Metric Learning for Shape Classification: A Fast and Efficient Approach with Monte Carlo Methods

• Other Authors: Cellat, Serdar (author)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Mathematics
• Online Access: http://purl.flvc.org/fsu/fd/2018_Sp_Cellat_fsu_0071E_14295

Quantifying shape variation within a group of individuals, identifying morphological contrasts between populations and categorizing these groups according to morphological similarities and dissimilarities are central problems in developmental evolutionary biology and genetics. In this dissertation, we present an approach to optimal shape categorization through the use of a new family of metrics for shapes represented by a finite collection of landmarks. We develop a technique to identify metrics that optimally differentiate and categorize shapes using Monte Carlo based optimization methods. We discuss the theory and the practice of the method and apply it to the categorization of 62 mice offsprings based on the shape of their skull. We also create a taxonomic classification tree for multiple species of fruit flies given the shape of their wings. The results of these experiments validate our method. === A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === Spring Semester 2018. === January 16, 2018. === Global Optimization, Metric Learning, Monte Carlo Optimization, Quasi Monte Carlo, Statistical Shape Analysis, Stochastic Optimization === Includes bibliographical references. === Washington Mio, Professor Co-Directing Dissertation; Giray Okten, Professor Co-Directing Dissertation; Sudhir Aggarwal, University Representative; Nick Cogan, Committee Member; Harsh Jain, Committee Member.