## The Annals of Applied Statistics

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

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

#### 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