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
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
In this thesis we consider the problem of facial expression recognition (FER) from video sequences. Our method is based on subspace representations and Grassmann manifold based learning. We use Local Binary Pattern (LBP) at the frame level for representing the facial features. Next we develop a model to represent the video sequence in a lower dimensional expression subspace and also as a linear dynamical system using Autoregressive Moving Average (ARMA) model. As these subspaces lie on Grassmann space, we use Grassmann manifold based learning techniques such as kernel Fisher Discriminant Analysis with Grassmann kernels for classification. We consider six expressions namely, Angry (AN), Disgust (Di), Fear (Fe), Happy (Ha), Sadness (Sa) and Surprise (Su) for classification. We perform experiments on extended Cohn-Kanade (CK+) facial expression database to evaluate the expression recognition performance. Our method demonstrates good expression recognition performance outperforming other state of the art FER algorithms. We achieve an average recognition accuracy of 97.41% using a method based on expression subspace, kernel-FDA and Support Vector Machines (SVM) classifier. By using a simpler classifier, 1-Nearest Neighbor (1-NN) along with kernel-FDA, we achieve a recognition accuracy of 97.09%. We find that to process a group of 19 frames in a video sequence, LBP feature extraction requires majority of computation time (97 %) which is about 1.662 seconds on the Intel Core i3, dual core platform. However when only 3 frames (onset, middle and peak) of a video sequence are used, the computational complexity is reduced by about 83.75 % to 260 milliseconds at the expense of drop in the recognition accuracy to 92.88 %.
ContributorsYellamraju, Anirudh (Author) / Chakrabarti, Chaitali (Thesis advisor) / Turaga, Pavan (Thesis advisor) / Karam, Lina (Committee member) / Arizona State University (Publisher)
Created2014
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
This thesis introduces new techniques for clustering distributional data according to their geometric similarities. This work builds upon the optimal transportation (OT) problem that seeks global minimum cost for matching distributional data and leverages the connection between OT and power diagrams to solve different clustering problems. The OT formulation is based on the variational principle to differentiate hard cluster assignments, which was missing in the literature. This thesis shows multiple techniques to regularize and generalize OT to cope with various tasks including clustering, aligning, and interpolating distributional data. It also discusses the connections of the new formulation to other OT and clustering formulations to better understand their gaps and the means to close them. Finally, this thesis demonstrates the advantages of the proposed OT techniques in solving machine learning problems and their downstream applications in computer graphics, computer vision, and image processing.
ContributorsMi, Liang (Author) / Wang, Yalin (Thesis advisor) / Chen, Kewei (Committee member) / Karam, Lina (Committee member) / Li, Baoxin (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2020