voltage profiles can be correctly predicted. In contrast to traditional methods involving phase calculation, this technique uses raw data from time domains and is computationally inexpensive in terms of both memory and speed for practical applications. This establishes a connection between power system fault analysis and cascading analysis. Finally, a multi-stage model predictive control (MPC) based load shedding scheme for ensuring power system voltage stability is proposed. It has been demonstrated that optimal action in the process of load shedding for voltage stability during emergencies can be achieved as a consequence. Based on above discussions, a framework for analysing power system voltage stability and ensuring its enhancement is proposed, with such a framework able to be used as an effective means of cascading failure analysis. In summary, the research reported in this thesis provides a composite framework for power system data analysis in a market environment. It covers advanced techniques of computational intelligence and machine learning, also proposes effective solutions for both the market operation and the system stability related problems facing today’s power industry.

Dans le domaine d'optimisation de forme de structures, la réduction des coûts et l'amélioration des produits sont des défis permanents à relever. Pour ce faire, le procédé de mise en forme doit être optimisé. Optimiser le procédé revient alors à résoudre un problème d'optimisation. Généralement ce problème est un problème d'optimisation multicritère très coûteux en terme de temps de calcul, où on cherche à minimiser plusieurs fonctions coût en présence d'un certain nombre de contraintes. Pour résoudre ce type de problème, on a développé un algorithme robuste, efficace et fiable. Cet algorithme, consiste à coupler un algorithme de capture de front de Pareto (NBI ou NNCM) avec un métamodèle (RBF), c'est-à-dire des approximations des résultats des simulations coûteuses. D'après l'ensemble des résultats obtenus par cette approche, il est intéressant de souligner que la capture de front de Pareto génère un ensemble des solutions non dominées. Pour savoir lesquelles choisir, le cas échéant, il est nécessaire de faire appel à des algorithmes de sélection, comme par exemple Nash et Kalai-Smorodinsky. Ces deux approches, issues de la théorie des jeux, ont été utilisées pour notre travail. L'ensemble des algorithmes sont validés sur deux cas industriels proposés par notre partenaire industriel. Le premier concerne un modèle 2D du fond de la canette (elasto-plasticité) et le second est un modèle 3D de la traverse (élasticité linéaire). Les résultats obtenus confirment l'efficacité de nos algorithmes développés.

Cette thèse porte sur des méthode de résolution d'équations matricielles appliquées à la résolution numérique d'équations aux dérivées partielles ou des problèmes de contrôle linéaire. On s'intéressen en premier lieu à des équations matricielles linéaires. Après avoir donné un aperçu des méthodes classiques employées pour les équations de Sylvester et de Lyapunov, on s'intéresse au cas d'équations linéaires générales de la forme M(X)=C, où M est un opérateur linéaire matriciel. On expose la méthode de GMRES globale qui s'avère particulièrement utile dans le cas où M(X) ne peut s'exprimer comme un polynôme du premier degré en X à coefficients matriciels, ce qui est le cas dans certains problèmes de résolution numérique d'équations aux dérivées partielles. Nous proposons une approche, noté LR-BA-ADI consistant à utiliser un préconditionnement de type ADI qui transforme l'équation de Sylvester en une équation de Stein que nous résolvons par une méthode de Krylox par blocs. Enfin, nous proposons une méthode de type Newton-Krylov par blocs avec préconditionnement ADI pour les équations de Riccati issues de problèmes de contrôle linéaire quadratique. Cette méthode est dérivée de la méthode LR-BA-ADI. Des résultats de convergence et de majoration de l'erreur sont donnés. Dans la seconde partie de ce travail, nous appliquons les méthodes exposées dans la première partie de ce travail à des problèmes d'équations aux dérivées partielles. Nous nous intéressons d'abord à la résolution numérique d'équations couplées de type Burgers évolutives en dimension 2. Ensuite, nous nous intéressons au cas où le domaine borné est choisi quelconque. Nous établissons des résultats théoriques de l'existence de tels interpolants faisant appel à des techniques d'algèbre linéaire.

The notion of designing circuits based on charge sensing, charge adaptation, and charge programming is explored in this research. This design concept leads to a low-power capacitive sensing interface circuit that has been designed and tested with a MEMS microphone and a capacitive micromachined ultrasonic transducer. Moreover, by using the charge programming technique, a designed floating-gate based large-scale field-programmable analog array (FPAA) containing a universal sensor interface sets the stage for reconfigurable smart sensory systems. Based on the same charge programming technique, a compact programmable analog radial-basis-function (RBF) based classifier and a resultant analog vector quantizer have been developed and tested. Measurement results have shown that the analog RBF-based classifier is at least two orders of magnitude more power-efficient than an equivalent digital processor. Furthermore, an adaptive bump circuit that can facilitate unsupervised learning in the analog domain has also been proposed. A projection neural network for a support vector machine, a powerful and more complicated binary classification algorithm, has also been proposed. This neural network is suitable for analog VLSI implementation and has been simulated and verified on the transistor level. These analog classifiers can be integrated at the interface to build smart sensory systems.

