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dc.contributor.advisorBryant, David
dc.contributor.advisorSpillner, Andreas
dc.contributor.authorBalvočiūtė, Monika
dc.date.available2016-03-17T22:02:52Z
dc.date.copyright2016
dc.identifier.citationBalvočiūtė, M. (2016). Flat Embeddings of Genetic and Distance Data (Thesis, Doctor of Philosophy). University of Otago. Retrieved from http://hdl.handle.net/10523/6286en
dc.identifier.urihttp://hdl.handle.net/10523/6286
dc.description.abstractThe idea of displaying data in the plane is very attractive in many different fields of research. This thesis will focus on distance-based phylogenetics and multidimensional scaling (MDS). Both types of method can be viewed as a high-dimensional data reduction to pairwise distances and visualization of the data based on these distances. The difference between phylogenetics and multidimensional scaling is that the first one aims at finding a network or a tree structure that fits the distances, whereas MDS does not fix any structure and objects are simply placed in a low-dimensional space so that distances in the solution fit distances in the input as good as possible. Chapter 1 provides an introduction to the phylogenetics and multidimensional scaling. Chapter 2 focuses on the theoretical background of flat split systems (planar split networks). We prove equivalences between flat split systems, planar split networks and loop-free acyclic oriented matroids of rank three. The latter is a convenient mathematical structure that we used to design the algorithm for computing planar split networks that is described in Chapter 3. We base our approach on the well established agglomerative algorithms Neighbor-Joining and Neighbor-Net. In Chapter 4 we introduce multidimensional scaling and propose a new method for computing MDS plots that is based on the agglomerative approach and spring embeddings. Chapter 5 presents several case studies that we use to compare both of our methods and some classical agglomerative approaches in the distance-based phylogenetics.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherUniversity of Otago
dc.rightsAll items in OUR Archive are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.
dc.subjectphylogenetics
dc.subjectsplit networks
dc.subjectmultidimensional scaling
dc.subjectplannar embeddings
dc.subjectoriented matroids
dc.subjectsplits
dc.titleFlat Embeddings of Genetic and Distance Data
dc.typeThesis
dc.date.updated2016-03-17T14:21:54Z
dc.language.rfc3066en
thesis.degree.disciplineMathematics & Statistics
thesis.degree.nameDoctor of Philosophy
thesis.degree.grantorUniversity of Otago
thesis.degree.levelDoctoral
otago.openaccessOpen
otago.evidence.presentYes
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