Note
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Comparison of embeddings of covariance matrices¶
Comparison of several embeddings of a set of ERP covariance matrices extracted on MEG data: SE, LLE and t-SNE
Spectral Embedding (SE) is based on computing the low-dimensional representation that best preserves locality instead of local linearity in LLE [1].
Locally Linear Embedding (LLE) assumes that the local neighborhood of a matrix on the manifold can be well approximated by the affine subspace spanned by the k-nearest neighbors of the matrix and finds a low-dimensional embedding of the data based on these affine approximations.
t-SNE reduces SPD matrices into lower dimensional SPD matrices by computing conditional probabilities that represent similarities [2]. This fully Riemannian algorithm helps preserve the non-Euclidean structure of the data.
# Authors: Pedro Rodrigues <pedro.rodrigues01@gmail.com>,
# Gabriel Wagner vom Berg <gabriel@bccn-berlin.de>
# Thibault de Surrel <thibault.de-surrel@lamsade.dauphine.fr>
#
# License: BSD (3-clause)
import matplotlib.pyplot as plt
import mne
from mne import io
from mne.datasets import sample
from sklearn.model_selection import train_test_split
from pyriemann.estimation import XdawnCovariances
from pyriemann.utils.viz import plot_embedding
print(__doc__)
Set parameters and read data¶
data_path = str(sample.data_path())
raw_fname = data_path + "/MEG/sample/sample_audvis_filt-0-40_raw.fif"
event_fname = data_path + "/MEG/sample/sample_audvis_filt-0-40_raw-eve.fif"
tmin, tmax = -0., 1
event_id = dict(aud_l=1, aud_r=2, vis_l=3, vis_r=4)
# Setup for reading the raw data
raw = io.Raw(raw_fname, preload=True, verbose=False)
raw.filter(2, None, method="iir") # replace baselining with high-pass
events = mne.read_events(event_fname)
raw.info["bads"] = ["MEG 2443"] # set bad channels
picks = mne.pick_types(raw.info, meg=True, eeg=False, stim=False, eog=False,
exclude="bads")
# Read epochs
epochs = mne.Epochs(raw, events, event_id, tmin, tmax, proj=False,
picks=picks, baseline=None, preload=True, verbose=False)
X = epochs.get_data(copy=False)
y = epochs.events[:, -1]
Using default location ~/mne_data for sample...
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Download complete in 58s (1576.2 MB)
Filtering raw data in 1 contiguous segment
Setting up high-pass filter at 2 Hz
IIR filter parameters
---------------------
Butterworth highpass zero-phase (two-pass forward and reverse) non-causal filter:
- Filter order 8 (effective, after forward-backward)
- Cutoff at 2.00 Hz: -6.02 dB
Extract Xdawn covariance matrices¶
nfilter = 4
xdwn = XdawnCovariances(estimator="scm", nfilter=nfilter)
split = train_test_split(X, y, train_size=0.25, random_state=42)
Xtrain, Xtest, ytrain, ytest = split
covs = xdwn.fit(Xtrain, ytrain).transform(Xtest)
Spectral Embedding (SE)¶
plot_embedding(covs, ytest, metric="riemann", embd_type="Spectral",
normalize=True)
plt.show()
Locally Linear Embedding (LLE)¶
plot_embedding(covs, ytest, metric="riemann", embd_type="LocallyLinear",
normalize=False)
plt.show()
TNSE¶
plot_embedding(covs, ytest, metric="riemann", embd_type="TSNE",
normalize=False, max_iter=50)
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyriemann/checkouts/latest/pyriemann/optimization/positive_definite.py:284: UserWarning: Convergence not reached. Try increasing max_iter.
warnings.warn("Convergence not reached. Try increasing max_iter.")
References¶
Total running time of the script: (1 minutes 5.976 seconds)