pyriemann.spatialfilters.AJDC¶

class pyriemann.spatialfilters.AJDC(window=128, overlap=0.5, fmin=None, fmax=None, fs=None, dim_red=None, verbose=True)¶

AJDC algorithm.

The approximate joint diagonalization of Fourier cospectral matrices (AJDC) [1] is a versatile tool for blind source separation (BSS) tasks based on Second-Order Statistics (SOS), estimating spectrally uncorrelated sources.

It can be applied:

on a single subject, to solve the classical BSS problem [1],
on several subjects, to solve the group BSS (gBSS) problem [2],
on several experimental conditions (for eg, baseline versus task), to exploit the diversity of source energy between conditions in addition to generic coloration and time-varying energy [1].

AJDC estimates Fourier cospectral matrices by the Welch’s method, and applies a trace-normalization. If necessary, it averages cospectra across subjects, and concatenates them along experimental conditions. Then, a dimension reduction and a whitening are applied on cospectra. An approximate joint diagonalization (AJD) [3] allows to estimate the joint diagonalizer, not constrained to be orthogonal. Finally, forward and backward spatial filters are computed.

Parameters:

windowint, default=128

The length of the FFT window used for spectral estimation.

overlapfloat, default=0.5

The percentage of overlap between window.

fminfloat | None, default=None

The minimal frequency to be returned. Since BSS models assume zero-mean processes, the first cospectrum (0 Hz) must be excluded.

fmaxfloat | None, default=None

The maximal frequency to be returned.

fsfloat | None, default=None

The sampling frequency of the signal.

dim_redNone | dict, default=None

Parameter for dimension reduction of cospectra, because Pham’s AJD is sensitive to matrices conditioning.

If None :: no dimension reduction during whitening.
If {"n_components": val} :: dimension reduction defining the number of components; val must be an integer superior to 1.
If {"expl_var": val} :: dimension reduction selecting the number of components such that the amount of variance that needs to be explained is greater than the percentage specified by val. val must be a float in (0,1], typically 0.99.
If {"max_cond": val} :: dimension reduction selecting the number of components such that the condition number of the mean matrix is lower than val. This threshold has a physiological interpretation, because it can be viewed as the ratio between the power of the strongest component (usually, eye-blink source) and the power of the lowest component you don’t want to keep (acquisition sensor noise). val must be a float strictly superior to 1, typically 100.
If {"warm_restart": val} :: dimension reduction defining the number of components from an initial joint diagonalizer, and then run AJD from this solution. val must be a square ndarray.

verbosebool, default=True

Verbose flag.

Attributes:

n_channels_int: If fit, the number of channels of the signal.
freqs_ndarray, shape (n_freqs,): If fit, the frequencies associated to cospectra.
n_sources_int: If fit, the number of components of the source space.
diag_filters_ndarray, shape (n_sources_, n_sources_): If fit, the diagonalization filters, also called joint diagonalizer.
forward_filters_ndarray, shape (n_sources_, n_channels_): If fit, the spatial filters used to transform signal into source, also called deximing or separating matrix.
backward_filters_ndarray, shape (n_channels_, n_sources_): If fit, the spatial filters used to transform source into signal, also called mixing matrix.

Examples using `pyriemann.spatialfilters.AJDC`¶

Artifact Correction by AJDC-based Blind Source Separation

pyriemann.spatialfilters.AJDC¶

Examples using pyriemann.spatialfilters.AJDC¶

Examples using `pyriemann.spatialfilters.AJDC`¶