Theses and dissertations

This collection includes both ASU Theses and Dissertations, submitted by graduate students, and the Barrett, Honors College theses submitted by undergraduate students. 

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Recursive Bayesian Estimation on Projective Spaces: Theoretical Foundations and Practical Algorithms

Description
This thesis develops geometrically and statistically rigorous foundations for multivariate analysis and bayesian inference posed on grassmannian manifolds. Requisite to the development of key elements of statistical theory in a geometric realm are closed-form, analytic expressions for many differential geometric objects, e.g., tangent vectors, metrics, geodesics, volume forms. The first…

This thesis develops geometrically and statistically rigorous foundations for multivariate analysis and bayesian inference posed on grassmannian manifolds. Requisite to the development of key elements of statistical theory in a geometric realm are closed-form, analytic expressions for many differential geometric objects, e.g., tangent vectors, metrics, geodesics, volume forms. The first part of this thesis is devoted to a mathematical exposition of these. In particular, it leverages the classical work of Alan James to derive the exterior calculus of differential forms on special grassmannians for invariant measures with respect to which integration is permissible. Motivated by various multi-­sensor remote sensing applications, the second part of this thesis describes the problem of recursively estimating the state of a dynamical system propagating on the Grassmann manifold. Fundamental to the bayesian treatment of this problem is the choice of a suitable probability distribution to a priori model the state. Using the Method of Maximum Entropy, a derivation of maximum-­entropy probability distributions on the state space that uses the developed geometric theory is characterized. Statistical analyses of these distributions, including parameter estimation, are also presented. These probability distributions and the statistical analysis thereof are original contributions. Using the bayesian framework, two recursive estimation algorithms, both of which rely on noisy measurements on (special cases of) the Grassmann manifold, are the devised and implemented numerically. The first is applied to an idealized scenario, the second to a more practically motivated scenario. The novelty of both of these algorithms lies in the use of thederived maximum­entropy probability measures as models for the priors. Numerical simulations demonstrate that, under mild assumptions, both estimation algorithms produce accurate and statistically meaningful outputs. This thesis aims to chart the interface between differential geometry and statistical signal processing. It is my deepest hope that the geometric-statistical approach underlying this work facilitates and encourages the development of new theories and new computational methods in geometry. Application of these, in turn, will bring new insights and bettersolutions to a number of extant and emerging problems in signal processing.
ContributorsCrider, Lauren N (Author) / Cochran, Douglas (Thesis advisor) / Kotschwar, Brett (Committee member) / Scharf, Louis (Committee member) / Taylor, Thomas (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2021

LYFE: Learning Your Formed Experiences

Description

In this thesis, I explored the interconnected ways in which human experience can shape and be shaped by environments of the future, such as interactive environments and spaces, embedded with sensors, enlivened by advanced algorithms for sensor data processing. I have developed an abstract representational experience into the vast and…

In this thesis, I explored the interconnected ways in which human experience can shape and be shaped by environments of the future, such as interactive environments and spaces, embedded with sensors, enlivened by advanced algorithms for sensor data processing. I have developed an abstract representational experience into the vast and continual journey through life that shapes how we can use sensory immersion. The experimental work was housed in the iStage: an advanced black box space in the School of Arts, Media, and Engineering, which consists of video cameras, motion capture systems, spatial audio systems, and controllable lighting and projector systems. The malleable and interactive space of the iStage transformed into a reflective tool in which to gain insight into the overall shared, but very individual, emotional odyssey. Additionally, I surveyed participants after engaging in the experience to better understand their perceptions and interpretations of the experience. With the responses of participants' experiences and collective reflection upon the project I can begin to think about future iterations and how they might contain applications in health and/or wellness.
ContributorsHaagen, Jordan (Author) / Turaga, Pavan (Thesis director) / Drummond Otten, Caitlin (Committee member) / Barrett, The Honors College (Contributor) / Arts, Media and Engineering Sch T (Contributor) / School of Human Evolution & Social Change (Contributor)
Created2022-05
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Haagen Final Project (Spring 2022)

ContributorsHaagen, Jordan (Author) / Turaga, Pavan (Thesis director) / Drummond Otten, Caitlin (Committee member) / Barrett, The Honors College (Contributor) / Arts, Media and Engineering Sch T (Contributor)
Created2022-05
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Final Installation Showcase

ContributorsHaagen, Jordan (Author) / Turaga, Pavan (Thesis director) / Drummond Otten, Caitlin (Committee member) / Barrett, The Honors College (Contributor) / Arts, Media and Engineering Sch T (Contributor)
Created2022-05