Classifying Healthy Children and Children with Attention Deficit through Features Derived from Sparse and Nonnegative Tensor Factorization Using Event-Related Potential
In this study, we use features extracted by Nonnegative Tensor Factorization (NTF) from event-related potentials (ERPs) to discriminate healthy children and children with attention deficit (AD). The peak amplitude of an ERP has been extensively used to discriminate different groups of subjects for the clinical research. However, such discriminations sometimes fail because the peak amplitude may vary severely with the increased number of subjects and wider range of ages and it can be easily affected by many factors. This study formulates a framework, using NTF to extract features of the evoked brain activities from time-frequency represented ERPs. Through using the estimated features of a ne…
Extract Mismatch Negativity and P3a through Two-Dimensional Nonnegative Decomposition on Time-Frequency Represented Event-Related Potentials
This study compares the row-wise unfolding nonnegative tensor factorization (NTF) and the standard nonnegative matrix factorization (NMF) in extracting time-frequency represented event-related potentials—mismatch negativity (MMN) and P3a from EEG under the two-dimensional decomposition The criterion to judge performance of NMF and NTF is based on psychology knowledge of MMN and P3a MMN is elicited by an oddball paradigm and may be proportionally modulated by the attention So, participants are usually instructed to ignore the stimuli However the deviant stimulus inevitably attracts some attention of the participant towards the stimuli Thus, P3a often follows MMN As a result, if P3a was large…
Validating rationale of group-level component analysis based on estimating number of sources in EEG through model order selection
This study addresses how to validate the rationale of group component analysis (CA) for blind source separation through estimating the number of sources in each individual EEG dataset via model order selection. Control children, typically reading children with risk for reading disability (RD), and children with RD participated in the experiment. Passive oddball paradigm was used for eliciting mismatch negativity during EEG data collection. Data were cleaned by two digital filters with pass bands of 1-30 Hz and 1-15 Hz and a wavelet filter with the pass band narrower than 1-12 Hz. Three model order selection methods were used to estimate the number of sources in each filtered EEG dataset. Un…
Identical fits of nonnegative matrix/tensor factorization may correspond to different extracted event-related potentials
Nonnegative Matrix / Tensor factorization (NMF/NTF) have been used in the study of EEG, and the fit (explained variation) is often used to evaluate the performance of a nonnegative decomposition algorithm. However, this parameter only reveals the information derived from the mathematical model and just exhibits the reliability of the algorithms, and the property of EEG can not be reflected. If fits of two algorithms are identical, it is necessary to examine whether the desired components extracted by them are identical too. In order to verify this doubt, we performed NMF and NTF on the same dataset of an auditory event-related potentials (ERPs), and found that the identical fits of NMF and …
LOW-RANK APPROXIMATION BASED NON-NEGATIVE MULTI-WAY ARRAY DECOMPOSITION ON EVENT-RELATED POTENTIALS
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 NCP…
Determining the number of sources in high-density EEG recordings of event-related potentials by model order selection
To high-density electroencephalography (EEG) recordings, determining the number of sources to separate the signal and the noise subspace is very important. A mostly used criterion is that percentage of variance of raw data explained by the selected principal components composing the signal space should be over 90%. Recently, a model order selection method named as GAP has been proposed. We investigated the two methods by performing independent component analysis (ICA) on the estimated signal subspace, assuming the number of selected principal components composing the signal subspace is equal to the number of sources of brain activities. Through examining wavelet-filtered EEG recordings (128…
Low-rank approximation based non-negative multi-way array decomposition on event-related potentials
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…
Nonnegative Tensor Train Decompositions for Multi-domain Feature Extraction and Clustering
Tensor train (TT) is one of the modern tensor decomposition models for low-rank approximation of high-order tensors. For nonnegative multiway array data analysis, we propose a nonnegative TT (NTT) decomposition algorithm for the NTT model and a hybrid model called the NTT-Tucker model. By employing the hierarchical alternating least squares approach, each fiber vector of core tensors is optimized efficiently at each iteration. We compared the performances of the proposed method with a standard nonnegative Tucker decomposition (NTD) algorithm by using benchmark data sets including event-related potential data and facial image data in multi-domain feature extraction and clustering tasks. It i…
Multi-domain feature extraction for small event-related potentials through nonnegative multi-way array decomposition from low dense array EEG
Non-negative Canonical Polyadic decomposition (NCPD) and non-negative Tucker decomposition (NTD) were compared for extracting the multi-domain feature of visual mismatch negativity (vMMN), a small event-related potential (ERP), for the cognitive research. Since signal-to-noise ratio in vMMN is low, NTD outperformed NCPD. Moreover, we proposed an approach to select the multi-domain feature of an ERP among all extracted features and discussed determination of numbers of extracted components in NCPD and NTD regarding the ERP context.
BENEFITS OF MULTI-DOMAIN FEATURE OF MISMATCH NEGATIVITY EXTRACTED BY NON-NEGATIVE TENSOR FACTORIZATION FROM EEG COLLECTED BY LOW-DENSITY ARRAY
Through exploiting temporal, spectral, time-frequency representations, and spatial properties of mismatch negativity (MMN) simultaneously, this study extracts a multi-domain feature of MMN mainly using non-negative tensor factorization. In our experiment, the peak amplitude of MMN between children with reading disability and children with attention deficit was not significantly different, whereas the new feature of MMN significantly discriminated the two groups of children. This is because the feature was derived from multi-domain information with significant reduction of the heterogeneous effect of datasets.
Multi-domain Feature of Event-Related Potential Extracted by Nonnegative Tensor Factorization: 5 vs. 14 Electrodes EEG Data
As nonnegative tensor factorization (NTF) is particularly useful for the problem of underdetermined linear transform model, we performed NTF on the EEG data recorded from 14 electrodes to extract the multi-domain feature of N170 which is a visual event-related potential (ERP), as well as 5 typical electrodes in occipital-temporal sites for N170 and in frontal-central sites for vertex positive potential (VPP) which is the counterpart of N170, respectively. We found that the multi-domain feature of N170 from 5 electrodes was very similar to that from 14 electrodes and more discriminative for different groups of participants than that of VPP from 5 electrodes. Hence, we conclude that when the …
Exploiting ongoing EEG with multilinear partial least squares during free-listening to music
During real-world experiences, determining the stimulus-relevant brain activity is excitingly attractive and is very challenging, particularly in electroencephalography. Here, spectrograms of ongoing electroencephalogram (EEG) of one participant constructed a third-order tensor with three factors of time, frequency and space; and the stimulus data consisting of acoustical features derived from the naturalistic and continuous music formulated a matrix with two factors of time and the number of features. Thus, the multilinear partial least squares (PLS) conforming to the canonical polyadic (CP) model was performed on the tensor and the matrix for decomposing the ongoing EEG. Consequently, we …