NonLinear Principal Component Analysis (NLPCA) using three-hidden-layer feed-forward neural networks can produce solutions that over-fit the data and are non-unique. These problems have been dealt with by subjective methods during the network training. This study shows that these problems are intrinsic due to the three-hidden-layer architecture. A simplified two-hidden-layer feed-forward neural network that has no encoding layer and no bottleneck and output biases is proposed. This new, compact NLPCA model alleviates these problems without employing the subjective methods and is called quasi-objective. The compact NLPCA is applied to the zonal winds observed at seven pressure levels between 10 and 70 hPa in the equatorial stratosphere to represent the Quasi-Biennial Oscillation (QBO) and investigate its variability and structure. The two nonlinear principal components of the dataset offer a clear picture of the QBO. In particular, their structure shows that the QBO phase consists of a predominant 28.4-month cycle that is modulated by an 11-year cycle and a longer-period cycle. The significant difference in variability of the winds between cold and warm seasons and the tendency for a seasonal synchronization of the QBO phases are well captured. The one-dimensional NLPCA approximation of the dataset provides a better representation of the QBO than the classical principal component analysis and a better description of the asymmetry of the QBO between westerly and easterly shear zones and between their transitions. The compact NLPCA is then applied to the Arctic Oscillation (AO) index and aforementioned zonal winds to investigate the relationship of the AO with the QBO. The NLPCA of the AO index and zonal-winds dataset shows clearly that, of covariation of the two oscillations, the phase defined by the two nonlinear principal components progresses with a predominant 28.4-month periodicity, plus the 11-year and longer-period modulations. Large positive values of the AO index occur when westerlies prevail near the middle and upper levels of the equatorial stratosphere. Large negative values of the AO index arise when easterlies occupy over half the layer of the equatorial stratosphere.

NonLinear Principal Component Analysis (NLPCA) using three-hidden-layer feed-forward neural networks can produce solutions that over-fit the data and are non-unique. These problems have been dealt with by subjective methods during the network training. This study shows that these problems are intrinsic due to the three-hidden-layer architecture. A simplified two-hidden-layer feed-forward neural network that has no encoding layer and no bottleneck and output biases is proposed. This new, compact NLPCA model alleviates these problems without employing the subjective methods and is called quasi-objective. The compact NLPCA is applied to the zonal winds observed at seven pressure levels between 10 and 70 hPa in the equatorial stratosphere to represent the Quasi-Biennial Oscillation (QBO) and investigate its variability and structure. The two nonlinear principal components of the dataset offer a clear picture of the QBO. In particular, their structure shows that the QBO phase consists of a predominant 28.4-month cycle that is modulated by an 11-year cycle and a longer-period cycle. The significant difference in variability of the winds between cold and warm seasons and the tendency for a seasonal synchronization of the QBO phases are well captured. The one-dimensional NLPCA approximation of the dataset provides a better representation of the QBO than the classical principal component analysis and a better description of the asymmetry of the QBO between westerly and easterly shear zones and between their transitions. The compact NLPCA is then applied to the Arctic Oscillation (AO) index and aforementioned zonal winds to investigate the relationship of the AO with the QBO. The NLPCA of the AO index and zonal-winds dataset shows clearly that, of covariation of the two oscillations, the phase defined by the two nonlinear principal components progresses with a predominant 28.4-month periodicity, plus the 11-year and longer-period modulations. Large positive values of the AO index occur when westerlies prevail near the middle and upper levels of the equatorial stratosphere. Large negative values of the AO index arise when easterlies occupy over half the layer of the equatorial stratosphere. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

Tornado outbreaks have significant human impact, so it is imperative forecasts of these phenomena are accurate. As a synoptic setup lays the foundation for a forecast, synoptic-scale aspects of Storm Prediction Center (SPC) outbreak forecasts of varying accuracy were assessed. The percentages of the number of tornado outbreaks within SPC 10% tornado probability polygons were calculated. False alarm events were separately considered. The outbreaks were separated into quartiles using a point-in-polygon algorithm. Statistical composite fields were created to represent the synoptic conditions of these groups and facilitate comparison. Overall, temperature advection had the greatest differences between the groups. Additionally, there were significant differences in the jet streak strengths and amounts of vertical wind shear. The events forecasted with low accuracy consisted of the weakest synoptic-scale setups. These results suggest it is possible that events with weak synoptic setups should be regarded as areas of concern by tornado outbreak forecasters.

Optical flow and its extensions have been widely used in motion detection and computer vision. In the study, principal component analysis (PCA) is applied to analyze optical flows for better motion detection performance. The joint optical flow and PCA approach can efficiently detect moving objects and suppress small turbulence. It is effective in both static and dynamic background. It is particularly useful for motion detection from outdoor videos with low quality and small moving objects. Experimental results demonstrate that this approach outperforms other existing methods by extracting the moving objects more completely with lower false alarms. Saving strategies are developed to reduce computational complexity of optical flow calculation and PCA. Graphic processing unit (GPU)-based parallel implementation is developed, which shows excellent speed up performance.

