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xdawn.py
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xdawn.py
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# Authors: Alexandre Barachant <alexandre.barachant@gmail.com>
# Asish Panda <asishrocks95@gmail.com>
# Jean-Remi King <jeanremi.king@gmail.com>
#
# License: BSD-3-Clause
import numpy as np
from .. import EvokedArray, Evoked
from ..cov import Covariance, _regularized_covariance
from ..decoding import TransformerMixin, BaseEstimator
from ..epochs import BaseEpochs
from ..io import BaseRaw
from ..io.pick import _pick_data_channels, pick_info
from ..utils import logger, _check_option
def _construct_signal_from_epochs(epochs, events, sfreq, tmin):
"""Reconstruct pseudo continuous signal from epochs."""
n_epochs, n_channels, n_times = epochs.shape
tmax = tmin + n_times / float(sfreq)
start = (np.min(events[:, 0]) + int(tmin * sfreq))
stop = (np.max(events[:, 0]) + int(tmax * sfreq) + 1)
n_samples = stop - start
n_epochs, n_channels, n_times = epochs.shape
events_pos = events[:, 0] - events[0, 0]
raw = np.zeros((n_channels, n_samples))
for idx in range(n_epochs):
onset = events_pos[idx]
offset = onset + n_times
raw[:, onset:offset] = epochs[idx]
return raw
def _least_square_evoked(epochs_data, events, tmin, sfreq):
"""Least square estimation of evoked response from epochs data.
Parameters
----------
epochs_data : array, shape (n_channels, n_times)
The epochs data to estimate evoked.
events : array, shape (n_events, 3)
The events typically returned by the read_events function.
If some events don't match the events of interest as specified
by event_id, they will be ignored.
tmin : float
Start time before event.
sfreq : float
Sampling frequency.
Returns
-------
evokeds : array, shape (n_class, n_components, n_times)
An concatenated array of evoked data for each event type.
toeplitz : array, shape (n_class * n_components, n_channels)
An concatenated array of toeplitz matrix for each event type.
"""
from scipy import linalg
n_epochs, n_channels, n_times = epochs_data.shape
tmax = tmin + n_times / float(sfreq)
# Deal with shuffled epochs
events = events.copy()
events[:, 0] -= events[0, 0] + int(tmin * sfreq)
# Construct raw signal
raw = _construct_signal_from_epochs(epochs_data, events, sfreq, tmin)
# Compute the independent evoked responses per condition, while correcting
# for event overlaps.
n_min, n_max = int(tmin * sfreq), int(tmax * sfreq)
window = n_max - n_min
n_samples = raw.shape[1]
toeplitz = list()
classes = np.unique(events[:, 2])
for ii, this_class in enumerate(classes):
# select events by type
sel = events[:, 2] == this_class
# build toeplitz matrix
trig = np.zeros((n_samples, 1))
ix_trig = (events[sel, 0]) + n_min
trig[ix_trig] = 1
toeplitz.append(linalg.toeplitz(trig[0:window], trig))
# Concatenate toeplitz
toeplitz = np.array(toeplitz)
X = np.concatenate(toeplitz)
# least square estimation
predictor = np.dot(linalg.pinv(np.dot(X, X.T)), X)
evokeds = np.dot(predictor, raw.T)
evokeds = np.transpose(np.vsplit(evokeds, len(classes)), (0, 2, 1))
return evokeds, toeplitz
def _fit_xdawn(epochs_data, y, n_components, reg=None, signal_cov=None,
events=None, tmin=0., sfreq=1., method_params=None, info=None):
"""Fit filters and coefs using Xdawn Algorithm.
Xdawn is a spatial filtering method designed to improve the signal
to signal + noise ratio (SSNR) of the event related responses. Xdawn was
originally designed for P300 evoked potential by enhancing the target
response with respect to the non-target response. This implementation is a
generalization to any type of event related response.
Parameters
----------
epochs_data : array, shape (n_epochs, n_channels, n_times)
The epochs data.
y : array, shape (n_epochs)
The epochs class.
n_components : int (default 2)
The number of components to decompose the signals signals.
reg : float | str | None (default None)
If not None (same as ``'empirical'``, default), allow
regularization for covariance estimation.
If float, shrinkage is used (0 <= shrinkage <= 1).
