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plot_simulated_data.py
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plot_simulated_data.py
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"""
=================================================
Example of pattern recognition on simulated data
=================================================
This example simulates data according to a very simple sketch of brain
imaging data and applies machine learning techniques to predict output
values.
"""
# Licence : BSD
print __doc__
from time import time
import numpy as np
import matplotlib.pyplot as plt
from scipy import linalg, ndimage
from sklearn import linear_model, svm
from sklearn.utils import check_random_state
from sklearn.cross_validation import KFold
from sklearn.feature_selection import f_regression
import nibabel
from nilearn import decoding
import nilearn.masking
###############################################################################
# Function to generate data
def create_simulation_data(snr=0, n_samples=2 * 100, size=12, random_state=1):
generator = check_random_state(random_state)
roi_size = 2 # size / 3
smooth_X = 1
### Coefs
w = np.zeros((size, size, size))
w[0:roi_size, 0:roi_size, 0:roi_size] = -0.6
w[-roi_size:, -roi_size:, 0:roi_size] = 0.5
w[0:roi_size, -roi_size:, -roi_size:] = -0.6
w[-roi_size:, 0:roi_size:, -roi_size:] = 0.5
w[(size - roi_size) / 2:(size + roi_size) / 2,
(size - roi_size) / 2:(size + roi_size) / 2,
(size - roi_size) / 2:(size + roi_size) / 2] = 0.5
w = w.ravel()
### Generate smooth background noise
XX = generator.randn(n_samples, size, size, size)
noise = []
for i in range(n_samples):
Xi = ndimage.filters.gaussian_filter(XX[i, :, :, :], smooth_X)
Xi = Xi.ravel()
noise.append(Xi)
noise = np.array(noise)
### Generate the signal y
y = generator.randn(n_samples)
X = np.dot(y[:, np.newaxis], w[np.newaxis])
norm_noise = linalg.norm(X, 2) / np.exp(snr / 20.)
noise_coef = norm_noise / linalg.norm(noise, 2)
noise *= noise_coef
snr = 20 * np.log(linalg.norm(X, 2) / linalg.norm(noise, 2))
print ("SNR: %.1f dB" % snr)
### Mixing of signal + noise and splitting into train/test
X += noise
X -= X.mean(axis=-1)[:, np.newaxis]
X /= X.std(axis=-1)[:, np.newaxis]
X_test = X[n_samples / 2:, :]
X_train = X[:n_samples / 2, :]
y_test = y[n_samples / 2:]
y = y[:n_samples / 2]
return X_train, X_test, y, y_test, snr, noise, w, size
def plot_slices(data, title=None):
plt.figure(figsize=(5.5, 2.2))
vmax = np.abs(data).max()
for i in (0, 6, 11):
plt.subplot(1, 3, i / 5 + 1)
plt.imshow(data[:, :, i], vmin=-vmax, vmax=vmax,
interpolation="nearest", cmap=plt.cm.RdBu_r)
plt.xticks(())
plt.yticks(())
plt.subplots_adjust(hspace=0.05, wspace=0.05, left=.03, right=.97, top=.9)
if title is not None:
plt.suptitle(title, y=.95)
###############################################################################
# Create data
X_train, X_test, y_train, y_test, snr, _, coefs, size = \
create_simulation_data(snr=-10, n_samples=100, size=12)
# Create masks for SearchLight. process_mask is the voxels where SearchLight
# computation is performed. It is a subset of the brain mask, just to reduce
# computation time.
mask = np.ones((size, size, size), np.bool)
mask_img = nibabel.Nifti1Image(mask.astype(np.int), np.eye(4))
process_mask = np.zeros((size, size, size), np.bool)
process_mask[:, :, 0] = True
process_mask[:, :, 6] = True
process_mask[:, :, 11] = True
process_mask_img = nibabel.Nifti1Image(process_mask.astype(np.int), np.eye(4))
coefs = np.reshape(coefs, [size, size, size])
plot_slices(coefs, title="Ground truth")
###############################################################################
# Compute the results and estimated coef maps for different estimators
classifiers = [
('bayesian_ridge', linear_model.BayesianRidge(normalize=True)),
('enet_cv', linear_model.ElasticNetCV(alphas=[5, 1, 0.5, 0.1],
l1_ratio=0.05)),
('ridge_cv', linear_model.RidgeCV(alphas=[100, 10, 1, 0.1], cv=5)),
('svr', svm.SVR(kernel='linear', C=0.001)),
('searchlight', decoding.SearchLight(
mask_img, process_mask_img=process_mask_img,
radius=2.7, scoring='r2', estimator=svm.SVR(kernel="linear"),
cv=KFold(y_train.size, n_folds=4),
verbose=1, n_jobs=1))
]
# Run the estimators
for name, classifier in classifiers:
t1 = time()
if name != "searchlight":
classifier.fit(X_train, y_train)
else:
X = nilearn.masking.unmask(X_train, mask_img)
classifier.fit(X, y_train)
del X
elapsed_time = time() - t1
if name != 'searchlight':
coefs = classifier.coef_
coefs = np.reshape(coefs, [size, size, size])
score = classifier.score(X_test, y_test)
title = '%s: prediction score %.3f, training time: %.2fs' % (
classifier.__class__.__name__, score,
elapsed_time)
else: # Searchlight
coefs = classifier.scores_
title = '%s: training time: %.2fs' % (
classifier.__class__.__name__,
elapsed_time)
# We use the plot_slices function provided in the example to
# plot the results
plot_slices(coefs, title=title)
print title
f_values, p_values = f_regression(X_train, y_train)
p_values = np.reshape(p_values, (size, size, size))
p_values = -np.log10(p_values)
p_values[np.isnan(p_values)] = 0
p_values[p_values > 10] = 10
plot_slices(p_values, title="f_regress")
plt.show()