The aim of this study is evaluation of using multi-dimensional statistical analyses methods as a tool for simulations of reliability of distribution network. Prefered methods are a cluster analysis (CLU) and a principal component analysis (PCA). CLU is used for a division of objects on the basis of their signs and a calculation of the distance between objects into groups whose characteristics should be similar. The readout can reveal a secret structure in data. PCA is used for a location of a structure in signs of multi-dimensional matrix data. Signs present separate quantities describing the given object. PCA uses a dissolution of a primary matrix data to structural and noise matrix data. It concerns the transformation of primary matrix data into new grid system of principal components. New conversion data are called a score. Principal components generating orthogonal system of new position. Distribution network from the aspect of reliability can be characterized by a number of new statistical quantities. Reliability indicators might be: interruption numbers, interruption time. Integral reliability indicators might be: system average interruption frequency index (SAIFI) and system average interruption duration index (SAIDI). In conclusion, there is a comparison of performed SAIFI simulation according to negatively binomial division and provided values from a distribution company. It is performed a test at description of sign dependences and outlet divisions.

The aim of this work was to develop the method for classification of ECG beats into two classes, namely ischemic and non-ischemic beats. Heart beats (P-QRS-T cycles) selected from animals orthogonal ECGs were preprocessed and used as the input signals. Spectral features vectors (values of cross spectral coherency), principal component and HRV parameters were derived from the beats. The beats were classified using feedforward multilayer neural network designed in Matlab. Classification performance reached the value approx. from 87,2 to 100%. Presented results can be suitable in future studies aimed at automatic classification of ECG.

This semester thesis is focused on automated measurement of ECG signal. The theoretical part describes the rise and options ECG signal. Furthermore, the issue is staged principal components analysis, whose output is used as input signal for seasons. They describe the basic methods used in measurement to ECG signal. The practical part is designed in measurement algorithm for ECG signal that has been tested on basic CSE database. The results are discussed in the conclusion.

This diploma thesis is dealing with the detection of blood vessels pulsation in retinal sequences. The goal is to create an algorithm for objective evaluation of pulsation in retinal video sequences.

Principal Component Analysis (PCA) is a widely used dimensional reduction method that aims to find a low dimension sub space of highly correlated data for its major information to be used in further analysis. Machine learning methods based on PCA are popular in high dimensional data analysis, such as video and image processing. In video processing, the Robust PCA (RPCA), which is a modified method of the traditional PCA, has good properties in separating moving objects from the background, but it may have difficulties in separating those when light intensity of the background varies significantly in time. To overcome the difficulties, a modified PCA method, called Regression PCA (RegPCA), is proposed. The method is developed by combining the traditional PCA and regression approaches together, and it can be easily combined with RPCA for video processing. We focus the presentation of RegPCA with the combination of RPCA on video processing and find that it is more reliable than RPCA only. We use RegPCA to separate moving object from the background in a color video and get a better result than that given by RPCA. In the implementation, we first derive the explanatory variables by the background information. we then process a number of frames of the video and use those as a set of response variables. We remove the impact of the background by regressing the response against the explanatory variables by a regression model. The regression model provides a set of residuals, which can be further analyzed by RPCA. We compare the results of RegRPCA against those of RPCA only. It is evident that the moving objects can be completely removed from the background using our method but not in RPCA. Note that our result is based on a combination of RegPCA with RPCA. Our proposed method provides a new implementation of RPCA under the framework of regression approaches, which can be used to account for the impact of risk factors. This problem cannot be addressed by the application of RPCA only.

COVID-19 has affected the lives of millions of people worldwide. This thesis includes two statistical studies on the response to COVID-19. The first study explores the impact of lockdown timing on COVID-19 transmission across US counties. We used functional principal component analysis to extract COVID-19 transmission patterns from county-wise case counts, and used supervised machine learning to identify risk factors, with the timing of lockdowns being the most significant. In particular, we found a critical time point for lockdowns, as lockdowns implemented after this time point were associated with significantly more cases and faster spread. The second study proposes an adaptive sample pooling strategy for efficient COVID-19 diagnostic testing. When testing a cohort, our strategy dynamically updates the prevalence estimate after each test if possible, and uses the updated information to choose the optimal pool size for the subsequent test. Simulation studies show that compared to traditional pooling strategies, our strategy reduces the number of tests required to test a cohort and is more resilient to inaccurate prevalence inputs. We have developed a dashboard application to guide the clinicians through the test procedure when using our strategy. / Graduate / 2023-05-27