For str options, ``reg`` will be passed as ``method`` to
:func:`mne.compute_covariance`.
signal_cov : None | Covariance | array, shape (n_channels, n_channels)
The signal covariance used for whitening of the data.
if None, the covariance is estimated from the epochs signal.
events : array, shape (n_epochs, 3)
The epochs events, used to correct for epochs overlap.
tmin : float
Epochs starting time. Only used if events is passed to correct for
epochs overlap.
sfreq : float
Sampling frequency. Only used if events is passed to correct for
epochs overlap.
Returns
-------
filters : array, shape (n_channels, n_channels)
The Xdawn components used to decompose the data for each event type.
Each row corresponds to one component.
patterns : array, shape (n_channels, n_channels)
The Xdawn patterns used to restore the signals for each event type.
evokeds : array, shape (n_class, n_components, n_times)
The independent evoked responses per condition.
"""
from scipy import linalg
if not isinstance(epochs_data, np.ndarray) or epochs_data.ndim != 3:
raise ValueError('epochs_data must be 3D ndarray')
classes = np.unique(y)
# XXX Eventually this could be made to deal with rank deficiency properly
# by exposing this "rank" parameter, but this will require refactoring
# the linalg.eigh call to operate in the lower-dimension
# subspace, then project back out.
# Retrieve or compute whitening covariance
if signal_cov is None:
signal_cov = _regularized_covariance(
np.hstack(epochs_data), reg, method_params, info, rank='full')
elif isinstance(signal_cov, Covariance):
signal_cov = signal_cov.data
if not isinstance(signal_cov, np.ndarray) or (
not np.array_equal(signal_cov.shape,
np.tile(epochs_data.shape[1], 2))):
raise ValueError('signal_cov must be None, a covariance instance, '
'or an array of shape (n_chans, n_chans)')
# Get prototype events
if events is not None:
evokeds, toeplitzs = _least_square_evoked(
epochs_data, events, tmin, sfreq)
else:
evokeds, toeplitzs = list(), list()
for c in classes:
# Prototyped response for each class
evokeds.append(np.mean(epochs_data[y == c, :, :], axis=0))
toeplitzs.append(1.)
filters = list()
patterns = list()
for evo, toeplitz in zip(evokeds, toeplitzs):
# Estimate covariance matrix of the prototype response
evo = np.dot(evo, toeplitz)
evo_cov = _regularized_covariance(evo, reg, method_params, info,
rank='full')
# Fit spatial filters
try:
evals, evecs = linalg.eigh(evo_cov, signal_cov)
except np.linalg.LinAlgError as exp:
raise ValueError('Could not compute eigenvalues, ensure '
'proper regularization (%s)' % (exp,))
evecs = evecs[:, np.argsort(evals)[::-1]] # sort eigenvectors
evecs /= np.apply_along_axis(np.linalg.norm, 0, evecs)
_patterns = np.linalg.pinv(evecs.T)
filters.append(evecs[:, :n_components].T)
patterns.append(_patterns[:, :n_components].T)
filters = np.concatenate(filters, axis=0)
patterns = np.concatenate(patterns, axis=0)
evokeds = np.array(evokeds)
return filters, patterns, evokeds
class _XdawnTransformer(BaseEstimator, TransformerMixin):
"""Implementation of the Xdawn Algorithm compatible with scikit-learn.
Xdawn is a spatial filtering method designed to improve the signal
to signal + noise ratio (SSNR) of the event related responses. Xdawn was
originally designed for P300 evoked potential by enhancing the target
response with respect to the non-target response. This implementation is a
generalization to any type of event related response.
.. note:: _XdawnTransformer does not correct for epochs overlap. To correct
overlaps see ``Xdawn``.
Parameters
----------
n_components : int (default 2)
The number of components to decompose the signals.
reg : float | str | None (default None)
If not None (same as ``'empirical'``, default), allow
regularization for covariance estimation.
If float, shrinkage is used (0 <= shrinkage <= 1).
For str options, ``reg`` will be passed to ``method`` to
:func:`mne.compute_covariance`.
signal_cov : None | Covariance | array, shape (n_channels, n_channels)
The signal covariance used for whitening of the data.
if None, the covariance is estimated from the epochs signal.
method_params : dict | None
Parameters to pass to :func:`mne.compute_covariance`.
