cedalion.sigdecomp package
Submodules
cedalion.sigdecomp.ERBM module
Independent Component Analysis by Entropy Bound Rate Minimization (ICA-ERBM) based on Li and Adali [LA10a] and Fu et al. [FPA+14]. 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.
- cedalion.sigdecomp.ERBM.ERBM(X, p=None)
ICA-ERBM: ICA by Entropy Rate Bound Minimization (real-valued version).
- Parameters:
X (np.ndarray, (Channels, Time Points)) – the [N x T] input multivariate time series with dimensionality N observations/channels and T time points
p (int) – the filter length for the invertible filter source model, does not need to be specified. Default is p = (11, T/50).
- 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))
References
This code is based on the matlab version of bss by Xi-Lin Li (Li and Adali [LA10a]) Xi-Lin Li, Tulay Adali, “Blind spatiotemporal separation of second and/or higher-order correlated sources by entropy rate minimization,” IEEE International Conference on Acoustics, Speech and Signal Processing 2010. The original matlab version is available at https://mlsp.umbc.edu/resources.html under the name “Real-valued ICA by entropy bound minimization (ICA-EBM)”
- cedalion.sigdecomp.ERBM.calculate_cos_sin_mtx(p)
Helper function for ERBM ICA: calculates the cos and sin matrix for integral calculation in ERBM ICA.
- Parameters:
p (int) – the filter length for the invertible filter source model
- Return type:
None- Returns:
None
- cedalion.sigdecomp.ERBM.cnstd_and_gain(a)
Helper function for ERBM ICA: returns constraint direction used for calculating projected gradient and gain of filter a.
- Parameters:
a (np.ndarray, (p, 1)) – the filter coefficients [p x 1]
- Returns:
the constraint direction [p x 1] G (np.ndarray, (1,)): the gain of the filter a
- Return type:
b (np.ndarray, (p, 1))
- cedalion.sigdecomp.ERBM.inv_sqrtmH(B)
Helper function for ERBM ICA: 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.ERBM.lfc(x, p, choice, a0)
Helper function for ERBM ICA: computes the linear filtering coefficients (LFC) with length p for entropy rate estimation, and the estimated entropy rate.
- Parameters:
x (np.ndarray, (Time Points, 1)) – the source estimate [T x 1]
p (int) – the filter length for the source model
choice – can be ‘sub’, ‘super’ or ‘unknown’; any other input is handled as ‘unknown’
a0 (np.ndarray or empty list) – is the intial guess [p x 1] or an empty list []
- Returns:
the filter coefficients [p x 1] min_cost (np.ndarray, (1, 1)): the entropy rate estimation [1 x 1]
- Return type:
a (np.ndarray, (p, 1))
- cedalion.sigdecomp.ERBM.pre_processing(X)
Helper function for ERBM ICA: Preprocessing (removal of mean, patial pre-whitening, temporal pre-filtering)
- 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 pre-processed input multivariate time series P (np.ndarray, (Channels, Channels)): the pre-whitening matrix
- Return type:
X (np.ndarray, (Channels, Time Points))
- cedalion.sigdecomp.ERBM.simplified_ppval(pp, xs)
- Helper function for ERBM ICA: 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 module
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.
- cedalion.sigdecomp.ICA_EBM.ICA_EBM(X)
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))
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.inv_sqrtmH(B)
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)
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.simplified_ppval(pp, xs)
- 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.symdecor(M)
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))
cedalion.sigdecomp.dummy module
- cedalion.sigdecomp.dummy.split_frequency_bands(ts)
Extract signal components in different frequency bands.
This is not intended for real use but should act rather as an example how signal decomposition methods could be implemented.
- Return type:
DataArray