The research in this dissertation addresses reduced rank adaptive signal processing, with specific emphasis on the multistage Wiener filter (MWF). The MWF is a generalization of the classical Wiener filter that performs a stage-by-stage decomposition based on orthogonal projections. Truncation of this decomposition produces a reduced rank filter with many benefits, for example, improved performance. This dissertation extends knowledge of the MWF in four areas. The first area is rank and sample support compression. This dissertation examines, under a wide variety of conditions, the size of the adaptive subspace required by the MWF (i.e., the rank) as well as the required number of training samples. Comparisons are made with other algorithms such as the eigenvector-based principal components algorithm. The second area investigated in this dissertation concerns "soft stops", i.e., the insertion of diagonal loading into the MWF. Several methods for inserting loading into the MWF are described, as well as methods for choosing the amount of loading. The next area investigated is MWF rank selection. The MWF will outperform the classical Wiener filter when the rank is properly chosen. This dissertation presents six approaches for selecting MWF rank. The algorithms are compared to one another and an overall design space taxonomy is presented. Finally, as digital modelling capabilities become more sophisticated there is emerging interest in augmenting adaptive processing algorithms to incorporate prior knowledge. This dissertation presents two methods for augmenting the MWF, one based on linear constraints and a second based on non-zero weight vector initialization. Both approaches are evaluated under ideal and perturbed conditions. Together the research described in this dissertation increases the utility and robustness of the multistage Wiener filter. The analysis is presented in the context of adaptive array processing, both spatial array processing and space-time adaptive processing for airborne radar. The results, however, are applicable across the entire spectrum of adaptive signal processing applications. / Ph. D.

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Type 2 diabetes (T2DM) is a growing concern worldwide, particularly among Aboriginal Canadians. Diet has been associated with diabetes risk, and dietary pattern analysis (DPA) provides a method in which whole dietary patterns may be explored in relation to disease. Factor analysis (FA) and reduced rank regression (RRR) of data from the Sandy Lake Health and Diabetes Project identified patterns associated with incident T2DM at follow-up. A RRR-derived pattern characterized by tea, hot cereal, and peas, and low intake of high-sugar foods and beef was positively associated with diabetes; however, the relationship was attenuated with adjustment for age and other covariates. A FA-derived pattern characterized by processed foods was positively associated with incident T2DM in a multivariate model (OR=1.38; CIs: 1.02, 1.86 per unit), suggesting intake of processed foods may predict T2DM risk.

The primary objective of this study was to assess the relationship between dietary patterns with diabetes and mortality risk from all-cause and cardiovascular disease while controlling for the confounding effects of fitness. The secondary objective was to examine the combined effects of dietary patterns and fitness on chronic disease and mortality risk. Participants consisted of 13,621 men and women from the Aerobics Center Longitudinal Study who completed a standardized medical examination and 3-day diet record between 1987 and 1999. Reduced rank regression was used to identify dietary patterns that were predictive of unfavorable profiles of cholesterol, white blood cell count, glucose, mean arterial pressure, HDL-cholesterol, uric acid, triglycerides, and body mass index. One primary dietary pattern emerged, which was labeled the “Unhealthy Eating Index”. This pattern was characterized by a large consumption of processed meat, red meat, white potato products, non-whole grains, added fat, and a small consumption of non-citrus fruits. After adjustment for covariates, the odds ratio for diabetes and the hazard ratio for all-cause mortality were 2.55 (95% confidence interval: 1.81-3.58) and 1.40 (1.02-1.91) in the highest quintile of the Unhealthy Eating Index when compared to the lowest quintile, respectively. After controlling for fitness, these risk estimates were reduced by 51.6% and 55.0%. The Unhealthy Eating Index was not a significant predictor of cardiovascular disease mortality before or after controlling for fitness. Examining the combined effects of dietary patterns and fitness revealed that both variables were independent predictors of diabetes (Ptrend <0.0001), while fitness (Ptrend <0.0001) but not unhealthy eating (Ptrend=0.071) significantly predicted all-cause mortality risk. These results suggest that both diet and fitness must be considered when studying disease. / Thesis (Master, Community Health & Epidemiology) -- Queen's University, 2009-07-08 07:11:06.809

Type 2 diabetes (T2DM) is a growing concern worldwide, particularly among Aboriginal Canadians. Diet has been associated with diabetes risk, and dietary pattern analysis (DPA) provides a method in which whole dietary patterns may be explored in relation to disease. Factor analysis (FA) and reduced rank regression (RRR) of data from the Sandy Lake Health and Diabetes Project identified patterns associated with incident T2DM at follow-up. A RRR-derived pattern characterized by tea, hot cereal, and peas, and low intake of high-sugar foods and beef was positively associated with diabetes; however, the relationship was attenuated with adjustment for age and other covariates. A FA-derived pattern characterized by processed foods was positively associated with incident T2DM in a multivariate model (OR=1.38; CIs: 1.02, 1.86 per unit), suggesting intake of processed foods may predict T2DM risk.