.. versionadded:: 0.16
Attributes
----------
classes_ : array, shape (n_classes)
The event indices of the classes.
filters_ : array, shape (n_channels, n_channels)
The Xdawn components used to decompose the data for each event type.
patterns_ : array, shape (n_channels, n_channels)
The Xdawn patterns used to restore the signals for each event type.
"""
def __init__(self, n_components=2, reg=None, signal_cov=None,
method_params=None):
"""Init."""
self.n_components = n_components
self.signal_cov = signal_cov
self.reg = reg
self.method_params = method_params
def fit(self, X, y=None):
"""Fit Xdawn spatial filters.
Parameters
----------
X : array, shape (n_epochs, n_channels, n_samples)
The target data.
y : array, shape (n_epochs,) | None
The target labels. If None, Xdawn fit on the average evoked.
Returns
-------
self : Xdawn instance
The Xdawn instance.
"""
X, y = self._check_Xy(X, y)
# Main function
self.classes_ = np.unique(y)
self.filters_, self.patterns_, _ = _fit_xdawn(
X, y, n_components=self.n_components, reg=self.reg,
signal_cov=self.signal_cov, method_params=self.method_params)
return self
def transform(self, X):
"""Transform data with spatial filters.
Parameters
----------
X : array, shape (n_epochs, n_channels, n_samples)
The target data.
Returns
-------
X : array, shape (n_epochs, n_components * n_classes, n_samples)
The transformed data.
"""
X, _ = self._check_Xy(X)
# Check size
if self.filters_.shape[1] != X.shape[1]:
raise ValueError('X must have %i channels, got %i instead.' % (
self.filters_.shape[1], X.shape[1]))
# Transform
X = np.dot(self.filters_, X)
X = X.transpose((1, 0, 2))
return X
def inverse_transform(self, X):
"""Remove selected components from the signal.
Given the unmixing matrix, transform data, zero out components,
and inverse transform the data. This procedure will reconstruct
the signals from which the dynamics described by the excluded
components is subtracted.
Parameters
----------
X : array, shape (n_epochs, n_components * n_classes, n_times)
The transformed data.
Returns
-------
X : array, shape (n_epochs, n_channels * n_classes, n_times)
The inverse transform data.
"""
# Check size
X, _ = self._check_Xy(X)
n_epochs, n_comp, n_times = X.shape
if n_comp != (self.n_components * len(self.classes_)):
raise ValueError('X must have %i components, got %i instead' % (
self.n_components * len(self.classes_), n_comp))
# Transform
return np.dot(self.patterns_.T, X).transpose(1, 0, 2)
def _check_Xy(self, X, y=None):
"""Check X and y types and dimensions."""
# Check data
if not isinstance(X, np.ndarray) or X.ndim != 3:
raise ValueError('X must be an array of shape (n_epochs, '
'n_channels, n_samples).')
if y is None:
y = np.ones(len(X))
y = np.asarray(y)
if len(X) != len(y):
raise ValueError('X and y must have the same length')
return X, y
class Xdawn(_XdawnTransformer):
"""Implementation of the Xdawn Algorithm.
Xdawn :footcite:`RivetEtAl2009,RivetEtAl2011` is a spatial
filtering method designed to improve the signal to signal + noise
ratio (SSNR) of the ERP responses. Xdawn was originally designed for
P300 evoked potential by enhancing the target response with respect
to the non-target response. This implementation is a generalization
to any type of ERP.
Parameters
----------
n_components : int, (default 2)
The number of components to decompose the signals.
signal_cov : None | Covariance | ndarray, shape (n_channels, n_channels)
(default None). The signal covariance used for whitening of the data.
if None, the covariance is estimated from the epochs signal.
correct_overlap : 'auto' or bool (default 'auto')
Compute the independent evoked responses per condition, while
correcting for event overlaps if any. If 'auto', then
overlapp_correction = True if the events do overlap.
reg : float | str | None (default None)
If not None (same as ``'empirical'``, default), allow
regularization for covariance estimation.
If float, shrinkage is used (0 <= shrinkage <= 1).
For str options, ``reg`` will be passed as ``method`` to
:func:`mne.compute_covariance`.