The power industry has undergone significant restructuring throughout the world since the 1990s. In particular, its traditional, vertically monopolistic structures have been reformed into competitive markets in pursuit of increased efficiency in electricity production and utilization. However, along with market deregulation, power systems presently face severe challenges. One is power system stability, a problem that has attracted widespread concern because of severe blackouts experienced in the USA, the UK, Italy, and other countries. Another is that electricity market operation warrants more effective planning, management, and direction techniques due to the ever expanding large-scale interconnection of power grids. Moreover, many exterior constraints, such as environmental protection influences and associated government regulations, now need to be taken into consideration. All these have made existing challenges even more complex. One consequence is that more advanced power system data analysis methods are required in the deregulated, market-oriented environment. At the same time, the computational power of modern computers and the application of databases have facilitated the effective employment of new data analysis techniques. In this thesis, the reported research is directed at developing computational intelligence based techniques to solve several power system problems that emerge in deregulated electricity markets. Four major contributions are included in the thesis: a newly proposed quantum-inspired particle swarm optimization and self-adaptive learning scheme for radial basis function neural networks; online wavelet denoising techniques; electricity regional reference price forecasting methods in the electricity market; and power system security assessment approaches for deregulated markets, including fault analysis, voltage profile prediction under contingencies, and machine learning based load shedding scheme for voltage stability enhancement. Evolutionary algorithms (EAs) inspired by biological evolution mechanisms have had great success in power system stability analysis and operation planning. Here, a new quantum-inspired particle swarm optimization (QPSO) is proposed. Its inspiration stems from quantum computation theory, whose mechanism is totally different from those of original EAs. The benchmark data sets and economic load dispatch research results show that the QPSO improves on other versions of evolutionary algorithms in terms of both speed and accuracy. Compared to the original PSO, it greatly enhances the searching ability and efficiently manages system constraints. Then, fuzzy C-means (FCM) and QPSO are applied to train radial basis function (RBF) neural networks with the capacity to auto-configure the network structures and obtain the model parameters. The benchmark data sets test results suggest that the proposed training algorithms ensure good performance on data clustering, also improve training and generalization capabilities of RBF neural networks. Wavelet analysis has been widely used in signal estimation, classification, and compression. Denoising with traditional wavelet transforms always exhibits visual artefacts because of translation-variant. Furthermore, in most cases, wavelet denoising of real-time signals is actualized via offline processing which limits the efficacy of such real-time applications. In the present context, an online wavelet denoising method using a moving window technique is proposed. Problems that may occur in real-time wavelet denoising, such as border distortion and pseudo-Gibbs phenomena, are effectively solved by using window extension and window circle spinning methods. This provides an effective data pre-processing technique for the online application of other data analysis approaches. In a competitive electricity market, price forecasting is one of the essential functions required of a generation company and the system operator. It provides critical information for building up effective risk management plans by market participants, especially those companies that generate and retail electrical power. Here, an RBF neural network is adopted as a predictor of the electricity market regional reference price in the Australian national electricity market (NEM). Furthermore, the wavelet denoising technique is adopted to pre-process the historical price data. The promising network prediction performance with respect to price data demonstrates the efficiency of the proposed method, with real-time wavelet denoising making feasible the online application of the proposed price prediction method. Along with market deregulation, power system security assessment has attracted great concern from both academic and industry analysts, especially after several devastating blackouts in the USA, the UK, and Russia. This thesis goes on to propose an efficient composite method for cascading failure prevention comprising three major stages. Firstly, a hybrid method based on principal component analysis (PCA) and specific statistic measures is used to detect system faults. Secondly, the RBF neural network is then used for power network bus voltage profile prediction. Tests are carried out by means of the “N-1” and “N-1-1” methods applied in the New England power system through PSS/E dynamic simulations. Results show that system faults can be reliably detected and voltage profiles can be correctly predicted. In contrast to traditional methods involving phase calculation, this technique uses raw data from time domains and is computationally inexpensive in terms of both memory and speed for practical applications. This establishes a connection between power system fault analysis and cascading analysis. Finally, a multi-stage model predictive control (MPC) based load shedding scheme for ensuring power system voltage stability is proposed. It has been demonstrated that optimal action in the process of load shedding for voltage stability during emergencies can be achieved as a consequence. Based on above discussions, a framework for analysing power system voltage stability and ensuring its enhancement is proposed, with such a framework able to be used as an effective means of cascading failure analysis. In summary, the research reported in this thesis provides a composite framework for power system data analysis in a market environment. It covers advanced techniques of computational intelligence and machine learning, also proposes effective solutions for both the market operation and the system stability related problems facing today’s power industry.