Submitted by LUCAS HENRIQUE BRITO SALES null (lucash.b.s@hotmail.com) on 2017-07-31T16:19:43Z No. of bitstreams: 1 Dissertação FINAL_Lucas Brito.pdf: 2624281 bytes, checksum: 4b18f17d4f492f2f78b7d31bebab7f64 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-08-03T15:04:42Z (GMT) No. of bitstreams: 1 sales_lhb_me_jabo.pdf: 2624281 bytes, checksum: 4b18f17d4f492f2f78b7d31bebab7f64 (MD5) / Made available in DSpace on 2017-08-03T15:04:42Z (GMT). No. of bitstreams: 1 sales_lhb_me_jabo.pdf: 2624281 bytes, checksum: 4b18f17d4f492f2f78b7d31bebab7f64 (MD5) Previous issue date: 2017-06-14 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / A análise de componentes principais (PCA) e análise de fatores (FA) são amplamen-te utilizadas no processamento de dados visando a redução da dimensionalidade. No entanto, poucos são os estudos que empregou estes métodos em um conjunto de características importantes em bovinos da raça nelore com a finalidade de mode-lar a estrutura de (co)variância dos dados. O objetivo deste estudo foi estimar pa-râmetros genéticos para as características de crescimento, carcaça e qualidade da carne em machos Nelore, utilizando diferentes modelos multi-características visando a redução da dimensionalidade dos dados. Um total de 3.865; 4.121; 4.109; 4.188; 4.213; 3.320 e 16.575 registros de peso da carcaça quente (PCQ), área de olho de lombo (AOL), espessura de gordura subcutânea (EGS), escore de marmorização (MARM), maciez, mensurada pela força de cisalhamento (SF), lipídios (LP) e peso ao sobreano (PS), respectivamente, foram usados. As análises foram realizadas por meio de cinco modelos: multi-característica padrão, três modelos de posto reduzido ajustando os primeiros três (PC3), quatro (PC4) e cinco (PC5) componentes princi-pais genéticos e um modelo utilizando análise de fatores com três (FA3) fatores. Os modelos foram comparados pelo Critério de Informação de Akaike (AIC) e Critério Bayesiano de Schwarz (BIC), levando em consideração o número de parâmetros. Foram considerados para todos os modelos os efeitos aleatórios genético aditivo direto e residual, e os efeitos fixos do grupo de contemporâneos e o efeito linear da idade do animal ao abate como covariável, exceto para peso ao sobreano. Os mo-delos de análise de fatores e componentes principais genéticos selecionados por ambos os critérios de seleção foram o PC3 (BIC), PC4 (AIC) e o FA3 (AIC e BIC), com 46, 50 e 53 parâmetros, respectivamente. No entanto, o modelo que mais se aproximou do modelo multi-característica padrão foi o PC4, sendo então, o mais indicado devido a semelhança das estimativas de (co)variância. As estimativas de herdabilidade variaram de 0,06 (LP) a 0,31 (AOL) com MV e 0,04 (LP) a 0,30 (AOL) com o PC4. As maiores estimativas de correlações genéticas foram entre as carac-terísticas PCQ x SF, PCQ x PS e MARM x LP, sendo similar nos modelos MV e PC4. As maiores estimativas de correlações fenotípicas foram entre as característi-cas de peso e AOL (PS x SF), (PS x AOL) e (SF x AOL). Em geral, foram necessá-rios quatro componentes principais para modelar a estrutura das (co)variâncias ge-néticas para as características de crescimento, carcaça e qualidade da carne. O modelo de posto reduzido indicado pelo o AIC (PC4) reduziu o número de parâme-tros a serem estimados em 21,4%, sem diminuir a qualidade do ajuste. / Principal component (PCA) and factor analysis (FA) are widely used in data processing to reduce dimensionality. However, few studies have used these methods in a set of important traits in Nelore cattle for the purpose of modeling the covariance structure data. The aim of this study was to estimate genetic parameters for growth, carcass and meat quality traits in Nellore males, using different multivariate models to reduce the dimensionality data. A total of 3.865; 4.121; 4.109; 4.188; 4.123 3.320 and 16.575 records, hot carcass weight (HCW), 12-13th rib eye area (REA), backfat thickness (BF), marbling score (MS), warner-wraztler wear force (WBSF), lipid content (LC), and weight at 550 days (W550), respectively, were used. The analyzes were performed using five models: standard multi-characteristic, three reduced-rank models, and adjusted the first three (PC3), four (PC4) and five (PC5) genetic main components, and a model using factor analysis with three (FA3) factors. The models were compared by the Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (BIC), taking into account the parameters number. The random effects of the direct and residual additive genetic and the fixed effects of the contemporaneous group and the linear effect of animal age on slaughter were considered as covariate, except for yearling weight. The analysis models of genetic factors and main components selected by both selection criteria were PC3 (BIC), PC4 (AIC) and FA3 (AIC and BIC), with 46, 50 and 53 parameters, respectively. However, the model that most approached the standard multi-characteristic model was PC4, and is therefore most appropriate due to the similarity of covariance estimates. Estimates of heritability ranged from 0.06 (LP) to 0.31 (AOL) with MV and 0.04 (LP) to 0.30 (AOL) with PC4. The highest estimates of genetic correlations were among the characteristics PCQ x SF, PCQ x PS and MARM x LP, being similar in the MV and PC4 models. The highest estimates of phenotypic correlations were among the weight and AOL (PS x SF), (PS x AOL) and (SF x AOL) traits. In general, four main components were required to model the structure of the genetic covariances for growth, carcass and meat quality traits. The reduced rank model indicated by the AIC (PC4) reduced the parameters number to be estimated by 21.4%, without decreasing the quality of the adjustment. / CNPq: 184428-1

