cedalion.sigdecomp.ICA_EBM

Independent Component Analysis by Entropy Bound Minimization (ICA-EBM) based on Li and Adali [LA10b]. This code is based on converted matlab versions provided by the MLSP Lab at the University of Maryland, which is available here: https://mlsp.umbc.edu/resources.html.

Functions

ICA_EBM(X)

Calculates the blind source separation demixing matrix corresponding to X.

inv_sqrtmH(B)

Helper function for ICA EBM: computes the inverse square root of a matrix.

pre_processing(X)

Helper function for ICA EBM: pre-processing (DC removal & spatial pre-whitening).

simplified_ppval(pp, xs)

Helper function for ICA EBM: simplified version of ppval.

symdecor(M)

Helper function for ICA EBM: fast symmetric orthogonalization.
cedalion.sigdecomp.ICA_EBM.ICA_EBM(X: ndarray) → ndarray[source]

Calculates the blind source separation demixing matrix corresponding to X.

ICA-EBM: ICA by Entropy Bound Minimization (real-valued version) Four nonlinearities x^4, |x|/(1+|x|), x|x|/(10+|x|), and x/(1+x^2) are used for entropy bound calculation

Parameters:

X (np.ndarray, (Channels, Time Points)) – the [N x T] input multivariate time series with dimensionality N observations/channels and T time points

Returns:

the [N x N] demixing matrix with weights for N channels/sources.

To obtain the independent components, the demixed signals can be calculated as S = W @ X.

Return type:

W (np.ndarray, (Channels, Channels))

Initial Contributors:

References

This code is based on the matlab version by Xi-Lin Li (Li and Adali [LA10b]) Xi-Lin Li and Tulay Adali, “Independent component analysis by entropy bound minimization,” IEEE Trans. Signal Processing, vol. 58, no. 10, pp. 5151-5164, Oct. 2010. The original matlab version is available at https://mlsp.umbc.edu/resources.html under the name “Real-valued ICA by entropy rate bound minimization (ICA-ERBM)”

cedalion.sigdecomp.ICA_EBM.simplified_ppval(pp: dict, xs: float) → float[source]
Helper function for ICA EBM: simplified version of ppval.

This function evaluates a piecewise polynomial at a specific point.

Parameters:

  • pp (dict) – a dictionary containing the piecewise polynomial representation of a function

  • xs (float) – the evaluation point

Returns:

the value of the function at xs

Return type:

v (float)

cedalion.sigdecomp.ICA_EBM.inv_sqrtmH(B: ndarray) → ndarray[source]

Helper function for ICA EBM: computes the inverse square root of a matrix.

Parameters:

B (np.ndarray) – a square matrix

Returns:

the inverse square root of B

Return type:

A (np.ndarray)

cedalion.sigdecomp.ICA_EBM.pre_processing(X: ndarray) → tuple[ndarray, ndarray][source]

Helper function for ICA EBM: pre-processing (DC removal & spatial pre-whitening).

Parameters:

X (np.ndarray, (Channels, Time Points)) – the data matrix [N x T]

Returns:

the pre-processed data matrix [N x T] P (np.ndarray, (Channels, Channels)): the pre-whitening matrix [N x N]

Return type:

X (np.ndarray, (Channels, Time Points))

cedalion.sigdecomp.ICA_EBM.symdecor(M: ndarray) → ndarray[source]

Helper function for ICA EBM: fast symmetric orthogonalization.

Parameters:

M (np.ndarray, (Channels, Channels)) – the matrix to be orthogonalized [N x N]

Returns:

the orthogonalized matrix [N x N]

Return type:

W (np.ndarray, (Channels, Channels))