传感器空间解码：跨时间与条件的泛化#

本示例运行 [1] 中描述的分析。它展示如何拟合一个线性分类器，在给定时点找出具有判别性的地形图，随后评估该线性模型能否准确预测另一组条件的所有时间采样点。

# Authors: Jean-Rémi King <jeanremi.king@gmail.com>
#          Alexandre Gramfort <alexandre.gramfort@inria.fr>
#          Denis Engemann <denis.engemann@gmail.com>
#
# License: BSD-3-Clause
# Copyright the MNE-Python contributors.

import matplotlib.pyplot as plt
from sklearn.linear_model import LogisticRegression
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler

import mne
from mne.datasets import sample
from mne.decoding import GeneralizingEstimator

# Preprocess data
data_path = sample.data_path()
# Load and filter data, set up epochs
meg_path = data_path / "MEG" / "sample"
raw_fname = meg_path / "sample_audvis_filt-0-40_raw.fif"
events_fname = meg_path / "sample_audvis_filt-0-40_raw-eve.fif"
raw = mne.io.read_raw_fif(raw_fname, preload=True)
picks = mne.pick_types(raw.info, meg=True, exclude="bads")  # Pick MEG channels
raw.filter(1.0, 30.0, fir_design="firwin")  # Band pass filtering signals
events = mne.read_events(events_fname)
event_id = {
    "Auditory/Left": 1,
    "Auditory/Right": 2,
    "Visual/Left": 3,
    "Visual/Right": 4,
}
tmin = -0.050
tmax = 0.400
# decimate to make the example faster to run, but then use verbose='error' in
# the Epochs constructor to suppress warning about decimation causing aliasing
decim = 2
epochs = mne.Epochs(
    raw,
    events,
    event_id=event_id,
    tmin=tmin,
    tmax=tmax,
    proj=True,
    picks=picks,
    baseline=None,
    preload=True,
    reject=dict(mag=5e-12),
    decim=decim,
    verbose="error",
)

Opening raw data file /home/circleci/mne_data/MNE-sample-data/MEG/sample/sample_audvis_filt-0-40_raw.fif...
    Read a total of 4 projection items:
        PCA-v1 (1 x 102)  idle
        PCA-v2 (1 x 102)  idle
        PCA-v3 (1 x 102)  idle
        Average EEG reference (1 x 60)  idle
    Range : 6450 ... 48149 =     42.956 ...   320.665 secs
Ready.
Reading 0 ... 41699  =      0.000 ...   277.709 secs...
Filtering raw data in 1 contiguous segment
Setting up band-pass filter from 1 - 30 Hz

FIR filter parameters
---------------------
Designing a one-pass, zero-phase, non-causal bandpass filter:
- Windowed time-domain design (firwin) method
- Hamming window with 0.0194 passband ripple and 53 dB stopband attenuation
- Lower passband edge: 1.00
- Lower transition bandwidth: 1.00 Hz (-6 dB cutoff frequency: 0.50 Hz)
- Upper passband edge: 30.00 Hz
- Upper transition bandwidth: 7.50 Hz (-6 dB cutoff frequency: 33.75 Hz)
- Filter length: 497 samples (3.310 s)

我们在所有左侧视觉 vs 听觉试次上训练分类器，并在所有右侧视觉 vs 听觉试次上测试。

clf = make_pipeline(
    StandardScaler(),
    # liblinear is faster than lbfgs
    LogisticRegression(solver="liblinear", random_state=131),
)
time_gen = GeneralizingEstimator(clf, scoring="roc_auc", n_jobs=None, verbose=True)

# Fit classifiers on the epochs where the stimulus was presented to the left.
# Note that the experimental condition y indicates auditory or visual
time_gen.fit(X=epochs["Left"].get_data(copy=False), y=epochs["Left"].events[:, 2] > 2)

  0%|          | Fitting GeneralizingEstimator : 0/35 [00:00<?,       ?it/s]
 14%|█▍        | Fitting GeneralizingEstimator : 5/35 [00:00<00:00,  148.07it/s]
 34%|███▍      | Fitting GeneralizingEstimator : 12/35 [00:00<00:00,  178.62it/s]
 54%|█████▍    | Fitting GeneralizingEstimator : 19/35 [00:00<00:00,  189.09it/s]
 74%|███████▍  | Fitting GeneralizingEstimator : 26/35 [00:00<00:00,  194.33it/s]
 91%|█████████▏| Fitting GeneralizingEstimator : 32/35 [00:00<00:00,  190.94it/s]
100%|██████████| Fitting GeneralizingEstimator : 35/35 [00:00<00:00,  194.80it/s]

<GeneralizingEstimator(base_estimator=Pipeline(steps=[('standardscaler', StandardScaler()), ('logisticregression', LogisticRegression(random_state=131, solver='liblinear'))]), scoring='roc_auc', verbose=True, fitted with 35 estimators, fitted with 35 estimators>

