Functional Data Analysis using a Topological Summary Statistic: the Smooth Euler Characteristic Transform
Lorin A. Crawford, Anthea Monod, Andrew Chen, Sayan Mukherjee, Raúl Rabadán · arXiv (Cornell University) · 2016
In medical imaging informatics, the quantification of shape features for statistical analyses is an important issue. To address this problem, we introduce a novel statistic, the smooth Euler characteristic transform (SECT), which is designed to include shape information as covariates in regression models by representing shapes and surfaces as a collection of curves. Due to its well-defined inner product structure, the SECT can be used in a wider range of functional and nonparametric modeling approaches than other previously proposed topological summary statistics. We apply the SECT to a cancer radiomics study and demonstrate that for tumors assayed by magnetic resonance imaging (MRI), shape quantification via the SECT is a better predictor of clinical outcomes in patients with glioblastoma multiforme (GBM) than molecular assays and other tumor shape quantification methods. Specifically, we demonstrate that SECT features alone explain more of the variance in patient survival than gene expression, volumetric features, and morphometric features.