Despite the importance of power systems in today’s societies, they suffer from aging infrastructure and need to improve the efficiency, reliability, and security. Two issues that significantly limit the current grid’s efficient energy delivery and consumption are: loadollowing generation dispatch, and energy theft. A loadollowing generation dispatch is usually employed in power systems, which makes continuous small changes so as to account for differences between the actual energy demand and the predicted values. This approach has led to an average utilization of energy generation capacity below 55% [49]. Moreover, energy theft causes several billion dollar losses to U.S. utility companies [31] [16], while in developing countries it can amount to 50% of the total energy delivered [48]. Recently, the Smart Grid has been proposed as a new electric grid to modernize current power grids and enhance its efficiency, reliability, and sustainability. Particularly, in the Smart Grid, a digital communication network is deployed to enable two-way communications between users and system operators. It thus makes it possible to shape the users’ load demand curves by means of demand response strategies. Additionally, in the Smart Grid, traditional meters will be replaced with cyber-physical devices, called smart meters, capable of recording and transmitting users’ real-time power consumption. Due to their monitoring capabilities, smart meters offer a great opportunity to detect energy theft in smart grids, but also raise serious concerns about users’ privacy. In this dissertation, we design optimal load scheduling schemes to enhance system efficiency, and develop energy theft detection algorithms that can preserve users’ privacy.

Access to huge amounts of various data with private information brings out a dual demand for preservation of data privacy and correctness of knowledge discovery, which are two apparently contradictory tasks. Low-rank approximations generated by matrix decompositions are a fundamental element in this dissertation for the privacy preserving data mining (PPDM) applications. Two categories of PPDM are studied: data value hiding (DVH) and data pattern hiding (DPH). A matrix-decomposition-based framework is designed to incorporate matrix decomposition techniques into data preprocessing to distort original data sets. With respect to the challenge in the DVH, how to protect sensitive/confidential attribute values without jeopardizing underlying data patterns, we propose singular value decomposition (SVD)-based and nonnegative matrix factorization (NMF)-based models. Some discussion on data distortion and data utility metrics is presented. Our experimental results on benchmark data sets demonstrate that our proposed models have potential for outperforming standard data perturbation models regarding the balance between data privacy and data utility. Based on an equivalence between the NMF and K-means clustering, a simultaneous data value and pattern hiding strategy is developed for data mining activities using K-means clustering. Three schemes are designed to make a slight alteration on submatrices such that user-specified cluster properties of data subjects are hidden. Performance evaluation demonstrates the efficacy of the proposed strategy since some optimal solutions can be computed with zero side effects on nonconfidential memberships. Accordingly, the protection of privacy is simplified by one modified data set with enhanced performance by this dual privacy protection. In addition, an improved incremental SVD-updating algorithm is applied to speed up the real-time performance of the SVD-based model for frequent data updates. The performance and effectiveness of the improved algorithm have been examined on synthetic and real data sets. Experimental results indicate that the introduction of the incremental matrix decomposition produces a significant speedup. It also provides potential support for the use of the SVD technique in the On-Line Analytical Processing for business data analysis.

This dissertation is comprised of two separate topics within the domain of polarization optical engineering. The first topic is a Mueller matrix roots decomposition, and the second topic is polarization computer generated holography. The first four chapters of the dissertation are on the topic of the Mueller matrix roots decomposition. Recently, an order-independent Mueller matrix decomposition was proposed in an effort to organize the nine depolarization degrees of freedom. Chapter 1 discusses relevant Mueller matrix decomposition prior art and the motivation for this work. In chapter 2, the critical computational issues involved in applying this Mueller matrix roots decomposition are addressed, along with a review of the principal root and common methods for its calculation. The choice of the pth root is optimized at p = 10⁵, and computational techniques are proposed which allow singular Mueller matrices and Mueller matrices with a half-wave of retardance to be evaluated with the matrix roots decomposition. A matrix roots algorithm is provided which incorporates these computational results. In chapter 3, the Mueller matrix roots decomposition is reviewed and a set of Mueller matrix generators are discussed. The parameterization of depolarization into three families, each with three degrees of freedom is explained. Analysis of the matrix roots parameters in terms of degree of polarization maps demonstrates that depolarizers fall into two distinct classes: amplitude depolarization in one class, and phase and diagonal depolarization in another class. It is shown that each depolarization family and degree of freedom can be produced by averaging two non-depolarizing Mueller matrix generators. This is extended to provide further insight on two sample measurements, which are analyzed using the matrix roots decomposition. Chapter 4 discusses additional properties of the Mueller matrix roots generators and parameters, along with a pupil aberration application of the matrix roots decomposition. Appendix C, adapted from a conference proceedings paper, presents an application of the matrix roots depolarization parameters for estimating the orientation of a one-dimensionally textured object. The last two chapters are on the topic of polarization computer generated holography. In chapter 5, an interlaced polarization computer-generated hologram (PCGH) is designed to produce specific irradiance and polarization states in the image plane. The PCGH produces a tangentially polarized annular pattern with correlated speckle, which is achieved by a novel application of a diffuser optimization method. Alternating columns of orthogonal linear polarizations illuminate an interlaced PCGH, producing a ratio of polarization of 88% measured on a fabricated sample. In chapter 6, an etched calcite square-wave retarder is designed, fabricated, and demonstrated as an illuminator for an interlaced polarization computer generated hologram (PCGH). The calcite square-wave retarder enables alternating columns of orthogonal linear polarizations to illuminate the interlaced PCGH. Together, these components produce a speckled, tangentially polarized PCGH diffraction pattern with a measured ratio of polarization of 84% and a degree of linear polarization of 0.81. An experimental alignment tolerance analysis is also reported.

