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.

As automation in the financial service industry continues to advance, online investment advice has emerged as an exciting new field. Vital to the accuracy of such service is the determination of the individual investors’ ability to bear financial risk. To do so, the statistical method of logistic regression is used. The aim of this thesis is to identify factors which are significant in determining a financial risk profile of a retail investor. In other words, the study seeks to map out the relationship between several socioeconomic- and psychometric variables to develop a predictive model able to determine the risk profile. The analysis is based on survey data from respondents living in Sweden. The main findings are that variables such as income, consumption rate, experience of a financial bear market, and various psychometric variables are significant in determining a financial risk profile. / I samband med en ökad automatiseringstrend har digital investeringsrådgivning dykt upp som ett nytt fenomen. Av central betydelse är tjänstens förmåga att bedöma en investerares förmåga till att bära finansiell risk. Logistik regression tillämpas för att bedöma en icke- professionell investerares vilja att bära finansiell risk. Målet med uppsatsen är således att identifiera ett antal faktorer med signifikant förmåga till att bedöma en icke-professionell investerares riskprofil. Med andra ord, så syftar denna uppsats till att studera förmågan hos ett antal socioekonomiska- och psykometriska variabler. För att därigenom utveckla en prediktiv modell som kan skatta en individs finansiella riskprofil. Analysen genomförs med hjälp av en enkätstudie hos respondenter bosatta i Sverige. Den huvudsakliga slutsatsen är att en individs inkomst, konsumtionstakt, tidigare erfarenheter av abnorma marknadsförhållanden, och diverse psykometriska komponenter besitter en betydande förmåga till att avgöra en individs finansiella risktolerans

Biomechanics research investigating the knee kinematics of youth participants is very limited. The most accurate method of measuring knee kinematics utilizes invasive procedures such as bone pins. However, various experimental techniques have improved the accuracy of gait kinematic analyses using minimally invasive methods. In this study, gait trials were conducted with two participants between the ages of 11 and 13 to obtain the knee flexion-extension (FE), adduction-abduction (AA) and internal-external (IE) rotation angles of the right knee. The objectives of this study were to (1) conduct pilot experiments with youth participants to test whether any adjustments were necessary in the experimental methods used for adult gait experiments, (2) apply a Triangular Cosserat Point Element (TCPE) analysis for Soft-Tissue Artifact (STA) correction of knee kinematics with youth participants, and (3) develop a code to conduct a Principal Component Analysis (PCA) to find the PCA-defined flexion axis and calculate knee angles with both STA and PCA-correction for youth participants. The kinematic results were analyzed for six gait trials on a participant-specific basis. The TCPE knee angle results were compared between uncorrected angles and another method of STA correction, Procrustes Solution, with a repeated measures ANOVA of the root mean square errors between each group and a post-hoc Tukey test. The PCA-corrected results were analyzed with a repeated measures ANOVA of the FE-AA correlations from a linear regression analysis between TCPE, PS, PCA-TCPE and PCA-PS angles. The results indicated that (1) youth experiments can be conducted with minor changes to experimental methods used for adult gait experiments, (2) TCPE and PS analyses did not yield statistically different knee kinematic results, and (3) PCA-correction did not reduce FE-AA correlations as predicted.

Early detection and mitigation of wildfires can reduce devastating property damage, firefighting costs, pollution, and loss of life. This thesis proposes the method of Principal Component Analysis (PCA) of images in the temporal domain to identify a smoke plume in wildfires. Temporal PCA is an effective motion detector, and spatial filtering of the output Principal Component images can segment the smoke plume region. The effective use of other image processing techniques to identify smoke plumes and heat plumes are compared. The best attributes of smoke plume detectors and heat plume detectors are evaluated for combination in an improved wildfire detection system. PCA of visible blue images at an image sampling rate of 2 seconds per image effectively exploits a smoke plume signal. PCA of infrared images is the fundamental technique for exploiting a heat plume signal. A system architecture is proposed for the implementation of image processing techniques. The real-world deployment and usability are described for this system.

No / Age progression that involves the reconstruction of facial appearance with a natural ageing effect has several applications. These include the search for missing people and identification of fugitives. The majority of age progression methods reported in the literature are data driven. Hence, such methods learn from training data and utilise statistical models such as 3D morphable models and active appearance models (AAM). Principal component analysis (PCA) which is a vital part of these models has an unfortunate drawback of averaging out texture details. Therefore, they work as a low pass filter and as such many of the face skin deformations and minor details become faded. Interestingly, recent work in 2D and 3D animation has shown that patches of the human face are somewhat similar when compared in isolation. Thus, researchers have proposed generating novel faces by compositing small face patches, usually from large image databases. Following these ideas, we propose a novel age progression model which synthesises aged faces using a hybrid of these two techniques. First, an invertible model of age synthesis is developed using AAM and sparse partial least squares regression (sPLS). Then the texture details of the face are enhanced using the patch-based synthesis approach. Our results show that the hybrid algorithm produces both unique and realistic images. Furthermore, our method demonstrates that the identity and ageing effects of subjects can be more emphasised.

