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.

Dabaoshan Mine Site (DMS) is the biggest polymetallic mine in South China. The Hengshi River receives acid mine drain (AMD) waste leaching from the tailings pond and run-off from the treatment plant which flows into the Wengjiang River, Beijiang River, before discharging into the Pearl River. Discharge from the mine site results in heavy metal contamination  near the mine and lower riparian areas along the river course. The present study focuses on the distribution and mobilization of As, Cd, Pb and Zn along the Hengshi River, groundwater, fluvial sediments and soil, with a special focus on As due to its high toxicity and the fact that mining is one of the main anthropogenic sources of As. Heavy metals, grain-size, XRD, %C and S analysis were done in order to determine the physicochemical characteristics of samples. The results were used for geochemical modeling (PHREEQ) and statistical (PCA) analysis to understand and predict the behavior of heavy metals. Potential ecological risk assessment was conducted by calculating contamination degree of heavy metals in soil and sediment and it’s theoretical toxical risk. Near the tailings pond, heavy metal concentration was 2-100 times higher than chinese surface water standard for agricultural use, which decreases downstream, mianly due to dilution, sorption, precipitation and co-precipitation with minerals. In groundwater, heavy metals concentration remained low. Due to the fact that most wells were abandoned or only for household use, potential risk from groundwater is low. The soils were disturbed by industrial or agricultural activities, and heavy metal concentration varied without showing any specific trend along the river. The potential ecological risk of heavy metals are ranked as: Cd>As>Cu>Pb>Zn in sediments; Cd>Cu>Pb>As>Zn in soil. As(Ⅲ) was the predominant species in surface water, and minerals identified in soil and sediment. Arsenic from most sites exceeded the Chinese soil standard for development land. Although arsenic was assumed to have a moderate ecological risk in sediments and low risk in soils, anthropogenic activities, such as land use change and untreated sewage discharge, might reduce and release arsenic into the environment, which poses potential risk to local residents.

In my first chapter I follow the methodology put forth by Bohn(1998), the market-based sustainability method to measure whether the sovereign debt is sustainable or not. I work with a panel of 125 countries for 26 years and along with incorporate different institutions ratings by ICRG’s political risk ratings. In my analysis I find out that the debt on average is sustainable for countries up to certain extent and thus giving us an inverted U shape debt-exports curve. I use country exports to find out if the debt is sustainable or not. I also find that better institutions do give an edge to countries when it comes to borrowing as it lowers the risk expectations on the lenders part. The findings do vary based on the country’s income level and based on its geographical location.

The purpose of this research is to identify whether synoptic patterns and variables were statistically significantly different between East Coast United States track bomb and ordinary cyclogenesis. The differentiation of East Coast track bomb and ordinary cyclogenesis was completed through the utility of the principal component analysis, a K-means cluster analysis, a subjective composite analysis, and permutation tests. The principal component analysis determined that there were three leading modes of variability within the bomb and ordinary composites. The K-means cluster analysis was used to cluster these leading patterns of variability into three distinct clusters for the bomb and ordinary cyclones. The subjective composite analysis, created by averaging all the variables from each cyclone in each cluster, identified several synoptic variables and patterns to be objectively compared through permutation tests. The permutation tests revealed that synoptic variables and patterns associated with bomb cyclogenesis statistically significantly differ from ordinary cyclogenesis.

In this dissertation, the general problem of the dimensionality reduction of hyperspectral imagery is considered. Data dimension can be reduced through compression, in which an original image is encoded into bitstream of greatly reduced size; through application of a transformation, in which a high-dimensional space is mapped into a low-dimensional space; and through a simple process of subsampling, wherein the number of pixels is reduced spatially during image acquisition. All three techniques are investigated in the course of the dissertation. For data compression, an approach to calculate an operational bitrate for JPEG2000 in conjunction with principal component analysis is proposed. It is shown that an optimal bitrate for such a lossy compression method can be estimated while maintaining both class separability as well as anomalous pixels in the original data. On the other hand, the transformation paradigm is studied for spectral dimensionality reduction; specifically, dataindependent random spectral projections are considered, while the compressive projection principal component analysis algorithm is adopted for data reconstruction. It is shown that, by incorporating both spectral and spatial partitioning of the original data, reconstruction accuracy can be improved. Additionally, a new supervised spectral dimensionality reduction approach using a sparsity-preserving graph is developed. The resulting sparse graph-based discriminant analysis is seen to yield superior classification performance at low dimensionality. Finally, for spatial dimensionality reduction, a simple spatial subsampling scheme is considered for a multitemporal hyperspectral image sequence, such that the original image is reconstructed using a sparse dictionary learned from a prior image in the sequence.

The goal of this study is to develop a smoke detecting algorithm using digital image processing techniques on multi-spectral (visible & infrared) video. By utilizing principal component analysis (PCA) followed by spatial filtering of principal component images the location of smoke can be accurately identified over a period of exposure time with a given frame capture rate. This result can be further analyzed with consideration of wind factor and fire detection range to determine if a fire is present within a scene. Infrared spectral data is shown to contribute little information concerning the smoke signature. Moreover, finalized processing techniques are focused on the blue spectral band as it is furthest away from the infrared spectral bands and because it experimentally yields the largest footprint in the processed principal component images in comparison to other spectral bands. A frame rate of .5 images/sec (1 image every 2 seconds) is determined to be the maximum such that temporal variance of smoke can be captured. The study also shows eigenvectors corresponding to the principal components that best represent smoke and are valuable indications of smoke temporal signature. Raw video data is taken through rigorous pre-processing schemes to align frames from respective spectral band both spatially and temporally. A multi-paradigm numerical computing program, MATLAB, is used to match the field of view across five spectral bands: Red, Green, Blue, Long-Wave Infrared, and Mid-Wave Infrared. Extracted frames are aligned temporally from key frames throughout the data capture. This alignment allows for more accurate digital processing for smoke signature. v Clustering analysis on RGB and HSV value systems reveal that color alone is not helpful to segment smoke. The feature values of trees and other false positives are shown to be too closely related to features of smoke for in solely one instance in time. A temporal principal component transform on the blue spectral band eliminates static false positives and emphasizes the temporal variance of moving smoke in images with higher order. A threshold adjustment is applied to a blurred blue principal component of non-unity principal component order and smoke results can be finalized using median filtering. These same processing techniques are applied to difference images as a more simple and traditional technique for identifying temporal variance and results are compared.