[Eeglablist] 答复：Re: Tensor Decomposition of EEG Signals

[CONG Fengyu 丛丰裕]

Dear Makoto

Glad to hear from you! To my surprise, you
know the meaning of my first name in Chinese characters! 
I answer your second question as the following:
It is new to me that applying three-way
data analysis on individual subject's independent components. I have not done
that before. Tensor decomposition is a kind of methods for blind source
separation (BSS). ICA is also a method for BSS. So, I need more time to digest
your suggestion. 
Your first question is hard to answer. 
In an ERP data set, there are modes
including time, space (channel), trial, stimulus, and subject (even group). Therefore,
we have the following matrices to denote the ERP data: A) the data in the level of single-trial
EEGM1) the matrix of ERP data of one single
trial of one stimulus of one subjectM2) the matrix of ERP data of concatenated
single trials of multiple stimuli of one subjectM3) the matrix of ERP data of concatenated
single trials of multiple stimuli of multiple subjectsB) the data in the level of averaged EEG
over single trials. M4) the matrix of averaged ERP data of one
stimulus of one subject M5) the matrix of averaged ERP data of multiple
stimuli of one subject M6) the matrix of averaged ERP data of multiple
stimuli of multiple subjects
I have found that ICA has been applied on
each matrix listed above. Usually, ICA is applied on M2, M3, and M6. Using EEGLAB
ICA tends to be performed on M2, which is the most frequently applied. 
For M2, I think it is also a kind of group
ICA since the variability of EEG data of multiple trials does exist. Without
investigation, it is hard to know whether the variability of single-trial
EEG data of multiple trials of one subject is smaller or bigger than the variability of averaged
EEG data of multiple subjects. 
I mainly work on MMN data. MMN is usually
produced by the difference wave in terms of the averaged EEG over single
trials. Moreover, in light of the several MMN datasets I have worked on, I have
found that the variability of single-trial MMN-EEG data among multiple trials
of one subject is stronger than the variability of averaged MMN-EEG data of multiple
subjects. Therefore, I use ICA in terms of M4 and M6. 
For M6, it is easy to do group-level
analysis since the ERP data are grouped together. However, there is strong assumption on different subjects.  For M4, I usually do the following way:1) Filtering the averaged EEG data using a
wavelet filter to reduce the number of sources (please check the frequency
response of the filter in Cong et al., NSM2014, and the effect in reducing the
number of sources in Cong et al., NSM2013&2011). Since the number of sources in the data is reduced, the requirement of number of samples of ICA to converge is also reduced. 2) Extracting R components from the
wavelet-filtered EEG data using ICASSO. 3) Choosing the components of interest in
terms of the temporal and spatial properties of ERPs. 4) Projecting the selected components of
interest back to the electrode field to correct the variance and polarity
indeterminacies. It is possible that the correction fails due to the poor ICA
decomposition (please read the reason in Cong et al., BSPC2011). My current suggestion
is to re-do the steps 3&4 again. If it also fails, I would not like to
suggest using ICA for decomposing the ERP data. 5) I do steps 1-4 for M4 for each stimulus
and each subject. Then, I analyze the new ERP data by ICA like the conventional
ERP data. 
The references mentioned above are as the
following: Fengyu Cong, Qiu-Hua Lin, Piia Astikainen, and Tapani
Ristaniemi，How to Validate
Similarity in Linear Transform Models of Event-related Potentials between
Experimental Conditions? Journal of Neuroscience
Methods, 2014, 236:76-85.Fengyu Cong, Zhaoshui He, Jarmo Hämäläinen, Paavo HT
Leppänen, Heikki Lyytinen, Andrzej Cichocki, Tapani Ristaniemi, Validating Rationale of Group-level
Component Analysis based on Estimating Number of Sources in EEG through Model
Order Selection, Journal of Neuroscience Methods, 2013, 212(1): 165–172.Fengyu Cong, Paavo H.T.
Leppänen, Piia Astikainen, Jarmo Hämäläinen, Jari K. Hietanen, Tapani
Ristaniemi, Dimension Reduction: Additional Benefit of an Optimal Filter for
Independent Component Analysis to Extract Event-related Potentials, Journal
of Neuroscience Methods, 2011, 201(1): 269-280.Fengyu Cong, Igor Kalyakin, Tapani Ristaniemi, Can
Back-Projection Fully Resolve Polarity Indeterminacy of ICA in Study of ERP?
Biomedical Signal Processing and Control, 2011, 6(4): 422-426.
Again, I welcome
your comments and suggestions. Best regards,Fengyu 

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 From: Makoto MiyakoshiDate: 2015-06-04 02:28To: CONG Fengyu 丛丰裕CC: EEGLABSubject: Re: [Eeglablist] Tensor Decomposition of EEG SignalsCongrats for publication! Without much reading, some thoughts and comments.> Electroencephalography (EEG) is one fundamental tool for functional brain imaging.I'm sure Scott will like this phrase.> However, the mostly applied computing tools for brain research are oriented for one-way or two-way data. We do not apply ICA on concatenated multiple-subject data (which is called group ICA) because we appreciate individual differences across subjects. This sounds good, but it's also a curse because the group-level analysis is so complicated. How do you integrate thousands of ICs from dozens of subjects in the final group-level analysis? We have been struggling against the issue over ten years.By the way please tell me if it is possible to apply your three-way data analysis on individual subject's independent components. I don't have math/physic background.MakotoDear Fengyu (rich and rich),On Fri, May 29, 2015 at 3:55 PM, CONG Fengyu 丛丰裕 <fengyu.cong at aliyun.com> wrote:Dear EEGLablist members,I would like to introduce my new review
paper to you. It is about Tensor Decomposition of EEG Signals and published in Journal
of Neuroscience Methods. The paper is open access and can be downloaded via http://www.sciencedirect.com/science/article/pii/S0165027015001016.
The demo of MATLAB codes and ERP data can be downloaded via http://www.escience.cn/people/cong/AdvancedSP_ERP.html
EEG signals tend to be represented by a
vector or a matrix to facilitate data processing and analysis with generally
understood methodologies like time-series analysis, spectral analysis and
matrix decomposition. Indeed, EEG signals are often naturally
born with more than two modes of time and space, and they can be denoted by a
multi-way array called as tensor. This review summarizes the current progress
of tensor decomposition of EEG signals with three aspects. The first is about the
existing modes and tensors of EEG signals. Second, two fundamental tensor
decomposition models, canonical polyadic decomposition (CPD, it is also called
parallel factor analysis-PARAFAC) and Tucker decomposition, are introduced and
compared. Moreover, the applications of the two models for EEG signals are
addressed. Particularly, the determination of the number of components for each
mode is discussed. Finally, the N-way partial least square and higher-order
partial least square are described for a potential trend to process and analyze
brain signals of two modalities simultaneously.Looking forward to your comments and
suggestions on tensor decomposition of EEG signals. Sincerely, Fengyu P.S.: The bibliography of the paper is as
the following: Fengyu Cong, Qiu-Hua Lin, Li-Dan Kuang,
Xiao-Feng Gong, Piia Astikainen, Tapani Ristaniemi, Tensor Decomposition of EEG
Signals: A Brief Review, Journal of Neuroscience Methods 248: 59–69, 2015.--Fengyu Cong, Ph.D., IEEE Senior MemberProfessor, Department of Biomedical Engineering, Dalian University of Technology, ChinaDocent (Adjunct Associate Professor), University of Jyvaskyla, FinlandEmail: cong at dlut.edu.cn, fengyu.cong at aliyun.comHomepage: http://www.escience.cn/people/cong/index.html_______________________________________________
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