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GeneralizingEstimator

iFitted

Parameters

	base_estimator	Pipeline(step...liblinear'))])
	scoring	'roc_auc'
	verbose	True
	n_jobs	None
	position	0
	allow_2d	False
	axis	-1

Fitted attributes

Name	Type	Value
classes_	ndarray[bool](2,)	[False, True]
estimators_	ndarray[object](35,)	[Pipeline(steps=[('standardscaler', StandardScaler()), ('logisticregression', LogisticRegression(random_state=131, solver='liblinear'))]), Pipeline(steps=[('standardscaler', StandardScaler()), ('logisticregression', LogisticRegression(random_state=131, solver='liblinear'))]), Pipeline(steps=[('standardscaler', StandardScaler()), ('logisticregression', LogisticRegression(random_state=131, solver='liblinear'))]), ..., Pipeline(steps=[('standardscaler', StandardScaler()), ('logisticregression', LogisticRegression(random_state=131, solver='liblinear'))]), Pipeline(steps=[('standardscaler', StandardScaler()), ('logisticregression', LogisticRegression(random_state=131, solver='liblinear'))]), Pipeline(steps=[('standardscaler', StandardScaler()), ('logisticregression', LogisticRegression(random_state=131, solver='liblinear'))])]
fit_params_	dict	{}
n_features_in_	int	305

base_estimator: Pipeline

StandardScaler

?Documentation for StandardScaler

Parameters

	copy copy: bool, default=True If False, try to avoid a copy and do inplace scaling instead. This is not guaranteed to always work inplace; e.g. if the data is not a NumPy array or scipy.sparse CSR matrix, a copy may still be returned.	True
	with_mean with_mean: bool, default=True If True, center the data before scaling. This does not work (and will raise an exception) when attempted on sparse matrices, because centering them entails building a dense matrix which in common use cases is likely to be too large to fit in memory.	True
	with_std with_std: bool, default=True If True, scale the data to unit variance (or equivalently, unit standard deviation).	True

