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AbideSubcortical_gaussian_cov_model.py
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AbideSubcortical_gaussian_cov_model.py
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import numpy as np
import spd_manifold
def log_lik(subject_cov, group_cov, sigma, whiten=True):
if whiten:
whitening = spd_manifold.inv_sqrtm(group_cov)
subject_cov = np.dot(np.dot(whitening, subject_cov), whitening)
group_cov = np.eye(n_rois)
return ( -n_rois**2*np.log(sigma)
- 1/(2*sigma**2) * (
np.sum((group_cov - subject_cov)**2)
+ np.sum(np.diag(group_cov - subject_cov)**2)
))
class CovRFX(object):
def __init__(self, whiten=True):
self.whiten = whiten
def fit(self, group_covs):
if self.whiten:
self.mean_cov = mean_cov = spd_manifold.log_mean(group_covs)
whitening = spd_manifold.inv_sqrtm(mean_cov)
group_covs = [np.dot(np.dot(whitening, g), whitening)
for g in group_covs]
mean_cov = np.eye(n_rois)
else:
self.mean_cov = mean_cov = np.mean(group_covs, axis=0)
self.sigma = 1./n_rois* np.sqrt(1./len(group_covs)*
np.sum(
np.sum((mean_cov - g)**2)
+ np.sum(np.diag(mean_cov - g)**2)
for g in group_covs
))
return self
def log_lik(self, subject_cov):
return log_lik(subject_cov, self.mean_cov, self.sigma,
whiten=self.whiten)
if __name__ == '__main__':
WHITEN = True
# load the controls
control_covs = np.load('controls.npy')
control_covs = np.mean(control_covs, 1)
n_controls, n_rois, _ = control_covs.shape
# load the patients
patient_covs = np.load('patients.npy')
patient_covs = np.mean(patient_covs, 1)
n_patients = len(patient_covs)
patient_nbs = [4, 13, 18, 15, 16, 20, 22, 27, 30, 36]
# 'test on control and patients'
control_model = CovRFX(whiten=WHITEN).fit(control_covs)
stop
control_fits = [control_model.log_lik(c) for c in control_covs]
patient_fits = [control_model.log_lik(p) for p in patient_covs]
patient_fit_cv = np.zeros(n_patients)
control_fit_cv = list()
for n in range(n_controls):
train = [control_covs[i]
for i in range(n_controls) if i!=n]
test = control_covs[n]
control_model.fit(train)
control_fit_cv.append(control_model.log_lik(test))
patient_fit_cv += np.array([control_model.log_lik(p)
for p in patient_covs])
patient_fit_cv /= n_controls
import matplotlib.pylab as pl
pl.rcParams['text.usetex'] = True
pl.rcParams['text.latex.preamble'] = r'\usepackage{amsfonts}'
pl.figure(1, figsize=(1, 3))
pl.clf()
ax = pl.axes([.2, .2, .5, .7])
pl.boxplot([control_fit_cv, patient_fit_cv], widths=.25)
pl.plot(1.26*np.ones(len(control_fit_cv)), control_fit_cv, '+k',
markeredgewidth=1)
pl.plot(2.26*np.ones(len(patient_fits)),
patient_fit_cv, '+k',
markeredgewidth=1)
pl.xticks((1.13, 2.13), ('controls', 'patients'), size=13)
if WHITEN:
title = 'Tangent\nspace'
else:
title = r'$\mathbb{R}^{n\times n}$'
pl.text(.1, .1, title,
transform=ax.transAxes,
horizontalalignment='left',
verticalalignment='bottom',
size=12)
#pl.axis([0.7, 2.5, 401, 799])
pl.xlim(.7, 2.5)
#pl.ylim(401, 799)
ax.yaxis.tick_right()
pl.ylabel('Log-likelihood', size=13)
ax.yaxis.set_label_position('right')
pl.draw()
#ax.yaxis.set_ticks_position('both')
pl.show()
pl.draw()
if WHITEN:
pl.savefig('model_likelihood_tangent.pdf')
else:
pl.savefig('model_likelihood_flat.pdf')