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Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
Symmetric positive definite (SPD) matrices have become fundamental computational objects in many areas. It is often of interest to average a collection of symmetric positive definite matrices. This dissertation investigates different...
Use of real, authentic whole tasks in training has been the focus of current instructional theories and practical educational approaches (Merrill, 2002; Reigeluth, 1999; van Merrienboer & Kirschner, 2001). However, teaching authentic...
Several waves of calls for writing centers to address digital and multimodal texts exist, dating back to the 1980s. While these conversations gained momentum at the turn of the century with the popularization of multiliteracy centers and...
Chan-Vese is a level set method that simultaneously evolves a level set surface and fits locally constant intensity models for the interior and exterior regions to minimize a Mumford-Shah integral. However, the length-based contour...
Quasi-Newton methods have gained popularity across various domains, providing efficient iterative algorithms for finding optimal solutions to unconstrained optimization problems. Their limited- memory variants offer advantages in terms...
Embodied interactions and learning have garnered a lot of interest among researchers and game designers in past years, especially with the recent development of consumer-level body sensory devices like the Microsoft Kinect. This study...
This dissertation proposes a Riemannian approach for computing geodesics for closed curves in elastic shape space. The application of two Riemannian unconstrained optimization algorithms, Riemannian Steepest Descent (RSD) algorithm and...
This dissertation considers the optimization problems that are in the form of minX∈Fv f(x)+λ∥X∥1, where f is smooth, Fv = {X ∈ Rn×q : XTX = Iq, v ∈ span(X)}, and v is a given positive vector. Clustering analysis is a fundamental machine...
There has been a great deal of research devoted to computer vision related assistive technologies. Unfortunately, this area of research has not produced many usable solutions. The long cane and the guard dog are still far more useful...
This dissertation uses Riemannian optimization theory to increase our understanding of the role extraction problem and algorithms. Recent ideas of using the low-rank projection of the neighborhood pattern similarity measure and our...
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. In this dissertation, ...
Tukey's depth offers a powerful tool for nonparametric inference and estimation but also encounters serious computational and methodological difficulties in modern statistical data analysis. This article studies how to generalize Tukey's...
Artificial Neural Networks form the basis of very powerful learning methods. It has been observed that a naive application of fully connected neural networks often leads to overfitting. In an attempt to circumvent this issue, a prior...
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