Intersection of Longest Paths in Graph Theory and Predicting Performance in Facial Recognition

A set of subsets is said to have the Helly property if the condition that each pair of subsets has a non-empty intersection implies that the intersection of all subsets has a non-empty intersection. In 1966, Gallai noticed that the set of all longest paths of a connected graph is pairwise intersecti...

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Main Author: Yates, Amy
Format: Others
Published: ScholarWorks @ Georgia State University 2017
Subjects:
Online Access:http://scholarworks.gsu.edu/math_diss/34
http://scholarworks.gsu.edu/cgi/viewcontent.cgi?article=1037&context=math_diss
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spelling ndltd-GEORGIA-oai-scholarworks.gsu.edu-math_diss-10372016-08-20T15:31:48Z Intersection of Longest Paths in Graph Theory and Predicting Performance in Facial Recognition Yates, Amy A set of subsets is said to have the Helly property if the condition that each pair of subsets has a non-empty intersection implies that the intersection of all subsets has a non-empty intersection. In 1966, Gallai noticed that the set of all longest paths of a connected graph is pairwise intersecting and asked if the set had the Helly property. While it is not true in general, a number of classes of graphs have been shown to have the property. In this dissertation, we show that K4-minor-free graphs, interval graphs, circular arc graphs, and the intersection graphs of spider graphs are classes that have this property. The accuracy of facial recognition algorithms on images taken in controlled conditions has improved significantly over the last two decades. As the focus is turning to more unconstrained or relaxed conditions and toward videos, there is a need to better understand what factors influence performance. If these factors were better understood, it would be easier to predict how well an algorithm will perform when new conditions are introduced. Previous studies have studied the effect of various factors on the verification rate (VR), but less attention has been paid to the false accept rate (FAR). In this dissertation, we study the effect various factors have on the FAR as well as the correlation between marginal FAR and VR. Using these relationships, we propose two models to predict marginal VR and demonstrate that the models predict better than using the previous global VR. 2017-01-06T08:00:00Z text application/pdf http://scholarworks.gsu.edu/math_diss/34 http://scholarworks.gsu.edu/cgi/viewcontent.cgi?article=1037&context=math_diss Mathematics Dissertations ScholarWorks @ Georgia State University longest paths helly property gallai question facial recognition predicting performance
collection NDLTD
format Others
sources NDLTD
topic longest paths
helly property
gallai question
facial recognition
predicting performance
spellingShingle longest paths
helly property
gallai question
facial recognition
predicting performance
Yates, Amy
Intersection of Longest Paths in Graph Theory and Predicting Performance in Facial Recognition
description A set of subsets is said to have the Helly property if the condition that each pair of subsets has a non-empty intersection implies that the intersection of all subsets has a non-empty intersection. In 1966, Gallai noticed that the set of all longest paths of a connected graph is pairwise intersecting and asked if the set had the Helly property. While it is not true in general, a number of classes of graphs have been shown to have the property. In this dissertation, we show that K4-minor-free graphs, interval graphs, circular arc graphs, and the intersection graphs of spider graphs are classes that have this property. The accuracy of facial recognition algorithms on images taken in controlled conditions has improved significantly over the last two decades. As the focus is turning to more unconstrained or relaxed conditions and toward videos, there is a need to better understand what factors influence performance. If these factors were better understood, it would be easier to predict how well an algorithm will perform when new conditions are introduced. Previous studies have studied the effect of various factors on the verification rate (VR), but less attention has been paid to the false accept rate (FAR). In this dissertation, we study the effect various factors have on the FAR as well as the correlation between marginal FAR and VR. Using these relationships, we propose two models to predict marginal VR and demonstrate that the models predict better than using the previous global VR.
author Yates, Amy
author_facet Yates, Amy
author_sort Yates, Amy
title Intersection of Longest Paths in Graph Theory and Predicting Performance in Facial Recognition
title_short Intersection of Longest Paths in Graph Theory and Predicting Performance in Facial Recognition
title_full Intersection of Longest Paths in Graph Theory and Predicting Performance in Facial Recognition
title_fullStr Intersection of Longest Paths in Graph Theory and Predicting Performance in Facial Recognition
title_full_unstemmed Intersection of Longest Paths in Graph Theory and Predicting Performance in Facial Recognition
title_sort intersection of longest paths in graph theory and predicting performance in facial recognition
publisher ScholarWorks @ Georgia State University
publishDate 2017
url http://scholarworks.gsu.edu/math_diss/34
http://scholarworks.gsu.edu/cgi/viewcontent.cgi?article=1037&context=math_diss
work_keys_str_mv AT yatesamy intersectionoflongestpathsingraphtheoryandpredictingperformanceinfacialrecognition
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