Parameter estimation in block term decomposition for noninvasive atrial fibrillation analysis

Abstract

Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia encountered in clinical practice. Recently, a tensor decomposition approach has been put forward for noninvasive analysis of AF from surface electrocardiogram (ECG) records. Multilead ECG data are stored in tensor form and factorized via the block term decomposition (BTD). An accurate selection of parameters, including the number of block terms and the rank of the Hankel matrix factors, is necessary to guarantee physiologically significant results by this approach. The present work proposes to estimate the matrix rank by exploiting the characteristics of atrial activity during AF, which can be approximated by an autoregressive (AR) model in short records. To test this idea, three AR model order estimates are considered: Akaike's information criterion, minimum description length and partial autocorrelation function. The quality of the resulting tensor decompositions is evaluated in terms of both computational and physiologically related indices. Numerical experiments demonstrate that these model order estimation methods can find matrix rank values leading to accurate BTD approximations of the AF ECG tensor and physiologically plausible results.