Wireless communications technologies have experienced an exponential development during the last decades. 5G is a prominent exponent whose one of its crucial component is the Massive MIMO technology. By supporting multiple streams of signals it allows a revamped signal reconstruction in terms of mobile traffic size, data rate, latency, and reliability. In this thesis work, we isolated this technology into a SIMOapproach (Single-Input Multiple-Output) to explore a Machine Learning modeling to address the so-called Channel Prediction problem. Generally, the algorithms available to perform Channel Estimation in FDD and TDD deployments incur computational complexity downsides and require explicit feedback from client devices, which is typically prohibitive. This thesis work focuses on Channel Prediction by aims of employing Machine and deep Learning models in order to reduce the computational complexity by further relying in statistical modeling/learning. We explored the cross-Frequency Subband prediction intra-TTI (Transmission Time Interval) by means of proposing 3 three models. These intended to leverage frequency Multipath Components dependencies along TTIs. The first two ones are Probabilistic Principal Components Analysis (PPCA) and its Bayesiancounterpart, Bayesian Principal Components Analysis (BPCA). Then, we implemented Deep Learning Variational Encoder-Decoder (VED) architecture. These three models are intended to deal with the hugely high-dimensional space of the 4 datasets used by its intrinsic dimensionality reduction. The PPCA method was on average five times better than the VED alternative in terms of MSE accounting for all the datasets used.

Early alcohol, tobacco and drug use prior to 18 years old are comorbid and correlated. This study included 6239 adults with major depressive disorder (MDD) in the past year and 72,010 controls from the combined data of 2013 and 2014 National Survey on Drug Use and Health (NSDUH). To deal with multicollinearity existing among 17 variables related to early alcohol, tobacco and drug use prior to 18 years old, we used principal component analysis (PCA) to infer PC scores and then use weighted multiple logistic regression analyses to estimate the associations of potential factors and PC scores with MDD. The odds ratios (ORs) with 95% confidence intervals (CIs) were estimated. The overall prevalence of MDD was 6.7%. The first four PCs could explain 57% of the total variance. Weighted multiple logistic regression showed that PC1 (a measure of psychotherapeutic drugs and illicit drugs other than marijuana use), PC2 (a measure of cocaine and hallucinogens), PC3 (a measure of early alcohol, cigarettes, and marijuana use), and PC4 (a measure of cigar, smokeless tobacco use and illicit drugs use) revealed significant associations with MDD (OR = 1.12, 95% CI = 1.08–1.16, OR = 1.08, 95% CI = 1.04–1.12, OR = 1.13, 95% CI = 1.07–1.18, and OR = 1.15, 95% CI = 1.09–1.21, respectively). In conclusion, PCA can be used to reduce the indicators in complex survey data. Early alcohol, tobacco and drug use prior to 18 years old were found to be associated with increased odds of adult MDD.

Raman spectroscopy is a noninvasive technique that can provide complex information on the vibrational state of the molecules. It defines the unique fingerprint that allow the identification of the various chemical components within a given sample. The aim of the following thesis work is to analyze Raman maps related to three pairs of different cells, highlighting differences and similarities through multivariate algorithms. The first pair of analyzed cells are human embryonic stem cells (hESCs), while the other two pairs are induced pluripotent stem cells (iPSCs) derived from T lymphocytes and keratinocytes, respectively. Although two different multivariate techniques were employed, ie Principal Component Analysis and Cluster Analysis, the same results were achieved: the iPSCs derived from T-lymphocytes show a higher content of genetic material both compared with the iPSCs derived from keratinocytes and the hESCs . On the other side, equally evident, was that iPS cells derived from keratinocytes assume a molecular distribution very similar to hESCs.

While multivariate data analysis is concerned with data in the form of random vectors, functional data analysis goes one big step farther, focusing on data that are infinite-dimensional, such as curves, shapes and images. We focus on functional data that are measured over time across multiple subjects. The first part of the thesis focuses on spatially correlated functional data. This correlation is modeled by correlating functional principal component scores. We propose a Spatial Principal Analysis by Conditional Expectation framework to explicitly estimate spatial correlations and reconstruct individual curves. This approach works even when the observed data per curve are extremely sparse. Assuming spatial stationarity, empirical between-curve correlations are calculated as the ratio of eigenvalues of the smoothed covariance surface Cov(Xi(s),Xi(t)) and cross-covariance surface Cov(Xi(s),Xj(t)). Then a parametric spatial correlation model is employed to fit empirical correlations. Finally, principal component scores are estimated to reconstruct the sparsely observed curves. This framework could naturally accommodate arbitrary covariance structures, but there is an enormous reduction in computation if one can assume the separability of temporal and spatial components. We propose hypothesis tests to examine the separability and isotropy effect of spatial correlation. Simulation studies and applications of empirical data show improvements in the curve reconstruction using our framework over the method where curves are assumed to be independent. In addition, asymptotic properties of estimates are discussed in details. In the second part of this work, we present a new approach to factor rotation for functional data. This is achieved by rotating the functional principal components toward a predefined space of periodic functions designed to decompose the total variation into components that are nearly-periodic and nearly-aperiodic with a predefined period. We show that the factor rotation can be obtained by the calculation of canonical correlations between appropriate spaces. Moreover, we demonstrate that our proposed rotations provide stable and interpretable results in the presence of highly complex covariance. This work is motivated by the goal of finding interpretable sources of variability in a gridded time series of vegetation index measurements obtained from remote sensing, and we demonstrate our methodology through the application of factor rotation of this data.