Functional variables serve important roles as predictors in a variety of pattern recognition and vision applications. Focusing on a specific subproblem, termed scalar-on-function regression, most current approaches adopt the standard L2 inner product to form a link between functional predictors and scalar responses. These methods may perform poorly when predictor functions contain nuisance phase variability, i.e., predictors are temporally misaligned due to noise. While a simple solution could be to pre-align predictors as a pre-processing step, before applying a regression model, this alignment is seldom optimal from the perspective of regression. In this dissertation, we propose a new approach, termed elastic functional regression, where alignment is included in the regression model itself, and is performed in conjunction with the estimation of other model parameters. This model is based on a norm-preserving warping of predictors, not the standard time warping of functions, and provides better prediction in situations where the shape or the amplitude of the predictor is more useful than its phase. We demonstrate the effectiveness of this framework using simulated and real data. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2018. / April 17, 2018. / Functional Data Analysis, Functional Regression Model, Phase Variation, Scalar-on-Function Regression / Includes bibliographical references. / Anuj Srivastava, Professor Directing Thesis; Eric Klassen, University Representative; Wei Wu, Committee Member; Fred Huffer, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_653363 |
| Contributors | Ahn, Kyungmin (author), Srivastava, Anuj, 1968- (professor directing thesis), Klassen, E., 1958- (university representative), Wu, Wei (committee member), Huffer, Fred W. (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Statistics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (84 pages), computer, application/pdf |
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