Objective: Patient-specific musculoskeletal models have emerged as a reliable method to study how tibiofemoral joint (TFJ) morphology influences anterior cruciate ligament (ACL) injuries. However, there are no such models for adolescent populations that can be scaled to accommodate growth. To serve as the foundation for such models, the objective of this thesis was therefore to i) build a patient-specific model of natural knee motion in an ACL-injured (ACLi) adolescent sample using joint congruency and ii) to attempt to reconstruct patient-specific simplified articular contacts using principal component analysis (PCA). Design: Twelve magnetic resonance images (MRI) of ACi adolescents were segmented and used to generate spheres of simplified TFJ articulations. A congruence-based optimization algorithm was used to determine the envelope of tibiofemoral configurations that optimize joint congruency. Descriptive statistics were used to compare model outputs to existing literature. Combinations of marker trajectories and anthropometrics were used to determine the feasibility of reconstructing articular sphere simplifications using PCA. Root-mean squared error (RMSE) was used to compare predicted sphere contacts to MRI-extracted contacts. Results: Average knee joint anglesof the femur with respect to the tibia was slightly abducted and externally rotated, with a range of motion (ROM) of 1.60º ± 0.66 and 7.64 º ± 2.34 across 102° of flexion respectively. The percent elongation of the posterior cruciate ligament (PCL) varied the most across participants (8.65 ± 6.2%) compared to the ACL (2.34 ± 2.1%), MCL (1.41 ± 0.5%) and LCL (1.75 ± 1.6%) respectively. The combination of femur markers and anthropometrics was able to reconstruct simplified tibiofemoral articulations the best, but not within 5 mm of RMSE. Conclusion: Inter-subject variability in passive kinematic motion derived from patient-specific morphology highlights the need for personalized and accessible musculoskeletal models in growing populations. Furthermore, simplified distal femur morphology can be reconstructed from anthropometrics and marker positions, but proximal tibia morphology requires more information.

<p dir="ltr">In most theoretical studies on missing data analysis, data is typically assumed to be missing according to a specific probabilistic model. However, such assumption may not accurately reflect real-world situations, and sometimes missing is not purely random. In this thesis, our focus is on analyzing incomplete data matrices without relying on any probabilistic model assumptions for the missing schemes. To characterize a missing scheme deterministically, we employ a graph whose adjacency matrix is a binary matrix that indicates whether each matrix entry is observed or not. Leveraging its graph properties, we mathematically represent the missing pattern of an incomplete data matrix and conduct a theoretical analysis of how this non-random missing pattern affects the solvability of specific problems related to incomplete data. This dissertation primarily focuses on three types of incomplete data problems characterized by their low-rank nature: structured prediction, matrix completion, and sparse PCA.</p><p dir="ltr">First, we investigate a basic structured prediction problem, which involves recovering binary node labels on a fixed undirected graph, where noisy binary observations corresponding to edges are given. Essentially, this setting parallels a simple binary rank-1 symmetric matrix completion problem, where missing entries are determined by a fixed undirected graph. Our aim is to establish the fundamental limit bounds of this problem, revealing a close association between the limits and graph properties, such as connectivity.</p><p dir="ltr">Second, we move on to the general low-rank matrix completion problem. In this study, we establish provable guarantees for exact and approximate low-rank matrix completion problems that can be applied to any non-random missing pattern, by utilizing the observation graph corresponding to the missing scheme. We theoretically and experimentally show that the standard constrained nuclear norm minimization algorithm can successfully recover the true matrix when the observation graph is well-connected and has similar node degrees. We also verify that matrix completion is achievable with a near-optimal sample complexity rate when the observation graph has uniform node degrees and its adjacency matrix has a large spectral gap.</p><p dir="ltr">Finally, we address the sparse PCA problem, featuring an approximate low-rank attribute. Missing data is common in situations where sparse PCA is useful, such as single-cell RNA sequence data analysis. We propose a semidefinite relaxation of the non-convex $\ell_1$-regularized PCA problem to solve sparse PCA on incomplete data. We demonstrate that the method is particularly effective when the observation pattern has favorable properties. Our theory is substantiated through synthetic and real data analysis, showcasing the superior performance of our algorithm compared to other sparse PCA approaches, especially when the observed data pattern has specific characteristics.</p>

<p>Preclinical rodent models were used to investigate the neural signatures of strategy change during the delay discounting decision making task. Neural signatures were assessed using advanced statistical techniques (de-mixed principal component analysis). </p>