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.
Displaying 1 - 10 of 26
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- All Subjects: Mathematics
- All Subjects: Sparse matrices
- Creators: Nishimura, Joel
- Creators: Turaga, Pavan
Description
Effective modeling of high dimensional data is crucial in information processing and machine learning. Classical subspace methods have been very effective in such applications. However, over the past few decades, there has been considerable research towards the development of new modeling paradigms that go beyond subspace methods. This dissertation focuses on the study of sparse models and their interplay with modern machine learning techniques such as manifold, ensemble and graph-based methods, along with their applications in image analysis and recovery. By considering graph relations between data samples while learning sparse models, graph-embedded codes can be obtained for use in unsupervised, supervised and semi-supervised problems. Using experiments on standard datasets, it is demonstrated that the codes obtained from the proposed methods outperform several baseline algorithms. In order to facilitate sparse learning with large scale data, the paradigm of ensemble sparse coding is proposed, and different strategies for constructing weak base models are developed. Experiments with image recovery and clustering demonstrate that these ensemble models perform better when compared to conventional sparse coding frameworks. When examples from the data manifold are available, manifold constraints can be incorporated with sparse models and two approaches are proposed to combine sparse coding with manifold projection. The improved performance of the proposed techniques in comparison to sparse coding approaches is demonstrated using several image recovery experiments. In addition to these approaches, it might be required in some applications to combine multiple sparse models with different regularizations. In particular, combining an unconstrained sparse model with non-negative sparse coding is important in image analysis, and it poses several algorithmic and theoretical challenges. A convex and an efficient greedy algorithm for recovering combined representations are proposed. Theoretical guarantees on sparsity thresholds for exact recovery using these algorithms are derived and recovery performance is also demonstrated using simulations on synthetic data. Finally, the problem of non-linear compressive sensing, where the measurement process is carried out in feature space obtained using non-linear transformations, is considered. An optimized non-linear measurement system is proposed, and improvements in recovery performance are demonstrated in comparison to using random measurements as well as optimized linear measurements.
ContributorsNatesan Ramamurthy, Karthikeyan (Author) / Spanias, Andreas (Thesis advisor) / Tsakalis, Konstantinos (Committee member) / Karam, Lina (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2013
Description
Image understanding has been playing an increasingly crucial role in vision applications. Sparse models form an important component in image understanding, since the statistics of natural images reveal the presence of sparse structure. Sparse methods lead to parsimonious models, in addition to being efficient for large scale learning. In sparse modeling, data is represented as a sparse linear combination of atoms from a "dictionary" matrix. This dissertation focuses on understanding different aspects of sparse learning, thereby enhancing the use of sparse methods by incorporating tools from machine learning. With the growing need to adapt models for large scale data, it is important to design dictionaries that can model the entire data space and not just the samples considered. By exploiting the relation of dictionary learning to 1-D subspace clustering, a multilevel dictionary learning algorithm is developed, and it is shown to outperform conventional sparse models in compressed recovery, and image denoising. Theoretical aspects of learning such as algorithmic stability and generalization are considered, and ensemble learning is incorporated for effective large scale learning. In addition to building strategies for efficiently implementing 1-D subspace clustering, a discriminative clustering approach is designed to estimate the unknown mixing process in blind source separation. By exploiting the non-linear relation between the image descriptors, and allowing the use of multiple features, sparse methods can be made more effective in recognition problems. The idea of multiple kernel sparse representations is developed, and algorithms for learning dictionaries in the feature space are presented. Using object recognition experiments on standard datasets it is shown that the proposed approaches outperform other sparse coding-based recognition frameworks. Furthermore, a segmentation technique based on multiple kernel sparse representations is developed, and successfully applied for automated brain tumor identification. Using sparse codes to define the relation between data samples can lead to a more robust graph embedding for unsupervised clustering. By performing discriminative embedding using sparse coding-based graphs, an algorithm for measuring the glomerular number in kidney MRI images is developed. Finally, approaches to build dictionaries for local sparse coding of image descriptors are presented, and applied to object recognition and image retrieval.
ContributorsJayaraman Thiagarajan, Jayaraman (Author) / Spanias, Andreas (Thesis advisor) / Frakes, David (Committee member) / Tepedelenlioğlu, Cihan (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2013
Description
We solve the problem of activity verification in the context of sustainability. Activity verification is the process of proving the user assertions pertaining to a certain activity performed by the user. Our motivation lies in incentivizing the user for engaging in sustainable activities like taking public transport or recycling. Such incentivization schemes require the system to verify the claim made by the user. The system verifies these claims by analyzing the supporting evidence captured by the user while performing the activity. The proliferation of portable smart-phones in the past few years has provided us with a ubiquitous and relatively cheap platform, having multiple sensors like accelerometer, gyroscope, microphone etc. to capture this evidence data in-situ. In this research, we investigate the supervised and semi-supervised learning techniques for activity verification. Both these techniques make use the data set constructed using the evidence submitted by the user. Supervised learning makes use of annotated evidence data to build a function to predict the class labels of the unlabeled data points. The evidence data captured can be either unimodal or multimodal in nature. We use the accelerometer data as evidence for transportation mode verification and image data as evidence for recycling verification. After training the system, we achieve maximum accuracy of 94% when classifying the transport mode and 81% when detecting recycle activity. In the case of recycle verification, we could improve the classification accuracy by asking the user for more evidence. We present some techniques to ask the user for the next best piece of evidence that maximizes the probability of classification. Using these techniques for detecting recycle activity, the accuracy increases to 93%. The major disadvantage of using supervised models is that it requires extensive annotated training data, which expensive to collect. Due to the limited training data, we look at the graph based inductive semi-supervised learning methods to propagate the labels among the unlabeled samples. In the semi-supervised approach, we represent each instance in the data set as a node in the graph. Since it is a complete graph, edges interconnect these nodes, with each edge having some weight representing the similarity between the points. We propagate the labels in this graph, based on the proximity of the data points to the labeled nodes. We estimate the performance of these algorithms by measuring how close the probability distribution of the data after label propagation is to the probability distribution of the ground truth data. Since labeling has a cost associated with it, in this thesis we propose two algorithms that help us in selecting minimum number of labeled points to propagate the labels accurately. Our proposed algorithm achieves a maximum of 73% increase in performance when compared to the baseline algorithm.
ContributorsDesai, Vaishnav (Author) / Sundaram, Hari (Thesis advisor) / Li, Baoxin (Thesis advisor) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2013
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
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