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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- Creators: Turaga, Pavan
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 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
Description
Despite the fact that machine learning supports the development of computer vision applications by shortening the development cycle, finding a general learning algorithm that solves a wide range of applications is still bounded by the ”no free lunch theorem”. The search for the right algorithm to solve a specific problem is driven by the problem itself, the data availability and many other requirements.
Automated visual inspection (AVI) systems represent a major part of these challenging computer vision applications. They are gaining growing interest in the manufacturing industry to detect defective products and keep these from reaching customers. The process of defect detection and classification in semiconductor units is challenging due to different acceptable variations that the manufacturing process introduces. Other variations are also typically introduced when using optical inspection systems due to changes in lighting conditions and misalignment of the imaged units, which makes the defect detection process more challenging.
In this thesis, a BagStack classification framework is proposed, which makes use of stacking and bagging concepts to handle both variance and bias errors. The classifier is designed to handle the data imbalance and overfitting problems by adaptively transforming the
multi-class classification problem into multiple binary classification problems, applying a bagging approach to train a set of base learners for each specific problem, adaptively specifying the number of base learners assigned to each problem, adaptively specifying the number of samples to use from each class, applying a novel data-imbalance aware cross-validation technique to generate the meta-data while taking into account the data imbalance problem at the meta-data level and, finally, using a multi-response random forest regression classifier as a meta-classifier. The BagStack classifier makes use of multiple features to solve the defect classification problem. In order to detect defects, a locally adaptive statistical background modeling is proposed. The proposed BagStack classifier outperforms state-of-the-art image classification techniques on our dataset in terms of overall classification accuracy and average per-class classification accuracy. The proposed detection method achieves high performance on the considered dataset in terms of recall and precision.
Automated visual inspection (AVI) systems represent a major part of these challenging computer vision applications. They are gaining growing interest in the manufacturing industry to detect defective products and keep these from reaching customers. The process of defect detection and classification in semiconductor units is challenging due to different acceptable variations that the manufacturing process introduces. Other variations are also typically introduced when using optical inspection systems due to changes in lighting conditions and misalignment of the imaged units, which makes the defect detection process more challenging.
In this thesis, a BagStack classification framework is proposed, which makes use of stacking and bagging concepts to handle both variance and bias errors. The classifier is designed to handle the data imbalance and overfitting problems by adaptively transforming the
multi-class classification problem into multiple binary classification problems, applying a bagging approach to train a set of base learners for each specific problem, adaptively specifying the number of base learners assigned to each problem, adaptively specifying the number of samples to use from each class, applying a novel data-imbalance aware cross-validation technique to generate the meta-data while taking into account the data imbalance problem at the meta-data level and, finally, using a multi-response random forest regression classifier as a meta-classifier. The BagStack classifier makes use of multiple features to solve the defect classification problem. In order to detect defects, a locally adaptive statistical background modeling is proposed. The proposed BagStack classifier outperforms state-of-the-art image classification techniques on our dataset in terms of overall classification accuracy and average per-class classification accuracy. The proposed detection method achieves high performance on the considered dataset in terms of recall and precision.
ContributorsHaddad, Bashar Muneer (Author) / Karam, Lina (Thesis advisor) / Li, Baoxin (Committee member) / He, Jingrui (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2019