Attributes
----------
filters_ : dict of ndarray
If fit, the Xdawn components used to decompose the data for each event
type, else empty. For each event type, the filters are in the rows of
the corresponding array.
patterns_ : dict of ndarray
If fit, the Xdawn patterns used to restore the signals for each event
type, else empty.
evokeds_ : dict of Evoked
If fit, the evoked response for each event type.
event_id_ : dict
The event id.
correct_overlap_ : bool
Whether overlap correction was applied.
See Also
--------
mne.decoding.CSP, mne.decoding.SPoC
Notes
-----
.. versionadded:: 0.10
References
----------
.. footbibliography::
"""
def __init__(self, n_components=2, signal_cov=None, correct_overlap='auto',
reg=None):
"""Init."""
super(Xdawn, self).__init__(n_components=n_components,
signal_cov=signal_cov, reg=reg)
self.correct_overlap = _check_option('correct_overlap',
correct_overlap,
['auto', True, False])
def fit(self, epochs, y=None):
"""Fit Xdawn from epochs.
Parameters
----------
epochs : instance of Epochs
An instance of Epoch on which Xdawn filters will be fitted.
y : ndarray | None (default None)
If None, used epochs.events[:, 2].
Returns
-------
self : instance of Xdawn
The Xdawn instance.
"""
# Check data
if not isinstance(epochs, BaseEpochs):
raise ValueError('epochs must be an Epochs object.')
picks = _pick_data_channels(epochs.info)
use_info = pick_info(epochs.info, picks)
X = epochs.get_data()[:, picks, :]
y = epochs.events[:, 2] if y is None else y
self.event_id_ = epochs.event_id
# Check that no baseline was applied with correct overlap
correct_overlap = self.correct_overlap
if correct_overlap == 'auto':
# Events are overlapped if the minimal inter-stimulus
# interval is smaller than the time window.
isi = np.diff(np.sort(epochs.events[:, 0]))
window = int((epochs.tmax - epochs.tmin) * epochs.info['sfreq'])
correct_overlap = isi.min() < window
if epochs.baseline and correct_overlap:
raise ValueError('Cannot apply correct_overlap if epochs'
' were baselined.')
events, tmin, sfreq = None, 0., 1.
if correct_overlap:
events = epochs.events
tmin = epochs.tmin
sfreq = epochs.info['sfreq']
self.correct_overlap_ = correct_overlap
# Note: In this original version of Xdawn we compute and keep all
# components. The selection comes at transform().
n_components = X.shape[1]
# Main fitting function
filters, patterns, evokeds = _fit_xdawn(
X, y, n_components=n_components, reg=self.reg,
signal_cov=self.signal_cov, events=events, tmin=tmin, sfreq=sfreq,
method_params=self.method_params, info=use_info)
# Re-order filters and patterns according to event_id
filters = filters.reshape(-1, n_components, filters.shape[-1])
patterns = patterns.reshape(-1, n_components, patterns.shape[-1])
self.filters_, self.patterns_, self.evokeds_ = dict(), dict(), dict()
idx = np.argsort([value for _, value in epochs.event_id.items()])
for eid, this_filter, this_pattern, this_evo in zip(
epochs.event_id, filters[idx], patterns[idx], evokeds[idx]):
self.filters_[eid] = this_filter
self.patterns_[eid] = this_pattern
n_events = len(epochs[eid])
evoked = EvokedArray(this_evo, use_info, tmin=epochs.tmin,
comment=eid, nave=n_events)
self.evokeds_[eid] = evoked
return self
def transform(self, inst):
"""Apply Xdawn dim reduction.
Parameters
----------
inst : Epochs | Evoked | ndarray, shape ([n_epochs, ]n_channels, n_times)
Data on which Xdawn filters will be applied.
Returns
-------
X : ndarray, shape ([n_epochs, ]n_components * n_event_types, n_times)
Spatially filtered signals.
""" # noqa: E501
if isinstance(inst, BaseEpochs):
X = inst.get_data()
elif isinstance(inst, Evoked):
X = inst.data
elif isinstance(inst, np.ndarray):
X = inst
if X.ndim not in (2, 3):
raise ValueError('X must be 2D or 3D, got %s' % (X.ndim,))
else:
raise ValueError('Data input must be of Epoch type or numpy array')
filters = [filt[:self.n_components]
for filt in self.filters_.values()]
filters = np.concatenate(filters, axis=0)
X = np.dot(filters, X)
if X.ndim == 3:
X = X.transpose((1, 0, 2))
return X
def apply(self, inst, event_id=None, include=None, exclude=None):
"""Remove selected components from the signal.
