Principal Component Analysis of Hybrid Functional and Vector Data

• Activity Number: 91 - High Dimensional Data, Causal Inference, Biostats Education, and More
• Type: Contributed
• Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
• Sponsor: ENAR
• Author(s): Jeong Hoon Jang*
• Companies: Indiana University
• Keywords: Dimension reduction; Functional data analysis; Multivariate data analysis; Multiple data modalities; Multivariate functional data; Principal component analysis

Abstract

We propose a practical principal component analysis (PCA) framework that provides a nonparametric means of simultaneously reducing the dimensions of and modeling functional and vector data. We first introduce a new hybrid Hilbert space that combines functional and vector objects as a single hybrid object. A PCA of hybrid functional and vector data (HFV-PCA), is then based on the eigen-decomposition of a covariance operator that captures the variability within and between hybrid functional and vector data. This approach leads to interpretable principal components that have the same structure as each observation and a single set of principal component scores that serves well as a low-dimensional proxy for hybrid functional and vector data. We propose a simple and robust estimation scheme where HFV-PCA components are estimated using the components estimated from the existing functional and classical PCA methods, and which allows flexible incorporation of sparse and irregular functional data as well as multivariate functional data. Our simulation results show satisfactory finite-sample performance of the proposed framework. Our method is demonstrated using a renal study.