Browsing by Subject "Canonical correlation analysis"
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Item Infinite dimensional discrimination and classification(Texas A&M University, 2007-09-17) Shin, HyejinModern data collection methods are now frequently returning observations that should be viewed as the result of digitized recording or sampling from stochastic processes rather than vectors of finite length. In spite of great demands, only a few classification methodologies for such data have been suggested and supporting theory is quite limited. The focus of this dissertation is on discrimination and classification in this infinite dimensional setting. The methodology and theory we develop are based on the abstract canonical correlation concept of Eubank and Hsing (2005), and motivated by the fact that Fisher's discriminant analysis method is intimately tied to canonical correlation analysis. Specifically, we have developed a theoretical framework for discrimination and classification of sample paths from stochastic processes through use of the Loeve-Parzen isomorphism that connects a second order process to the reproducing kernel Hilbert space generated by its covariance kernel. This approach provides a seamless transition between the finite and infinite dimensional settings and lends itself well to computation via smoothing and regularization. In addition, we have developed a new computational procedure and illustrated it with simulated data and Canadian weather data.Item Prediction of Tortilla Quality Using Multivariate Modeling of Kernel, Flour and Dough Properties(2014-01-10) Jondiko, Tom OAdvances in high-throughput wheat breeding techniques have resulted in the need for rapid, accurate and cost-effective means to predict tortilla making performance for larger numbers of early generation wheat lines. Currently, the most reliable approach is to process tortillas. This approach is laborious, time consuming, expensive and requires large sample size. This study used a multivariate discriminant analysis to predict tortilla quality using kernel, flour and dough properties. A discriminant rule (suitability = diameter > 165mm + day 16 flexibility score >3.0) was used to classify wheat lines for suitability in making good quality tortillas. One hundred eighty seven hard winter wheat (HWW) varieties from Texas were evaluated for kernel (hardness, diameter, and weight), flour (protein content, fractions and composition), dough (compression force, extensibility and stress relaxation from TA-XT2i) and tortilla properties (diameter, rheology and flexibility). The first three principal components explained 58% of variance. Multivariate normal distribution of the data was determined (Shapiro-Wilk p > 0.05). PCA identified significant correlation between stress relaxation force and rollability. Canonical correlation analysis revealed significant correlation between kernel and tortilla properties (p? = 0.75), kernel diameter and weight contributed the highest to this correlation. Flour and tortilla properties were highly correlated (p? = 0.74). Glutenin to Gliadin ratio (GGratio), IPP and peak time contributed highest to this correlation and can explain > 60% of variability in tortilla texture (force, distance and work to rupture). The second canonical variate of flour properties is a measure of flour protein content and can explain 26% of the variability in tortilla rollability. Dough and tortilla properties were significantly correlated (p? = 0.82, 0.68, 0.54, 0.38 and 0.29). Dough stress relaxation force after 25 seconds is negatively correlated with tortilla diameter (r = - 0.73). Kernel hardness, diameter and weight are the best predictors of tortilla texture after 16 days. Glutenin to gliadin ratio and IPP contributed significantly to tortilla texture. This is the first study to identify the contribution of protein content on tortilla rollability score. Dough extensibility can explain 37% of tortilla rollability. Stress relaxation is the best predictor of tortilla diameter. Tortilla quality variation is attributed to kernel, flour, and dough properties. Logistic regression and stepwise variable selection identified an optimum model comprised of kernel hardness, GGratio, dough extensibility and compression force as the most important variables. Cross-validation indicated 83% prediction efficiency for the model. This emphasizes the feasibility and practicality of the model using variables that are easily and quickly measured. This is the first model that can be used to simultaneously predict both tortilla diameter and rollability. It will be a useful tool for the flat bread wheat breeding programs, wheat millers, tortilla processors and wheat marketers in the United States of America.