Given the unmixing matrix, transform data,
zero out components, and inverse transform the data.
This procedure will reconstruct the signals from which
the dynamics described by the excluded components is subtracted.
Parameters
----------
inst : instance of Raw | Epochs | Evoked
The data to be processed.
event_id : dict | list of str | None (default None)
The kind of event to apply. if None, a dict of inst will be return
one for each type of event xdawn has been fitted.
include : array_like of int | None (default None)
The indices referring to columns in the ummixing matrix. The
components to be kept. If None, the first n_components (as defined
in the Xdawn constructor) will be kept.
exclude : array_like of int | None (default None)
The indices referring to columns in the ummixing matrix. The
components to be zeroed out. If None, all the components except the
first n_components will be exclude.
Returns
-------
out : dict
A dict of instance (from the same type as inst input) for each
event type in event_id.
"""
if event_id is None:
event_id = self.event_id_
if not isinstance(inst, (BaseRaw, BaseEpochs, Evoked)):
raise ValueError('Data input must be Raw, Epochs or Evoked type')
picks = _pick_data_channels(inst.info)
# Define the components to keep
default_exclude = list(range(self.n_components, len(inst.ch_names)))
if exclude is None:
exclude = default_exclude
else:
exclude = list(set(list(default_exclude) + list(exclude)))
if isinstance(inst, BaseRaw):
out = self._apply_raw(raw=inst, include=include, exclude=exclude,
event_id=event_id, picks=picks)
elif isinstance(inst, BaseEpochs):
out = self._apply_epochs(epochs=inst, include=include, picks=picks,
exclude=exclude, event_id=event_id)
elif isinstance(inst, Evoked):
out = self._apply_evoked(evoked=inst, include=include, picks=picks,
exclude=exclude, event_id=event_id)
return out
def _apply_raw(self, raw, include, exclude, event_id, picks):
"""Aux method."""
if not raw.preload:
raise ValueError('Raw data must be preloaded to apply Xdawn')
raws = dict()
for eid in event_id:
data = raw[picks, :][0]
data = self._pick_sources(data, include, exclude, eid)
raw_r = raw.copy()
raw_r[picks, :] = data
raws[eid] = raw_r
return raws
def _apply_epochs(self, epochs, include, exclude, event_id, picks):
"""Aux method."""
if not epochs.preload:
raise ValueError('Epochs must be preloaded to apply Xdawn')
# special case where epochs come picked but fit was 'unpicked'.
epochs_dict = dict()
data = np.hstack(epochs.get_data()[:, picks])
for eid in event_id:
data_r = self._pick_sources(data, include, exclude, eid)
data_r = np.array(np.split(data_r, len(epochs.events), 1))
epochs_r = epochs.copy().load_data()
epochs_r._data[:, picks, :] = data_r
epochs_dict[eid] = epochs_r
return epochs_dict
def _apply_evoked(self, evoked, include, exclude, event_id, picks):
"""Aux method."""
data = evoked.data[picks]
evokeds = dict()
for eid in event_id:
data_r = self._pick_sources(data, include, exclude, eid)
evokeds[eid] = evoked.copy()
# restore evoked
evokeds[eid].data[picks] = data_r
return evokeds
def _pick_sources(self, data, include, exclude, eid):
"""Aux method."""
logger.info('Transforming to Xdawn space')
# Apply unmixing
sources = np.dot(self.filters_[eid], data)
if include not in (None, list()):
mask = np.ones(len(sources), dtype=bool)
mask[np.unique(include)] = False
sources[mask] = 0.
logger.info('Zeroing out %i Xdawn components' % mask.sum())
elif exclude not in (None, list()):
exclude_ = np.unique(exclude)
sources[exclude_] = 0.
logger.info('Zeroing out %i Xdawn components' % len(exclude_))
logger.info('Inverse transforming to sensor space')
data = np.dot(self.patterns_[eid].T, sources)
return data
def inverse_transform(self):
"""Not implemented, see Xdawn.apply() instead."""
# Exists because of _XdawnTransformer
raise NotImplementedError('See Xdawn.apply()')