# Statistics Colloquium: Elastic Functional Data Analysis

### Event Description:

Bio: J. Derek Tucker is a Principal Member of the Technical Staff at Sandia National Laboratories. J. Derek Tucker received his B.S. in Electrical Engineering Cum Laude and M.S. in Electrical Engineering from Colorado State University in 2007 and 2009, respectively. Upon completion of these degrees, he began working as a Research Scientist at the Naval Surface Warfare Center Panama City Division in Panama City, FL. In 2014 he received the Ph.D. degree in Statistics from Florida State University In Tallahassee, FL under the co-advisement of Dr. Anuj Srivastava and Dr. Wei Wu. While at NSWC-PCD he led various development efforts in automatic target recognition algorithms for synthetic aperture sonar imagery. In the summer of 2014 he joined Sandia National Laboratories and is currently in the Statistical Sciences department. He currently is leading research projects in the area of satellite image registration and point processes modeling for monitoring applications. His research is focused on pattern theoretic approaches to problems in image analysis, computer vision, signal processing, and functional data analysis. In 2017, he received the Director of National Intelligence Team Award for his contributions to the Signal Location in Complex Environments (SLiCE) team.

Abstract: Functional data analysis (FDA) is an important research areas, due to its broad applications across many disciplines where functional data is prevalent. An essential component in solving these problems is the registration of points across functional objects. Without proper registration the results are often inferior and difficult to interpret. The current practice in the FDA literature is to treat registration as a pre-processing step, using off-the-shelf alignment procedures, and follow it up with statistical analysis of the resulting data. In contrast, an Elastic framework is a more comprehensive approach, where one solves for the registration and statistical inferences in a simultaneous fashion. Our goal is to use a metric with appropriate invariance properties, to form objective functions for alignment and to develop statistical models involving functional data. While these elastic metrics are complicated in general, we have developed a family of square-root transformations that map these metrics into simpler Euclidean metrics, thus enabling more standard statistical procedures. Specifically, we have developed techniques for elastic functional PCA, elastic tolerance bounds, and elastic regression models involving functional variables. I will demonstrate this ideas using simulated data and real data from various sources.