# pyriemann.estimation.Kernels¶

class pyriemann.estimation.Kernels(metric='linear', n_jobs=None, **kwds)

Estimation of kernel matrix between channels of time series.

Perform a kernel matrix estimation for each given time series, evaluating a kernel function between each pair of channels (rather than between pairs of time samples) and allowing to extract nonlinear channel relationship [1].

For an input time series $$X \in \mathbb{R}^{c \times t}$$, composed of $$c$$ channels and $$t$$ time samples, kernel function $$\kappa()$$ is computed between channels $$i$$ and $$j$$:

$K_{i,j} = \kappa \left( X[i], X[j] \right)$

Linear kernel is related to pyriemann.estimation.Covariances [1], but this class allows to generalize to nonlinear relationships.

Parameters
metricstring, default=’linear’

The metric to use when computing kernel function between channels [2]: ‘linear’, ‘poly’, ‘polynomial’, ‘rbf’, ‘laplacian’, ‘cosine’.

n_jobsint, default=None

The number of jobs to use for the computation [2]. This works by breaking down the pairwise matrix into n_jobs even slices and computing them in parallel.

**kwdsoptional keyword parameters

Any further parameters are passed directly to the kernel function [2].

Notes

New in version 0.4.

References

1(1,2)

Beyond Covariance: Feature Representation with Nonlinear Kernel Matrices L. Wang, J. Zhang, L. Zhou, C. Tang, W Li. ICCV, 2015.

2(1,2,3)

https://scikit-learn.org/stable/modules/generated/sklearn.metrics.pairwise.pairwise_kernels.html

__init__(metric='linear', n_jobs=None, **kwds)

Init.

fit(X, y=None)

Fit.

Do nothing. For compatibility purpose.

Parameters
Xndarray, shape (n_matrices, n_channels, n_times)

Multi-channel time-series.

yNone

Not used, here for compatibility with sklearn API.

Returns
selfKernels instance

The Kernels instance.

fit_transform(X, y=None, **fit_params)

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters
Xarray-like of shape (n_samples, n_features)

Input samples.

yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None

Target values (None for unsupervised transformations).

**fit_paramsdict

Returns
X_newndarray array of shape (n_samples, n_features_new)

Transformed array.

get_params(deep=True)

Get parameters for this estimator.

Parameters
deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns
paramsdict

Parameter names mapped to their values.

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters
**paramsdict

Estimator parameters.

Returns
selfestimator instance

Estimator instance.

transform(X)

Estimate kernel matrices from time series.

Parameters
Xndarray, shape (n_matrices, n_channels, n_times)

Multi-channel time-series.

Returns
Kndarray, shape (n_matrices, n_channels, n_channels)

Kernel matrices.