In this project, we design a search query optimization system based on the user’s relevance feedback by generating customized query strings for existing patent alerts. Firstly, the Rocchio algorithm is used to generate a search string by analyzing the characteristics of related patents and unrelated patents. Then the collaborative filtering recommendation algorithm is used to rank the query results, which considering the previous relevance feedback and patent features, instead of only considering the similarity between query and patents as the traditional method. In order to further explore the performance of the optimization system, we design and conduct a series of evaluation experiments regarding TF-IDF as a baseline method. Experiments show that, with the use of generated search strings, the proportion of unrelated patents in search results is significantly reduced over time. In 4 months, the precision of the retrieved results is optimized from 53.5% to 72%. What’s more, the rank performance of the method we proposed is better than the baseline method. In terms of precision, top10 of recommendation algorithm is about 5 percentage points higher than the baseline method, and top20 is about 7.5% higher. It can be concluded that the approach we proposed can effectively optimize patent search results by learning relevance feedback.

Singular value decomposition (SVD) is a popular decomposition method for solving least-squares estimation problems. However, for large datasets, SVD is very time consuming and memory demanding in obtaining least squares solutions. In this paper, we propose a least squares estimator based on an iterative divide-and-merge scheme for large-scale estimation problems. The estimator consists of several levels. At each level, the input matrices are subdivided into submatrices. The submatrices are decomposed by SVD respectively and the results are merged into smaller matrices which become the input of the next level. The process is iterated until the resulting matrices are small enough which can then be solved directly and efficiently by the SVD algorithm. However, the iterative divide-and-merge algorithms executed on a single machine is still time demanding on large scale datasets. We propose two distributed algorithms to overcome this shortcoming by permitting several machines to perform the decomposition and merging of the submatrices in each level in parallel. The first one is implemented in MapReduce on the Hadoop distributed platform which can run the tasks in parallel on a collection of computers. The second one is implemented on CUDA which can run the tasks in parallel using the Nvidia GPUs. Experimental results demonstrate that the proposed distributed algorithms can greatly reduce the time required to solve large-squares problems.

The fifth generation (5G) wireless communications technology will be a paradigm shift which does not only provide an explosive increment on the achievable data rate per cell, but also ideally decreases the costs and energy consumption per data link. The engineering requirements of 5G standard can be intuitively interpreted as highly enhanced spectral efficiency and energy efficiency. This thesis focuses on the practical implementation issues of the massive multiple-input multiple-output (MIMO) and energy harvesting systems. To begin with, massive MIMO, as one of the key technologies of 5G systems, can provide enormous enhancement in spectral efficiency. For a practical massive MIMO system, hybrid processing (precoding/combining), by restricting the number of RF chains to far less than the number of antenna elements, can significantly reduce the implementation cost compared to the full-complexity radio frequency (RF) chain configuration. This thesis designs the hybrid RF and baseband precoders/combiners for multi-stream transmission in the point-to-point (P2P) massive MIMO systems, by directly decomposing the pre-designed digital precoder/combiner of a large dimension. The performance of the matrix decomposition based hybrid processing (MD-HP) scheme is near-optimal compared to the singular value decomposition (SVD) based full-complexity processing. In addition, the downlink communication of a massive multiuser MIMO (MU-MIMO) system is also investigated, and a low-complexity hybrid block diagonalization (Hy-BD) scheme is developed to approach the performance of the traditional BD method. We aim to harvest the large array gain through the phase-only RF precoding and combining and then BD processing is performed on the equivalent baseband channel in the massive MU-MIMO scenario. The MD-HP and Hy-BD schemes are examined in both the large Rayleigh fading channels and millimeter wave channels. On the other hand, energy harvesting is an increasingly attractive and renewable source of power for wireless communications devices, which contributes to the enhancement of the system energy efficiency. This thesis also designs the energy cooperation assisted energy harvesting communication between a practical transmitter and receiver, whose hardware circuits consume non-zero power when active. The energy cooperation save-then-transmit (EC-ST) scheme aims to obtain the optimal active time ratio and energy cooperation power for the maximum throughput under additive white Gaussian channels and the minimum outage probability under block Rayleigh fading channels. / Graduate