In many high dimensional problems, the dependence structure among the variables can be quite complex. An appropriate use of the regularization techniques coupled with other classical statistical methods can often improve estimation and prediction accuracy and facilitate model interpretation, by seeking a parsimonious model representation that involves only the subset of revelent variables. We propose two regularized stochastic regression approaches, for efficiently estimating certain sparse dependence structure in the data. We first consider a multivariate regression setting, in which the large number of responses and predictors may be associated through only a few channels/pathways and each of these associations may only involve a few responses and predictors. We propose a regularized reduced-rank regression approach, in which the model estimation and rank determination are conducted simultaneously and the resulting regularized estimator of the coefficient matrix admits a sparse singular value decomposition (SVD). Secondly, we consider model selection of subset autoregressive moving-average (ARMA) modelling, for which automatic selection methods do not directly apply because the innovation process is latent. We propose to identify the optimal subset ARMA model by fitting a penalized regression, e.g. adaptive Lasso, of the time series on its lags and the lags of the residuals from a long autoregression fitted to the time-series data, where the residuals serve as proxies for the innovations. Computation algorithms and regularization parameter selection methods for both proposed approaches are developed, and their properties are explored both theoretically and by simulation. Under mild regularity conditions, the proposed methods are shown to be selection consistent, asymptotically normal and enjoy the oracle properties. We apply the proposed approaches to several applications across disciplines including cancer genetics, ecology and macroeconomics.

In this era of big data, multivariate time-series (MTS) data are prevalent in diverse domains and often high dimensional. However, there have been limited studies of building a capable classifier with MTS via classical machine learning methods that can deal with the double curse of dimensionality due to high variable dimension and long time series (large sample size). In this thesis, we propose two approaches to address this problem for multiclass classification with high dimensional MTS. Both approaches leverage the dynamics of an MTS captured by non-parametric modeling of its spectral density function. In the first approach, we introduce the reduced-rank spectral classifier (RRSC), which utilizes low-rank estimation and some new discrimination functions. We illustrate the efficacy of the RRSC with both simulations and real applications. For binary classification, we establish the consistency of the RRSC and provide an asymptotic formula for the misclassification error rates, under some regularity conditions. The second approach concerns the development of the random projection ensemble classifier for time series (RPECTS). This method first applies dimension reduction in the time domain via projecting the time-series variables into some low dimensional space, followed by measuring the disparity via some novel base classifier between the data and the candidate generating processes in the projected space. We assess the classification performance of our new approaches by simulations and compare them with some existing methods using real applications. Finally, we elaborate two R packages that implement the aforementioned methods.

