Low-rank approximation based non-negative multi-way array decomposition on event-related potentials.

Fengyu Cong,Guoxu Zhou,Qibin Zhao,Piia Astikainen,Qiang Wu,Tapani Ristaniemi,Asoke K Nandi,Jari K Hietanen,Andrzej Cichocki

doi:10.1142/s012906571440005x

Abstract

Non-negative tensor factorization (NTF) has been successfully applied to analyze event-related potentials (ERPs), and shown superiority in terms of capturing multi-domain features. However, the time-frequency representation of ERPs by higher-order tensors are usually large-scale, which prevents the popularity of most tensor factorization algorithms. To overcome this issue, we introduce a non-negative canonical polyadic decomposition (NCPD) based on low-rank approximation (LRA) and hierarchical alternating least square (HALS) techniques. We applied NCPD (LRAHALS and benchmark HALS) and CPD to extract multi-domain features of a visual ERP. The features and components extracted by LRAHALS NCPD and HALS NCPD were very similar, but LRAHALS NCPD was 70 times faster than HALS NCPD. Moreover, the desired multi-domain feature of the ERP by NCPD showed a significant group difference (control versus depressed participants) and a difference in emotion processing (fearful versus happy faces). This was more satisfactory than that by CPD, which revealed only a group difference.

Highlights

Event-related potentials (ERPs) have been extensively used in cognitive neuroscience research.[1]
In order to demonstrate the effectiveness of the LRAHALS negative canonical polyadic decomposition (NCPD), we studied the fourth-order tensor including time–frequency representation (TFR) of visual ERP data in a passive oddball paradigm
We have shown the low-rank approximation (LRA)-based negative tensor factorization (NTF) algorithms are much faster than the bench-mark hierarchical alternating least square (HALS) NTF algorithms both in canonical polyadic (CP) and Tucker[17] models

Summary

Introduction

Event-related potentials (ERPs) have been extensively used in cognitive neuroscience research.[1] The peak amplitude of an ERP is the common feature used to represent brain activity corresponding to an event, and is measured sequentially across multiple channels and participants. Statistical analyses of these data are often carried out to detect differences at the group or condition level.[1] Group analyses are of particular importance in paradigms where the signal-to-noise-ratio (SNR) is very low. Tensor decomposition is a signal processing method that has recently been developed and applied to group-level analyses of ERPs.[3,4] This method provides a novel approach for investigating brain activity simultaneously in multiple domains of cognitive neuroscience.[5,6,7,8,9]

Methods

Results

Conclusion