http://hdl.handle.net/10027/1128 Fri, 24 May 2013 15:37:43 GMT 2013-05-24T15:37:43Z http://hdl.handle.net/10027/9790 Visual Object Detection for Animal Behavior Research The main contribution of this thesis is the development and implementation of object recognition framework for zebras. The proposed image descriptors are particularly easy to understand, and provide an example of how simple yet effective specialized features can be devised for a given object category. In general, designing image descriptors is a challenging task due to a fact that categorizing objects in images is an inherently ambiguous process, with image formation process, compression, intra-class variation and occlusion all contributing to ambiguity on different levels. However, we can take advantage of some domain-specific features in order to provide compact and efficient image descriptors. According to experimental results, our recog- nition framework achieves comparable performance to the state of the art techniques generally used in computer vision, while maintaining very fast training times, and easily parallelizable classification implementation. Thu, 21 Feb 2013 06:00:00 GMT http://hdl.handle.net/10027/9790 2013-02-21T06:00:00Z http://hdl.handle.net/10027/9745 Temporal Scale of Dynamic Networks Networks have become an indispensable data abstraction that captures the nature of a diverse list of complex systems, such as on-line social interactions, email and cell phone communications, or protein interactions in a cell. All these systems are inherently dynamic and change over time. The abstraction of choice for incorporating time has been the "dynamic network'', a time series of graphs, each representing an aggregation of a small discrete time interval of the stream of interactions. While in many cases the system under observation naturally suggests the size of such a time interval, it is more often the case that the aggregation is arbitrary and is done for the convenience of the data representation and analysis. However, it is clear that the choice of the time interval at which the network is discretized and aggregated has great implications on the structures observed, analysis performed, and inference made about the nature of the network and the processes on it. This thesis is the first to establish a framework for the problem of Temporal Scale Inference (TSI) for dynamic networks. We formally define the TSI problem and explicitly present some of its associated challenges. We present an analytical framework for studying the characteristics of special cases of interaction streams as probabilistic processes. We give characterizations of a null model and define the notion of the "right" temporal scale of a list of structured interaction streams including the general class of oversampled, noisy stationary streams. We present an axiomatic framework that formalizes desired properties of the "right" temporal scale. This framework serves as a common ground for consistently comparing the performance of different heuristics for the TSI problem. We present two heuristics for identification of the inherent temporal scale of interaction streams. Overall, this thesis focuses on the analysis of the scale of dynamic networks with the objective to make the "art of looking at the right scale" more scientific. Thu, 21 Feb 2013 06:00:00 GMT http://hdl.handle.net/10027/9745 2013-02-21T06:00:00Z http://hdl.handle.net/10027/9735 Solving Polynomial Systems With Tropical Methods In this thesis, we develop a polyhedral method to solve polynomial systems. We are primarily interested in obtaining the Puiseux series representations of positive dimensional solution sets for square polynomial systems and systems, which consist of more equations than unknowns. By developing our polyhedral method, we aim to generalize polyhedral homotopies. Our polyhedral method can be seen as the symbolic-numeric version of the fundamental theorem of tropical algebraic geometry. We illustrate our polyhedral method on the cyclic n-roots problems and offer a tropical perspective on the lemma of Backelin. Thu, 21 Feb 2013 06:00:00 GMT http://hdl.handle.net/10027/9735 2013-02-21T06:00:00Z http://hdl.handle.net/10027/9674 On Multiple-Instance Learning of Halfspaces Diochnos, D. I.; Sloan, R. H. In multiple-instance learning the learner receives bags, i.e., sets of instances. A bag is labeled positive if it contains a positive example of the target. An Omega(d logr) lower bound is given for the VC-dimension of bags of size r for d-dimensional halfspaces and it is shown that the same lower bound holds for halfspaces over any large point set in general position. This lower bound improves an Omega(logr) lower bound of Sabato and Tishby, and it is sharp in order of magnitude. We also show that the hypothesis finding problem is NP-complete and formulate several open problems NOTICE: this is the author’s version of a work that was accepted for publication in Information Processing Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Information Processing Letters, [Vol 112, Issue 23, (2012)] DOI: 10.1016/j.ipl.2012.08.017 Sat, 01 Dec 2012 06:00:00 GMT http://hdl.handle.net/10027/9674 2012-12-01T06:00:00Z