# Authors: Alexandre Barachant # Asish Panda # Jean-Remi King # # License: BSD (3-clause) import numpy as np import copy as cp from scipy import linalg from .ica import _get_fast_dot from .. import EvokedArray, Evoked from ..cov import Covariance, _regularized_covariance from ..decoding import TransformerMixin, BaseEstimator from ..epochs import _BaseEpochs, EpochsArray from ..io import _BaseRaw from ..io.pick import _pick_data_channels from ..utils import logger from ..externals.six import iteritems, itervalues 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. """ 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) # Contruct 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.): """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, allow regularization for covariance estimation if float, shrinkage covariance is used (0 <= shrinkage <= 1). if str, optimal shrinkage using Ledoit-Wolf Shrinkage ('ledoit_wolf') or Oracle Approximating Shrinkage ('oas'). 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. 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. References ---------- [1] Rivet, B., Souloumiac, A., Attina, V., & Gibert, G. (2009). xDAWN algorithm to enhance evoked potentials: application to brain-computer interface. Biomedical Engineering, IEEE Transactions on, 56(8), 2035-2043. [2] Rivet, B., Cecotti, H., Souloumiac, A., Maby, E., & Mattout, J. (2011, August). Theoretical analysis of xDAWN algorithm: application to an efficient sensor selection in a P300 BCI. In Signal Processing Conference, 2011 19th European (pp. 1382-1386). IEEE. See Also -------- CSP XDawn """ n_epochs, n_channels, n_times = epochs_data.shape classes = np.unique(y) # Retrieve or compute whitening covariance if signal_cov is None: signal_cov = _regularized_covariance(np.hstack(epochs_data), reg) 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 = np.matrix(_regularized_covariance(evo, reg)) # Fit spatial filters evals, evecs = linalg.eigh(evo_cov, signal_cov) 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, allow regularization for covariance estimation if float, shrinkage covariance is used (0 <= shrinkage <= 1). if str, optimal shrinkage using Ledoit-Wolf Shrinkage ('ledoit_wolf') or Oracle Approximating Shrinkage ('oas'). 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. 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. References ---------- [1] Rivet, B., Souloumiac, A., Attina, V., & Gibert, G. (2009). xDAWN algorithm to enhance evoked potentials: application to brain-computer interface. Biomedical Engineering, IEEE Transactions on, 56(8), 2035-2043. [2] Rivet, B., Cecotti, H., Souloumiac, A., Maby, E., & Mattout, J. (2011, August). Theoretical analysis of xDAWN algorithm: application to an efficient sensor selection in a P300 BCI. In Signal Processing Conference, 2011 19th European (pp. 1382-1386). IEEE. See Also -------- Xdawn CSD """ def __init__(self, n_components=2, reg=None, signal_cov=None): """Init.""" self.n_components = n_components self.signal_cov = signal_cov self.reg = reg 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) 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_components, n_channels = self.patterns_.shape 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 fast_dot = _get_fast_dot() return fast_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 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, allow regularization for covariance estimation if float, shrinkage covariance is used (0 <= shrinkage <= 1). if str, optimal shrinkage using Ledoit-Wolf Shrinkage ('ledoit_wolf') or Oracle Approximating Shrinkage ('oas'). Attributes ---------- ``filters_`` : dict of ndarray If fit, the Xdawn components used to decompose the data for each event type, else empty. ``patterns_`` : dict of ndarray If fit, the Xdawn patterns used to restore the signals for each event type, else empty. ``evokeds_`` : dict of evoked instance If fit, the evoked response for each event type. ``event_id_`` : dict of event id The event id. ``correct_overlap_``: bool Whether overlap correction was applied. Notes ----- .. versionadded:: 0.10 See Also -------- CSP References ---------- [1] Rivet, B., Souloumiac, A., Attina, V., & Gibert, G. (2009). xDAWN algorithm to enhance evoked potentials: application to brain-computer interface. Biomedical Engineering, IEEE Transactions on, 56(8), 2035-2043. [2] Rivet, B., Cecotti, H., Souloumiac, A., Maby, E., & Mattout, J. (2011, August). Theoretical analysis of xDAWN algorithm: application to an efficient sensor selection in a P300 BCI. In Signal Processing Conference, 2011 19th European (pp. 1382-1386). IEEE. """ 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) if correct_overlap not in ['auto', True, False]: raise ValueError('correct_overlap must be a bool or "auto"') self.correct_overlap = correct_overlap def fit(self, epochs, y=None): """Fit Xdawn from epochs. Parameters ---------- epochs : Epochs object An instance of Epoch on which Xdawn filters will be fitted. y : ndarray | None (default None) If None, used epochs.events[:, 2]. Returns ------- self : Xdawn instance The Xdawn instance. """ # Check data if not isinstance(epochs, _BaseEpochs): raise ValueError('epochs must be an Epochs object.') X = epochs.get_data() X = X[:, _pick_data_channels(epochs.info), :] 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) # 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 iteritems(epochs.event_id)]) for eid, this_filter, this_pattern, this_evo in zip( epochs.event_id, filters[idx], patterns[idx], evokeds[idx]): self.filters_[eid] = this_filter.T self.patterns_[eid] = this_pattern.T n_events = len(epochs[eid]) evoked = EvokedArray(this_evo, epochs.info, tmin=epochs.tmin, comment=eid, nave=n_events) self.evokeds_[eid] = evoked return self def transform(self, epochs): """Apply Xdawn dim reduction. Parameters ---------- epochs : Epochs | 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. """ if isinstance(epochs, _BaseEpochs): X = epochs.get_data() elif isinstance(epochs, np.ndarray): X = epochs else: raise ValueError('Data input must be of Epoch type or numpy array') filters = [filt[:self.n_components] for filt in itervalues(self.filters_)] filters = np.concatenate(filters, axis=0) X = np.dot(filters, X) return X.transpose((1, 0, 2)) 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 of instance 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)) info_r = cp.deepcopy(epochs.info) epochs_r = EpochsArray(data=data_r, info=info_r, events=epochs.events, tmin=epochs.tmin, event_id=epochs.event_id, verbose=False) epochs_r.preload = True 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.""" fast_dot = _get_fast_dot() logger.info('Transforming to Xdawn space') # Apply unmixing sources = fast_dot(self.filters_[eid].T, data) if include not in (None, list()): mask = np.ones(len(sources), dtype=np.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 = fast_dot(self.patterns_[eid], sources) return data def inverse_transform(self): """Not implemented, see Xdawn.apply() instead. """ # Exists because of _XdawnTransformer raise NotImplementedError('See Xdawn.apply()')