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  Partner: UNT Libraries
 Department: Department of Mathematics
 Collection: UNT Theses and Dissertations
Nonparametric Estimation of Receiver Operating Characteristic Surfaces Via Bernstein Polynomials

Nonparametric Estimation of Receiver Operating Characteristic Surfaces Via Bernstein Polynomials

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Date: December 2012
Creator: Herath, Dushanthi N.
Description: Receiver operating characteristic (ROC) analysis is one of the most widely used methods in evaluating the accuracy of a classification method. It is used in many areas of decision making such as radiology, cardiology, machine learning as well as many other areas of medical sciences. The dissertation proposes a novel nonparametric estimation method of the ROC surface for the three-class classification problem via Bernstein polynomials. The proposed ROC surface estimator is shown to be uniformly consistent for estimating the true ROC surface. In addition, it is shown that the map from which the proposed estimator is constructed is Hadamard differentiable. The proposed ROC surface estimator is also demonstrated to lead to the explicit expression for the estimated volume under the ROC surface . Moreover, the exact mean squared error of the volume estimator is derived and some related results for the mean integrated squared error are also obtained. To assess the performance and accuracy of the proposed ROC and volume estimators, Monte-Carlo simulations are conducted. Finally, the method is applied to the analysis of two real data sets.
Contributing Partner: UNT Libraries
Semi-supervised and Self-evolving Learning Algorithms with Application to Anomaly Detection in Cloud Computing

Semi-supervised and Self-evolving Learning Algorithms with Application to Anomaly Detection in Cloud Computing

Date: December 2012
Creator: Pannu, Husanbir Singh
Description: Semi-supervised learning (SSL) is the most practical approach for classification among machine learning algorithms. It is similar to the humans way of learning and thus has great applications in text/image classification, bioinformatics, artificial intelligence, robotics etc. Labeled data is hard to obtain in real life experiments and may need human experts with experimental equipments to mark the labels, which can be slow and expensive. But unlabeled data is easily available in terms of web pages, data logs, images, audio, video les and DNA/RNA sequences. SSL uses large unlabeled and few labeled data to build better classifying functions which acquires higher accuracy and needs lesser human efforts. Thus it is of great empirical and theoretical interest. We contribute two SSL algorithms (i) adaptive anomaly detection (AAD) (ii) hybrid anomaly detection (HAD), which are self evolving and very efficient to detect anomalies in a large scale and complex data distributions. Our algorithms are capable of modifying an existing classier by both retiring old data and adding new data. This characteristic enables the proposed algorithms to handle massive and streaming datasets where other existing algorithms fail and run out of memory. As an application to semi-supervised anomaly detection and for experimental illustration, we ...
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Connectedness and Some Concepts Related to Connectedness of a Topological Space

Connectedness and Some Concepts Related to Connectedness of a Topological Space

Date: August 1969
Creator: Wallace, Michael A.
Description: The purpose of this thesis is to investigate the idea of topological "connectedness" by presenting some of the basic ideas concerning connectedness along with several related concepts.
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Borel Sets and Baire Functions

Borel Sets and Baire Functions

Date: January 1970
Creator: Wemple, Fred W.
Description: This paper examines the relationship between Borel sets and Baire functions.
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Regular Semigroups

Regular Semigroups

Date: August 1967
Creator: Penn, Howard L.
Description: This thesis describes semigroups and the properties of both regular and inverse semigroups.
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Linear Algebras

Linear Algebras

Date: August 1961
Creator: Smith, Nickie Lee
Description: This paper is primarily concerned with the fundamental properties of a linear algebra of finite order over a field. A discussion of linear sets of finite order over a field is used as an introduction to these properties.
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Measure Functions

Measure Functions

Date: August 1965
Creator: Ottwell, Otho F.
Description: This thesis examines measure functions. A measure function has as its domain of definition a class of sets. It also must satisfy a certain additive condition. To state a concise definition of a measure function, it is convenient to define set function and completely additive set function.
Contributing Partner: UNT Libraries
Elliptic Geometry

Elliptic Geometry

Date: January 1966
Creator: Robertson, Barbara McKinzie
Description: This thesis discusses elliptic geometry including the order and incidence properties, projective properties and congruence properties.
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Completing the Space of Step Functions

Completing the Space of Step Functions

Date: August 1972
Creator: Massey, Linda K.
Description: In this thesis a study is made of the space X of all step functions on [0,1]. This investigation includes determining a completion space, X*, for the incomplete space X, defining integration for X*, and proving some theorems about integration in X*.
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Continuous Multifunctions

Continuous Multifunctions

Date: August 1972
Creator: Rulon, Susan Ree
Description: This paper is a discussion of multifunctions, various types of continuity defined on multifunctions, and implications of continuity for the range and domain sets of the multifunctions.
Contributing Partner: UNT Libraries