cedalion.sigdecomp.multimodal.arc_erbm

Independent Component Analysis by Entropy Bound Rate Minimization (ICA-ERBM).

This code is based on Li and Adali [LA10a] and Fu et al. [FPA+14]. It was converted from matlab versions provided by the MLSP Lab at the University of Maryland, which is available here: https://mlsp.umbc.edu/resources.html.

Functions

arc_erbm(X, guess_mat[, p, pr_guess_mat])

Adaptive-reverse Constrained ICA by Entropy Rate Bound Minimization (arc-ERBM) is a spectrally constrained ICA algorithm.

auction(assignCost[, guard])

Performs assignment using Bertsekas' auction algorithm.

calculate_cos_sin_mtx(p)

Helper function for ERBM ICA: calculates the cos and sin matrix for integral calculation in ERBM ICA.

cnstd_and_gain(a)

Helper function for ERBM ICA: returns constraint direction used for calculating projected gradient and gain of filter a.

inv_sqrtmH(B)

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

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.

pre_processing(X)

Helper function for ERBM ICA: Preprocessing (removal of mean, patial pre-whitening, temporal pre-filtering)

simplified_ppval(pp, xs)

Helper function for ERBM ICA: simplified version of ppval.
cedalion.sigdecomp.multimodal.arc_erbm.arc_erbm(
X: ndarray,
guess_mat,
p: int = None,
pr_guess_mat=None,
) → ndarray[source]

Adaptive-reverse Constrained ICA by Entropy Rate Bound Minimization (arc-ERBM) is a spectrally constrained ICA algorithm.

Parameters:

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

  • guess_mat (np.ndarray, (Time Points/2 , Referenced Channels)) – Frequency reference signal for the reconstruction

  • p (int) – the filter length for the invertible filter source model, does not need to be specified. Default is p = minimum(11, T/50).

  • pr_guess_mat (np.ndarray, (Time Points, Referenced Channels)) – Optional time domain reference signal for the reconstruction, however, only frequency characteristics are used. Only needed if Phase Retrieval Projection constraint should be included.

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 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.multimodal.arc_erbm.lfc(x: ndarray, p: int, choice, a0) → tuple[ndarray, ndarray][source]

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.multimodal.arc_erbm.simplified_ppval(pp: dict, xs: float) → float[source]
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.multimodal.arc_erbm.cnstd_and_gain(a: ndarray) → tuple[ndarray, ndarray][source]

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.multimodal.arc_erbm.calculate_cos_sin_mtx(p: int) → None[source]

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

Returns:

None

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

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.multimodal.arc_erbm.inv_sqrtmH(B: ndarray) → ndarray[source]

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.multimodal.arc_erbm.auction(assignCost, guard=None)[source]

Performs assignment using Bertsekas’ auction algorithm.

Parameters: assignCost (ndarray): m x n matrix of costs for associating each row with each column. m >= n. guard (float, optional): Cost of column non-assignment. All assignments will have cost < guard.

Returns: colsol (ndarray): Column assignments, where colsol[j] gives the row assigned to column j. rowsol (ndarray): Row assignments, where rowsol[i] gives the column assigned to row i.