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Principal Components Analysis is a standard tool in data analysis, widely used in data-rich fields such as computer vision, data mining, bioinformatics, and econometrics. For a set of vectors in n dimensions and a natural number k less than n, the method returns a subspace of dimension k whose average squared distance to that set is as small as possible. Besides saving computation by reducing the dimension, projecting to this subspace can often reveal structure that was hidden in high dimension. This thesis considers several novel extensions of PCA, which provably reveals hidden structure where standard PCA fails to do so. First, we consider Robust PCA, which prevents a few points, possibly corrupted by an adversary, from having a large effect on the analysis. When applied to learning noisy logconcave mixture models, the algorithm requires only slightly more separation between component means than is required for the noiseless case. Second, we consider Isotropic PCA, which can go beyond the first two moments in identifying ``interesting' directions in data. The method leads to the first affine-invariant algorithm that can provably learn mixtures of Gaussians in high dimensions, improving significantly on known results. Thirdly, we define the ``Subgraph Parity Tensor' of order r of a graph and reduce the problem of finding planted cliques in random graphs to the problem of finding the top principal component of this tensor.

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Safe drinking water is paramount to a healthy society. Close to a hundred contaminants are regulated by the government. Utilities are using chloramines to disinfect water to reduce harmful byproducts that may present themselves with the use of chlorine alone. Using chlorine and ammonia to disinfect, ammonia oxidizing bacteria can present themselves in an unsuspecting utilities distribution network. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

Thesis (M.S.)--Missouri University of Science and Technology, 2009. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed November 25, 2009) Includes bibliographical references.

Thesis (M.A.)--West Virginia University, 2002. / Title from document title page. Document formatted into pages; contains ix, 61 p. : col. ill., col. maps. Includes abstract. Includes bibliographical references (p. 40-42).

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.

Thesis (M.S.)--Mississippi State University. Department of Electrical and Computer Engineering. / Title from title screen. Includes bibliographical references.

Thesis (M.S.)--University of Akron, Dept. of Biomedical Engineering, 2008. / "December, 2008." Title from electronic thesis title page (viewed 12/12/2009) Advisor, Dale H. Mugler; Committee members, Daniel B. Sheffer, Bruce C. Taylor; Department Chair, Daniel B. Sheffer; Dean of the College, George K. Haritos; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.

This dissertation develops statistical and data mining based methods for insurance fraud detection. Insurance fraud is very costly and has become a world concern in recent years. Great efforts have been made to develop models to identify potentially fraudulent claims for special investigations. In a broader context, insurance fraud detection is a classification task. Both supervised learning methods (where a dependent variable is available for training the model) and unsupervised learning methods (where no prior information of dependent variable is available for use) can be potentially employed to solve this problem. First, an unsupervised method is developed to improve detection effectiveness. Unsupervised methods are especially pertinent to insurance fraud detection since the nature of insurance claims (i.e., fraud or not) is very costly to obtain, if it can be identified at all. In addition, available unsupervised methods are limited and some of them are computationally intensive and the comprehension of the results may be ambiguous. An empirical demonstration of the proposed method is conducted on a widely used large dataset where labels are known for the dependent variable. The proposed unsupervised method is also empirically evaluated against prevalent supervised methods as a form of external validation. This method can be used in other applications as well. Second, another set of learning methods is then developed based on the proposed unsupervised method to further improve performance. These methods are developed in the context of a special class of data mining methods, active learning. The performance of these methods is also empirically evaluated using insurance fraud datasets. Finally, a method is proposed to estimate the fraud rate (i.e., the percentage of fraudulent claims in the entire claims set). Since the true nature of insurance claims (and any level of fraud) is unknown in most cases, there has not been any consensus on the estimated fraud rate. The proposed estimation method is designed based on the proposed unsupervised method. Implemented using insurance fraud datasets with the known nature of claims (i.e., fraud or not), this estimation method yields accurate estimates which are superior to those generated by a benchmark naïve estimation method. / text