Arrow's Impossibility Theorem outlines the flaws that effect any voting system that attempts to order a set of objects. For its entire history, American college football has been determining its champion based on a voting system. Much of the literature has dealt with why the voting system used is problematic, but there does not appear to be a large collection of work done to create a better, mathematical process. More generally, the inadequacies of ranking in football are a manifestation of the problem of ranking a set of objects. Herein, principal component analysis is used as a tool to provide a solution for the problem, in the context of American college football. To show its value, rankings based on principal component analysis are compared against the rankings used in American college football. / Thesis / Master of Science (MSc) / The problem of ranking is a ubiquitous problem, appearing everywhere from Google to ballot boxes. One of the more notable areas where this problem arises is in awarding the championship in American college football. This paper explains why this problem exists in American college football, and presents a bias-free mathematical solution that is compared against how American college football awards their championship.

There has been an exponential increase in satellite image data availability. Image data are now collected with different spatial, spectral, and temporal resolutions. Image fusion techniques are used extensively to combine different images having complementary information into one single composite. The fused image has rich information that will improve the performance of image analysis algorithms. Pansharpening is a pixel level fusion technique used to increase the spatial resolution of the multispectral image using spatial information from the high resolution panchromatic image while preserving the spectral information in the multispectral image. Resolution merge, image integration, and multisensor data fusion are some of the equivalent terms used for pansharpening. Pansharpening techniques are applied for enhancing certain features not visible in either of the single data alone, change detection using temporal data sets, improving geometric correction, and enhancing classification. Various pansharpening algorithms are available in the literature, and some have been incorporated in commercial remote sensing software packages such as ERDAS Imagine® and ENVI®. The performance of these algorithms varies both spectrally and spatially. Hence evaluation of the spectral and spatial quality of the pansharpened images using objective quality metrics is necessary. In this thesis, quantitative metrics for evaluating the quality of pansharpened images have been developed. For this study, the Intensity-Hue-Saturation (IHS) based sharpening, Brovey sharpening, Principal Component Analysis (PCA) based sharpening and a Wavelet-based sharpening method is used.

"The goal of this thesis is to extend the theory and practice of matrix completion algorithms, and how they can be utilized, improved, and scaled up to handle large data sets. Matrix completion involves predicting missing entries in real-world data matrices using the modeling assumption that the fully observed matrix is low-rank. Low-rank matrices appear across a broad selection of domains, and such a modeling assumption is similar in spirit to Principal Component Analysis. Our focus is on large scale problems, where the matrices have millions of rows and columns. In this thesis we provide new analysis for the convergence rates of matrix completion techniques using convex nuclear norm relaxation. In addition, we validate these results on both synthetic data and data from two real-world domains (recommender systems and Internet tomography). The results we obtain show that with an empirical, data-inspired understanding of various parameters in the algorithm, this matrix completion problem can be solved more efficiently than some previous theory suggests, and therefore can be extended to much larger problems with greater ease. "

Retinal pigment epithelium (RPE) is a principal site of pathogenesis in age-related macular de-generation (AMD). AMD is a main source of vision loss even blindness in the elderly and there is no effective treatment right now. Our aim is to describe the relationship between the morphology of RPE cells and the age and genotype of the eyes. We use principal component analysis (PCA) or functional principal component method (FPCA), support vector machine (SVM), and random forest (RF) methods to analyze the morphological data of RPE cells in mouse eyes to classify their age and genotype. Our analyses show that amongst all morphometric measures of RPE cells, cell shape measurements (eccentricity and solidity) are good for classification. But combination of cell shape and size (perimeter) provide best classification.

Due to the association of heart diseases and the patterns of the diastoles and systoles of heart in left ventricle, we analyze and classify the data gathered form Kaohsiung Veterans General Hospital by using the cardiology ultrasound images. We make use of the differences between the gray-scale values of diastoles and systoles in left ventricle to evaluate the function of heart. Following Chen (2011) and Kao (2011), we modified the way about the reduction and alignment of the image data. We also add some more subjects into the study. We treat images in two manners, saving the parts of concern. Since the ultrasound image after transformation to data form is expressed as a high-dimensional matrix, the principal component analysis is adapted to retain the important factors and reduce the dimensions. In this work, we compare the loadings calculated by the usual principal and sparse principal component analysis, then the factor scores are used to carry out the discriminant analysis and discuss the accuracy of classification. By the statistical methods in this work, the accuracy, sensitivity and specificity of the original classifications are over 80% and the cross validations are over 60%.

Magnetic Resonance Imaging (MRI) can obtain the tissues of in vivo non-invasively. Proton MR Spectroscopy uses the resonance principle to collect the signals of proton and transforms them to spectrums. It provides information of metabolites in patient¡¦s brain for doctors to observe the change of pathology. Observing the metabolites of brain abscess patients is most important process in clinical diagnosis and treatment. Then, doctors use different spectrums of echo time (TE) to enhance the accuracy in the diagnosis. In our study, we use independent component analysis (ICA) to analyze MR spectroscopy. After analyzing, the independent components represent the elements which compose the input data. Then, we use the projection which is mentioned by Ssu-Ying Lu¡¦s Thesis to help us observe the relationship between independent components and spectrums of patients. We also discuss the result of spectrums with using ICA and PCA and discover some questions (whether it need to do scale normalization before inputting data or not, the result of scale normalization doesn¡¦t expect, and the peak in some independent components confuse us by locating in indistinct place) to discuss and to find possible reason after experiments.