Rhythmic motion is ubiquitous in nature and technology. Various motions of organisms like the heart beating and walking require stable periodic execution. The stability of the rhythmic execution of human movement can be altered by neurological or orthopedic impairment. In robotics, successful development of legged robots heavily depends on the stability of the controlled limit-cycle. An accurate measure of the stability of rhythmic execution is critical to the diagnosis of several performed tasks like walking in human locomotion. Floquet multipliers have been widely used to assess the stability of a periodic motion. The conventional approach to extract the Floquet multipliers from actual data depends on the least squares method. We devise a new way to measure the Floquet multipliers with reduced bias and estimate orbital stability more accurately. We show that the conventional measure of the orbital stability has bias in the presence of noise, which is inevitable in every experiment and observation. Compared with previous method, the new method substantially reduces the bias, providing acceptable estimate of the orbital stability with fewer cycles even with different noise distributions or higher or lower noise levels. The new method can provide an unbiased estimate of orbital stability within a reasonably small number of cycles. This is important for experiments with human subjects or clinical evaluation of patients that require effective assessment of locomotor stability in planning rehabilitation programs. / Graduate / 2018-11-22

Dans cette thèse, nous nous intéressons à la recherche d'“items” et d'“itemsets” d'intérêt via la décomposition de matrice binaire (Binary Matrix Factorization, BMF) et à la recherche d'objets représentatifs. Pour cela, nous étudions l'état de l'art des techniques de décomposition matricielle. Nous établissons, dans le premier Chapitre, un lien entre BMF et le problème de programmation binaire quadratique sans contraintes (Unconstrained Binary Quadratic Programming, UBQP) afin d'utiliser les algorithmes et heuristiques existant dans la littérature pour UBQP et les appliquer à BMF.Nous proposons dans le Chapitre 2 une nouvelle heuristique adaptée au calcul de BMF. Cette technique efficace optimise les solutions de BMF ligne par ligne (ou colonne par colonne) en inversant 1 bit à chaque fois. En utilisant le lien établi dans le Chapitre 2 qui nous permet d'appliquer les algorithmes et heuristiques d'UBQP à BMF, nous comparons la méthode proposée (1-opt-BMF) avec les heuristiques spécialisées pour UBQP (1-opt-UBQP) ainsi que les heuristiques classiques (1-opt-Standard). Nous montrons ensuite, en théorie et en pratique, l'efficacité de 1-opt-BMF sur une large variété de données publiques. Dans le Chapitre 3, nous nous intéressons au problème de la recherche des itemsets représentatifs en utilisant BMF et 1-opt-BMF. Pour cela, nous considérons dans un premier temps le lien entre le problème de “frequent itemset mining” et BMF, et proposons une nouvelle méthode que nous appelons “Decomposition Itemset Miner” (DIM). Une série d'expérience montre la qualité des résultats obtenus et l'efficacité de notre méthode.Enfinf, nous nous intéressons, dans le Chapitre 4, à la recherche d'objets représentatifs (qui donnent une vue globale sur les données) dans des données de grandes dimensions. Nous examinons les méthodes disponibles dans la littérature en donnant les avantages et les inconvénients de chacune. Ensuite, nous défnissons mathématiquement le problème de sélection d'instance (Instance Selection Problem: ISP) et présentons trois variantes à ce problème ainsi que leur solutions. Dans les expériences, nous montrons que, bien qu'ISP puisse surpasser les autres méthodes dans certains cas, il vaut mieux le considérer en général comme une technique complémentaire dans le cadre de la recherche des objets représentatifs. / This thesis focuses on mining representative items and itemsets using Binary Matrix Factorization (BMF) and instance selection. To accomplish this task, we first, in Chapter 1, consider the BMF problem by studying the literature on matrix decomposition techniques and the state-of-the-art algorithms. Then, we establish a connection between BMF problem and Unconstrained Binary Quadratic Programming (UBQP) problem in order to use UBQP's algorithms and heuristics, available in the literature, in case of BMF solutions. Next, in Chapter 2, we propose a new, efficient heuristic which flips 1 bit at the time in order to improve the solutions of BMF. Using the established link discussed in Chapter 2, which enables us to use heuristics of UBQP, we compare the proposed technique, called 1-opt-BMF with that of UBQP, called 1opt-UBQP as well as the standard approach, called 1-opt-Standard. We then show, theoretically and experimentally, the efficiency of 1-opt-BMF on a wide range of publicly available datasets. Next, in Chapter 3, we explore addressing the problem of finding representative itemsets via BMF. To do that, we first consider the theoretical relation between the frequent itemset mining problem and BMF; while established, we propose a new technique called Decomposition Itemset Miner (DIM). We then design a set of experiments to show the efficiency of DIM and the quality of its results.Finally, in Chapter 4, we consider the problem of finding representative objects (instances) in big, high-dimensional datasets. These objects helps us to find objects providing a global, top-view of the data and are very important in data analysis process. We first study the available methods for finding representative objects and discuss the pros and cons of each. We then formally define the Instance Selection Problem (ISP), provide three variants of that and examine their complexities before providing their solutions. In the experimental section, we show that although the ISP solutions can outperform other methods in some cases, in general it should be considered as a complementary technique in the context of finding representative objects.

