Table 1.

List of Notation

Symbol	Definition
k	index for experimental conditions
i	index for trials
j	index for sample points in each trial
c	index for data channels
m	index for source signals
Nk	number of trials for each condition
Jk	number of sample points in each trial
C	number of data channels
M	number of source signals
A	mixing matrix
Â	estimated mixing matrix
am	the m-th column of A
ãc	the transpose of the c-th row of A
α(m)	precision parameter for am
${\mathbf{x}}_k^{(j)}$	multichannel EEG signals at the j-th sample for condition k
${\mathbf{z}}_k^{(j)}$	source signals at the j-th sample for condition k
${\mathit{\xi }}_k^{(j)}$	additive noise component at the j-th sample for condition k
Λk	source covariance matrix for condition k, with the variance for source m being ${\lambda }_k^{(m)}$
Ψk	noise covariance matrix for condition k, with the variance for channel c being ${\psi }_k^{(c)}$
ℝn	real n-dimensional vectors
ℝm×n	real m × n matrices
Γ(y)	gamma function (y > 0)
Ϝ (y)	digamma function defined as $\frac{\mathrm{d}\mathrm{\Gamma }(y)}{\mathrm{d}y}(y>0)$
𝒩(µ, Σ)	multivariate Gaussian distribution with mean µ and covariance Σ
𝒢a(a, b)	gamma distribution defined as $p(y|a,b)=\frac{1}{\mathrm{\Gamma }(a)}{b}^a{y}^{a-1}{e}^{-\mathit{\text{by}}}(y,a,b>0)$
𝒬	subspace of probability distributions
q*	variational distribution
ℒ(p)	variational lower bound as a functional of probability distribution p
Lmax	maximal value of the log-likelihood function for an estimated model
D(p ‖ q)	Kullback-Leibler (KL) divergence between probability distribution p and q
〈·〉p	mathematical expectation with respect to probability distribution p
B−1	inverse of matrix B
BT	transpose of matrix B
I	identity matrix
tr(B)	trace of matrix B
|B|	determinant of matrix B
d(B, C)	Amari index between matrix A and matrix B
diag(b)	diagonal matrix with vector b as diagonal entries
diag(B)	diagonal matrix with diagonal entries identical to those of matrix B
‖ b ‖2	l2 norm of vector b
ln	natural logarithm function
Const	constant
i.i.d.	independent and identically distributed