cedalion.sigdecomp.unimodal.spoc

Source Power Co-modulation (SPoC) algorithm.

Functions

standardize(x[, dim])

Standardize x along dimension dim.

Classes

SPoC([n_comp])

Source Power Co-modulation (SPoC_lambda) algorithm based on Dähne et al. [DMH+14].

class cedalion.sigdecomp.unimodal.spoc.SPoC(n_comp: int | None = None)

Bases: object

Source Power Co-modulation (SPoC_lambda) algorithm based on Dähne et al. [DMH+14].

Given a vector-valued time signal x(t) and a scalar target function z(t), SPoC finds spatial filters W that maximize the covariance between the bandpower of the projected x signal, P(W.T @ x), and z. Such a covariance defines the objective function of the problem, whose solution can be formulated as the one for a generalized eigenvalue problem. The reconstructed sources s are given by the backward model s = W.T @ x.

Assumptions:

x(t) is of shape Nx x Nt, where Nx is the number of channels and Nt the number of time points, and it is band-pass filtered in the frequency band of interest. z(e) is a standardize vector (zero mean and unit variance) of shape 1 x Ne, where Ne < Nt is the number of “epochs”. The latter represent labels for intervals of the original time series. Bandpower of the projected signal W.T @ x is then approximated by its variance within epochs.

Parameters:

• n_comp (int) – Number of components the algorithm will find in decreasing

• highest (order of scores/eigenvalue. n_comp=1 returns the component of the)

• None (eigenvalue. If)

• Nx (n_comp =)

• components. (the maximum possible number of)

fit(

x: Annotated[DataArray, DataArraySchema(dims='time', coords='time', 'time', 'samples')],

z: DataArray,

) → ndarray

Fit the model on the (x, z) dataset.

Solve the generalized eigenvalue problem and store the trained spatial filters W as a local state of the class.

Parameters:

• x (NDTimeSeries, (channel, time)) – Temporal signal

• Nt. (with Ne <)

• z (DataArray, (time)) – Target (scalar) function

• Ne (of shape 1 x)

• Nt.

• n_comp (int) – Number of components the algorithm will find in decreasing order of scores/eigenvalue. n_comp=1 returns the component of the highest eigenvalue. If None, n_comp = Nx, the maximum possible number of components.

Returns:

Array of Nx eigenvalues. The latter also coincide with

the corresponding covariances between P(W.T @ x) and z.

Return type:

scores

transform(

x: Annotated[DataArray, DataArraySchema(dims='time', coords='time', 'time', 'samples')],

get_bandpower: bool = True,

Ne: int | None = None,

) → DataArray | tuple[DataArray, DataArray]

Apply backward model to x to build reconstructed sources.

Get reconstructed sources s by projecting x along the spatial filtes. If get_bandpower = True, also estimate epoch-wise bandpower of the components via the per-epoch variance.

Parameters:

• x (NDTimeSeries, (channel, time)) – Temporal signal of shape Nx x Nt.

• get_bandpower – Wether to return only the reconstructed sources or also the epoch-wise bandpower.

• Ne – Number of epochs along which to estimate the bandpower.

Returns:

Reconstructed sources (W.T @ x). s_power: standardized epoch-wise bandpower of s (Var(W.T @ x)).

Return type:

s

cedalion.sigdecomp.unimodal.spoc.standardize(

x: Annotated[DataArray, DataArraySchema(dims='time', coords='time', 'time', 'samples')],

dim: str = 'time',

)

Standardize x along dimension dim.