Resumo: O objetivo da pesquisa descrita nesta tese foi estudar possíveis aplicações do método das rotações modificadas de Givens na solução de sistemas de equações lineares tipicamente observados em problemas de melhoramento animal. Duas aplicações foram consideradas: a predição de valores genéticos com base em informação fenotípica e genealógica, por meio da metodologia dos modelos mistos; e a predição de valores genéticos com base em informação molecular, obtida pela genotipagem de painéis densos de SNPs. Na primeira aplicação, delineou-se o emprego de um modelo animal reduzido, combinado a uma ordenação do sistema que permitiu uma abordagem multi-frontal de decomposição. As matrizes frontais foram definidas como sendo as partes da triangular superior pertinentes a cada rebanho. Com isso, o problema pôde ser desmembrado em n subproblemas em que n é o número de rebanhos. Um conjunto de programas foi desenvolvido de modo a decompor as matrizes de dados de cada rebanho independentemente, e depois combinar as informações de todos eles na solução do sistema triangular geral, por retro-substituição. Concluiu-se que o método pode ser empregado em um sistema para atualização de predições de valor genético sob modelo animal reduzido, em que se aninham os efeitos de vacas dentro de rebanhos. Na segunda aplicação, comparou-se o emprego das rotações de Givens com o método do Gradiente Conjugado, na solução de sistemas lineares envolvidos na estimação de efeitos de SNPs em valores genéticos. O método das rotações demandou menos tempo de processamento e mais memória. Concluiu-se que, dado o crescente avanço em capacidade computacional, o método das rotações pode ser um método numérico viável e apresenta a vantagem de permitir o cálculo dos erros-padrão das estimativas. / Abstract: The aim of this study was to investigate possible applications of the modified Givens rotations on the solution of linear systems that typically arise in animal breeding problems. Two applications were considered: prediction of breeding values based on phenotypes and relationships, using mixed model methods; and prediction of breeding values based on molecular information, using genotypes from high density SNP chips. In the first application, the use of a reduced animal model, combined with a specific ordering of the system, made it possible to apply a multi-frontal decomposition approach. The frontal matrices were defined as the parts of the upper triangular corresponding to each herd. In this way, the problem could be partitioned into n subproblems, where n is the number of herds. A set of programs was developed in order to factorize the data matrix of each herd independently, and then combine the information from all of them while solving the overall triangular system, by back-substitution. The conclusion was that Givens rotations can be used as a numerical method for updating predicted breeding values under a reduced animal model, if dam effects are nested within herds. In the second application, the modified Givens rotations were compared to the Conjugate Gradient method for solving linear systems that arise in the estimation of SNP effects on breeding values. Givens rotations required less processing time but a greater amount of high speed memory. The conclusion was that, given the increasing rate of advance in computer power, Givens rotations can be regarded as a feasible numerical method which presents the advantage that it allows for the calculation of standard errors of estimates. / Orientador: Sandra Aidar de Queiroz / Coorientador: Luiz Alberto Fries / Coorientador: Flávio Schramm Schenkel / Banca: João Meidanis / Banca: Ricardo da Fonseca / Banca: Roberto Carvalheiro / Banca: Adhemar Sanches / Doutor

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