LogisticRegression

?Documentation for LogisticRegression

Parameters

	random_state random_state: int, RandomState instance, default=None Only used for `solver` == 'sag', 'saga' or 'liblinear' to shuffle the data. It has no effect on the other solvers. See :term:`Glossary <random_state>` for details.	131
	solver solver: {'lbfgs', 'liblinear', 'newton-cg', 'newton-cholesky', 'sag', 'saga'}, default='lbfgs' Algorithm to use in the optimization problem. Default is 'lbfgs'. To choose a solver, you might want to consider the following aspects: - 'lbfgs' is a good default solver because it works reasonably well for a wide class of problems. - For :term:`multiclass` problems (`n_classes >= 3`), all solvers except 'liblinear' minimize the full multinomial loss, 'liblinear' will raise an error. - 'newton-cholesky' is a good choice for `n_samples` >> `n_features * n_classes`, especially with one-hot encoded categorical features with rare categories. Be aware that the memory usage of this solver has a quadratic dependency on `n_features * n_classes` because it explicitly computes the full Hessian matrix. - For small datasets, 'liblinear' is a good choice, whereas 'sag' and 'saga' are faster for large ones; - 'liblinear' can only handle binary classification by default. To apply a one-versus-rest scheme for the multiclass setting one can wrap it with the :class:`~sklearn.multiclass.OneVsRestClassifier`. .. warning:: The choice of the algorithm depends on the penalty chosen (`l1_ratio=0` for L2-penalty, `l1_ratio=1` for L1-penalty and `0 < l1_ratio < 1` for Elastic-Net) and on (multinomial) multiclass support: ================= ======================== ====================== solver l1_ratio multinomial multiclass ================= ======================== ====================== 'lbfgs' l1_ratio=0 yes 'liblinear' l1_ratio=1 or l1_ratio=0 no 'newton-cg' l1_ratio=0 yes 'newton-cholesky' l1_ratio=0 yes 'sag' l1_ratio=0 yes 'saga' 0<=l1_ratio<=1 yes ================= ======================== ====================== .. note:: 'sag' and 'saga' fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from :mod:`sklearn.preprocessing`. .. seealso:: Refer to the :ref:`User Guide <Logistic_regression>` for more information regarding :class:`LogisticRegression` and more specifically the :ref:`Table <logistic_regression_solvers>` summarizing solver/penalty supports. .. versionadded:: 0.17 Stochastic Average Gradient (SAG) descent solver. Multinomial support in version 0.18. .. versionadded:: 0.19 SAGA solver. .. versionchanged:: 0.22 The default solver changed from 'liblinear' to 'lbfgs' in 0.22. .. versionadded:: 1.2 newton-cholesky solver. Multinomial support in version 1.6.	'liblinear'
	penalty penalty: {'l1', 'l2', 'elasticnet', None}, default='l2' Specify the norm of the penalty: - `None`: no penalty is added; - `'l2'`: add an L2 penalty term and it is the default choice; - `'l1'`: add an L1 penalty term; - `'elasticnet'`: both L1 and L2 penalty terms are added. .. warning:: Some penalties may not work with some solvers. See the parameter `solver` below, to know the compatibility between the penalty and solver. .. versionadded:: 0.19 l1 penalty with SAGA solver (allowing 'multinomial' + L1) .. deprecated:: 1.8 `penalty` was deprecated in version 1.8 and will be removed in 1.10. Use `l1_ratio` and `C` instead. `l1_ratio=0` for `penalty='l2'`, `l1_ratio=1` for `penalty='l1'`, `l1_ratio` set to any float between 0 and 1 for `penalty='elasticnet'`, and `C=np.inf` for `penalty=None`.	'deprecated'
	C C: float, default=1.0 Inverse of regularization strength; must be a positive float. Like in support vector machines, smaller values specify stronger regularization. `C=np.inf` results in unpenalized logistic regression. For a visual example on the effect of tuning the `C` parameter with an L1 penalty, see: :ref:`sphx_glr_auto_examples_linear_model_plot_logistic_path.py`.	1.0
	l1_ratio l1_ratio: float, default=0.0 The Elastic-Net mixing parameter, with `0 <= l1_ratio <= 1`. Setting `l1_ratio=1` gives a pure L1-penalty, setting `l1_ratio=0` a pure L2-penalty. Any value between 0 and 1 gives an Elastic-Net penalty of the form `l1_ratio * L1 + (1 - l1_ratio) * L2`. .. warning:: Certain values of `l1_ratio`, i.e. some penalties, may not work with some solvers. See the parameter `solver` below, to know the compatibility between the penalty and solver. .. versionchanged:: 1.8 Default value changed from None to 0.0. .. deprecated:: 1.8 `None` is deprecated and will be removed in version 1.10. Always use `l1_ratio` to specify the penalty type.	0.0
	dual dual: bool, default=False Dual (constrained) or primal (regularized, see also :ref:`this equation <regularized-logistic-loss>`) formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer `dual=False` when n_samples > n_features.	False
	tol tol: float, default=1e-4 Tolerance for stopping criteria.	0.0001
	fit_intercept fit_intercept: bool, default=True Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function.	True
	intercept_scaling intercept_scaling: float, default=1 Useful only when the solver `liblinear` is used and `self.fit_intercept` is set to `True`. In this case, `x` becomes `[x, self.intercept_scaling]`, i.e. a "synthetic" feature with constant value equal to `intercept_scaling` is appended to the instance vector. The intercept becomes ``intercept_scaling * synthetic_feature_weight``. .. note:: The synthetic feature weight is subject to L1 or L2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) `intercept_scaling` has to be increased.	1
	class_weight class_weight: dict or 'balanced', default=None Weights associated with classes in the form ``{class_label: weight}``. If not given, all classes are supposed to have weight one. The "balanced" mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as ``n_samples / (n_classes * np.bincount(y))``. Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified. .. versionadded:: 0.17 class_weight='balanced'	None
	max_iter max_iter: int, default=100 Maximum number of iterations taken for the solvers to converge.	100
	verbose verbose: int, default=0 For the liblinear and lbfgs solvers set verbose to any positive number for verbosity.	0
	warm_start warm_start: bool, default=False When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. Useless for liblinear solver. See :term:`the Glossary <warm_start>`. .. versionadded:: 0.17 warm_start to support lbfgs, newton-cg, sag, saga solvers.	False
	n_jobs n_jobs: int, default=None Does not have any effect. .. deprecated:: 1.8 `n_jobs` is deprecated in version 1.8 and will be removed in 1.10.	None

在刺激呈现在右侧的分段上计算得分。

scores = time_gen.score(
    X=epochs["Right"].get_data(copy=False), y=epochs["Right"].events[:, 2] > 2
)

0%|          | Scoring GeneralizingEstimator : 0/1225 [00:00<?,       ?it/s]
1%|          | Scoring GeneralizingEstimator : 11/1225 [00:00<00:03,  325.98it/s]
2%|▏         | Scoring GeneralizingEstimator : 23/1225 [00:00<00:03,  341.69it/s]
3%|▎         | Scoring GeneralizingEstimator : 35/1225 [00:00<00:03,  347.06it/s]
3%|▎         | Scoring GeneralizingEstimator : 35/1225 [00:00<00:03,  335.57it/s]

绘图

fig, ax = plt.subplots(layout="constrained")
im = ax.matshow(
    scores,
    vmin=0,
    vmax=1.0,
    cmap="RdBu_r",
    origin="lower",
    extent=epochs.times[[0, -1, 0, -1]],
)
ax.axhline(0.0, color="k")
ax.axvline(0.0, color="k")
ax.xaxis.set_ticks_position("bottom")
ax.set_xlabel(
    'Condition: "Right"\nTesting Time (s)',
)
ax.set_ylabel('Condition: "Left"\nTraining Time (s)')
ax.set_title("Generalization across time and condition", fontweight="bold")
fig.colorbar(im, ax=ax, label="Performance (ROC AUC)")
plt.show()

Generalization across time and condition

参考文献#

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