A PCA approach for complex-valued functional data

H. A. Hernández Roig, P. Acedo, M. C. Aguilera-Morillo, R. E. Lillo, A. Menafoglio, A. Moreno-Oyervides, L. M. Sangalli

This work deals with complex-valued functional data defined over a real one-dimensional domain. It is motivated by a real data application concerning the study of spectroscopy measurements. In this scenario, it is usual to exclusively analyze the amplitude of the signals, disregarding its complex nature. As an alternative, we propose a functional principal components technique that allows the representation of the complex-valued data and the deployment of functional regression models. This approach is based on the Generalized Karhunen-Loève Representation Theorem and takes into account the general case of improper signals. We discuss the theoretical implications of this methodology as well as possible numerical solutions to the estimation problem.

Keywords: Functional data analysis, principal components, complex data, Karhunen-Loève representation, improper signals

Scheduled

GT06 Functional Data Analysis I. New methodologies
June 8, 2022  12:40 PM
Grade Hall

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