Functional Inverse Prediction with Elastic Shape Analysis

• Activity Number: 488 - Novel Methods for Unique Spatial Imaging Applications
• Type: Contributed
• Date/Time: Wednesday, August 10, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Katherine Goode* and James Derek Tucker and Daniel Ries
• Companies: Sandia National Laboratories and Sandia National Laboratories and Sandia National Labs
• Keywords: Functional data; Shape data; Inverse prediction; Elastic shape analysis; Joint functional principal components; Nuclear forensics

Abstract

Inverse prediction is typically implemented with scalar response data. We consider the scenario where the response variable is a continuous function (e.g., curves). One approach would be to extract summary statistics of the functions to obtain scalar responses and proceed as normal. However, this approach may lead to a loss of information and incorrect reasoning. Instead, we apply the elastic shape analysis (ESA) framework to compute functional principal components and use these as response variables representing the original functions. These principal components account for both the shape and sampling variabilities in functional data unlike traditional functional principal components, which only consider the vertical (amplitude) variability. We implement our approach on simulated data to understand the behavior of ESA on different functional characteristics. We compare the results to inverse predictions obtained using summary statistics and standard functional principal components and direct predictions. We then we apply the method to a nuclear forensics problem where there is interest in determining the underlying processing conditions of nuclear particulates.