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

Area of Science:

• Neuroscience
• Computational Neuroscience
• Signal Processing

Background:

• Non-negative tensor factorization (NTF) effectively analyzes event-related potentials (ERPs), capturing multi-domain features.
• Large-scale tensor representations of ERPs limit the application of many tensor factorization algorithms.
• Efficient methods are needed to analyze complex ERP data.

Purpose of the Study:

• To introduce a computationally efficient non-negative canonical polyadic decomposition (NCPD) method for analyzing large-scale ERP data.
• To evaluate the performance of the proposed NCPD method against existing techniques.
• To assess the ability of NCPD to extract meaningful features differentiating participant groups and emotional stimuli.

Main Methods:

• Developed a novel non-negative canonical polyadic decomposition (NCPD) algorithm incorporating low-rank approximation (LRA) and hierarchical alternating least squares (HALS) – termed LRAHALS NCPD.
• Applied LRAHALS NCPD and standard canonical polyadic decomposition (CPD) to extract multi-domain features from visual event-related potentials (ERPs).
• Compared the computational speed and feature extraction capabilities of LRAHALS NCPD against benchmark HALS NCPD and standard CPD.

Main Results:

• LRAHALS NCPD demonstrated comparable feature extraction to HALS NCPD but was approximately 70 times faster.
• The multi-domain features extracted by NCPD revealed significant differences between control and depressed participants.
• NCPD-extracted features also showed significant differences in emotion processing (fearful vs. happy faces), outperforming standard CPD.

Conclusions:

• The proposed LRAHALS NCPD offers a significant speed improvement for analyzing ERPs without compromising feature extraction quality.
• NCPD is a powerful tool for identifying subtle differences in neural processing related to clinical conditions and emotional stimuli.
• This method enhances the utility of tensor decomposition techniques for large-scale neurophysiological data analysis.