The Annals of Applied Statistics

Fréchet means of curves for signal averaging and application to ECG data analysis

Jérémie Bigot

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Abstract

Signal averaging is the process that consists in computing a mean shape from a set of noisy signals. In the presence of geometric variability in time in the data, the usual Euclidean mean of the raw data yields a mean pattern that does not reflect the typical shape of the observed signals. In this setting, it is necessary to use alignment techniques for a precise synchronization of the signals, and then to average the aligned data to obtain a consistent mean shape. In this paper, we study the numerical performances of Fréchet means of curves which are extensions of the usual Euclidean mean to spaces endowed with non-Euclidean metrics. This yields a new algorithm for signal averaging and for the estimation of the time variability of a set of signals. We apply this approach to the analysis of heartbeats from ECG records.

Article information

Source
Ann. Appl. Stat., Volume 7, Number 4 (2013), 2384-2401.

Dates
First available in Project Euclid: 23 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1387823324

Digital Object Identifier
doi:10.1214/13-AOAS676

Mathematical Reviews number (MathSciNet)
MR3161727

Zentralblatt MATH identifier
54.0036.03

Keywords
Signal averaging mean shape Fréchet means curve registration geometric variability deformable models ECG data

Citation

Bigot, Jérémie. Fréchet means of curves for signal averaging and application to ECG data analysis. Ann. Appl. Stat. 7 (2013), no. 4, 2384--2401. doi:10.1214/13-AOAS676. https://projecteuclid.org/euclid.aoas/1387823324


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