The research presented in this dissertation is on the development and application of advanced reduced rank adaptive signal processing techniques for high data rate wireless code division multiple access (CDMA) communications systems. This is an important area of research in the field of wireless communications. Current systems are moving towards the use of multiple simultaneous users in a given channel to increase system capacity as well as spatial and/or temporal diversity for improved performance in the presence of multipath and fading channels. Furthermore, to accommodate the demand for higher data rates, fast signal processing algorithms are required, which often translate into blind signal detection and estimation and the desire for optimal, low complexity detection techniques. The research presented here shows how minimum mean square error (MMSE) receivers implemented via the multistage Wiener filter (MWF) can be employed at the receiving end of a CDMA system to perform multiuser detection (MUD) or interference suppression (IS) with no loss in performance and significant signal subspace compression better than any previous reduced rank techniques have shown. This is important for optimizing performance because it implies a reduction in the number of required samples, so it lessens the requirement that the channel be stationary for a time duration long enough to obtain enough samples for an accurate MMSE estimate. The structure of these receivers is derived for synchronous and asynchronous systems for a multipath environment, and then it is shown that implementation of the receiver in a reduced rank subspace results in no loss in performance over full rank methods. It is also shown in some instances that reduced rank exceeds full rank performance. Multiuser detectors are also studied, and the optimal reduced rank detector is shown to be equivalent to a bank of parallel single user detectors performing interference suppression (IS). The performance as a function of rank for parallel and joint multiuser detectors are compared. The research is then extended to include joint space-code (i.e. a joint multiuser detector) and joint space-time processing algorithms which employ receiver diversity for low complexity diversity gain. Non-linear techniques, namely serial interference cancellation (SIC) and parallel interference cancellation (PIC), will also be studied. The conventional matched filter correlator will be replaced by the MWF, thereby incorporating IS at each stage of the interference canceller for improved performance. A closed form expression is derived for the probability of error, and performance gains are evaluated. It will be further shown how the receiver structure can be extended when space-time codes are employed at the transmitter for additional diversity gain with minimal impact on complexity. The MMSE solution is derived and implemented via the MWF with some examples. It is believed that these new techniques will have a significant impact on the design of fourth generation (4G) and beyond cellular CDMA systems. / Ph. D.

The research presented in this dissertation is on the development of advanced reduced rank adaptive signal processing for airborne radar space-time adaptive processing (STAP) and steering vector mismatch robustness. This is an important area of research in the field of airborne radar signal processing since practical STAP algorithms should be robust against various kinds of mismatch errors. The clutter return in an airborne radar has widely spread Doppler frequencies; therefore STAP, a two-dimensional adaptive filtering algorithm is required for effective clutter and jamming cancellation. Real-world effects in nonhomogeneous environments increase the number of adaptive degrees of freedom required to adequately suppress interference. The increasing computational complexity and the need to estimate the interference from a limited sample support make full rank STAP impractical. The research presented here shows that the reduced rank multistage Wiener filter (MWF) provides significant subspace compression better than any previous techniques in a nonhomogeneous environment. In addition, the impact of steering vector mismatch will also be examined on the MWF. In an airborne radar environment, it is well known that calibration errors and steering vector mismatch can seriously degrade adaptive array performance and result in signal cancellation. These errors can be caused by many non-ideal factors such as beam steering angle errors, multipath propagation, and phase errors due to array imperfections. Since the MWF centrally features the steering vector on its formulation, it is important to assess the impact of steering vector mismatch. In this dissertation, several novel techniques for increasing robustness are examined and applied to the MWF. These include derivative constraints, quiescent pattern control (QPC) techniques, and covariance matrix tapers (CMT). This research illustrates that a combination of CMT and QPC, denoted CMTQ, is very effective at mitigating the impact of steering vector mismatch. Use of CMTQ augmentation provides the steering vector mismatch robustness that we desire while improving the reduced-rank and reduced sample characteristics of the MWF. Results using Monte Carlo simulations and experimental Multichannel Airborne Radar Measurements (MCARM) data confirm that the use of CMTQ gives superior performance to steering vector errors at a much reduced rank and sample support as compared to conventional techniques. / Ph. D.