def signal_to_pproba(test, learn=None, method='prior', alpha=0.01, verbose=0):
"""
Convert a set of z-values to posterior probabilities of being active
Parameters
----------
test: array pf shape(n_samples, 1),
data that is assessed
learn: array pf shape(n_samples, 1), optional
data to learn a mixture model
method: string, optional, to be chosen within
['gauss_mixture', 'emp_null', 'gam_gauss', 'prior']
alpha: float in the [0,1], optional,
parameter that yields the prior probability that a region is active
should be chosen close to 0
"""
if method=='gauss_mixture':
prior_strength = 100
fixed_scale = True
bfp = en.three_classes_GMM_fit(
learn, test, alpha, prior_strength,verbose, fixed_scale)
bf0 = bfp[:,1]
elif method== 'emp_null':
enn = en.ENN(learn)
enn.learn()
bf0 = np.reshape(enn.fdr(test),np.size(bf0))
elif method=='gam_gauss':
bfp = en.Gamma_Gaussian_fit(learn, test, verbose)
bf0 = bfp[:,1]
elif method=='prior':
y0 = st.norm.pdf(test)
shape_, scale_ = 3., 2.
y1 = st.gamma.pdf(test, shape_, scale=scale_)
bf0 = np.ravel((1-alpha)*y0 / (alpha*y1 + (1-alpha)*y0))
else: raise ValueError, 'Unknown method'
return bf0
nim = load(mask_image)
mask = nim.get_data()
# read the functional image
rbeta = load(input_image)
beta = rbeta.get_data()
beta = beta[mask>0]
mf = mp.figure()
a1 = mp.subplot(1,3,1)
a2 = mp.subplot(1,3,2)
a3 = mp.subplot(1,3,3)
# fit beta's histogram with a Gamma-Gaussian mixture
bfm = np.array([2.5,3.0,3.5,4.0,4.5])
bfp = en.Gamma_Gaussian_fit(beta, bfm, verbose=2, mpaxes=a1)
# fit beta's histogram with a mixture of Gaussians
alpha = 0.01
pstrength = 100
bfq = en.three_classes_GMM_fit(beta, bfm, alpha, pstrength,
verbose=2, mpaxes=a2)
# fit the null mode of beta with the robust method
efdr = en.ENN(beta)
efdr.learn()
efdr.plot(bar=0,mpaxes=a3)
mf.set_size_inches(15, 5, forward=True)
mp.show()
def compute_individual_regions(Fbeta, lbeta, coord, dmax, xyz,
affine=np.eye(4), shape=None, smin=5,
theta=3.0, verbose=0, reshuffle=0):
"""
Compute the Bayesian Structural Activation paterns -
with statistical validation
Parameters
----------
Fbeta : nipy.neurospin.graph.field.Field instance
an describing the spatial relationships
in the dataset. nbnodes = Fbeta.V
lbeta: an array of shape (nbnodes, subjects):
the multi-subject statistical maps
coord array of shape (nnodes,3):
spatial coordinates of the nodes
dmax float>0:
expected cluster std in the common space in units of coord
xyz array of shape (nnodes,3):
the grid coordinates of the field
affine=np.eye(4), array of shape(4,4)
coordinate-defining affine transformation
shape=None, tuple of length 3 defining the size of the grid
implicit to the discrete ROI definition
smin = 5 (int): minimal size of the regions to validate them
theta = 3.0 (float): first level threshold
verbose=0: verbosity mode
reshuffle=0: if nonzero, reshuffle the positions; this affects bf and gfc
Returns
-------
bf list of nipy.neurospin.spatial_models.hroi.Nroi instances
representing individual ROIs
let nr be the number of terminal regions across subjects
gf0, array of shape (nr)
the mixture-based prior probability
that the terminal regions are true positives
sub, array of shape (nr)
the subject index associated with the terminal regions
gfc, array of shape (nr, coord.shape[1])
the coordinates of the of the terminal regions
"""
bf = []
gfc = []
gf0 = []
sub = []
nsubj = lbeta.shape[1]
nvox = lbeta.shape[0]
for s in range(nsubj):
# description in terms of blobs
beta = np.reshape(lbeta[:,s],(nvox,1))
Fbeta.set_field(beta)
nroi = hroi.NROI_from_field(Fbeta, affine, shape, xyz, refdim=0,
th=theta, smin=smin)
if nroi!=None:
nroi.set_discrete_feature_from_index('activation',beta)
bfm = nroi.discrete_to_roi_features('activation','average')
bfm = bfm[nroi.isleaf()]
# get the regions position
if reshuffle:
nroi = nroi.reduce_to_leaves()
## randomize the positions by taking any local maximum of the image
#idx, topidx = Fbeta.get_local_maxima()
#temp = idx[np.argsort(np.random.rand(len(idx)))[:nroi.k]]
temp = np.argsort(np.random.rand(nvox))[:nroi.k]
bfc = coord[temp]
nroi.parents = np.arange(nroi.k)
nroi.set_roi_feature('position',bfc)
else:
nroi.set_discrete_feature_from_index('position',coord)
bfc = nroi.discrete_to_roi_features('position','average')
bfc = bfc[nroi.isleaf()]
gfc.append(bfc)
# compute the prior proba of being null
beta = np.squeeze(beta)
beta = beta[beta!=0]
# use a GMM model...
alpha = 0.01
prior_strength = 100
fixed_scale = True
bfp = en.three_classes_GMM_fit(beta, bfm, alpha,
prior_strength,verbose, fixed_scale)
bf0 = bfp[:,1]
## ... or the emp_null heuristic
#enn = en.ENN(beta)
#enn.learn()
#bf0 = np.reshape(enn.fdr(bfm),np.size(bf0))
gf0.append(bf0)
sub.append(s*np.ones(np.size(bfm)))
nroi.set_roi_feature('label',np.arange(nroi.k))
bf.append(nroi)
return bf, gf0, sub, gfc
pl.imshow(gam_gaus_pp[..., 0], cmap=pl.cm.hot)
pl.title('Gamma-Gaussian mixture,\n first component posterior proba.')
pl.colorbar()
pl.subplot(3, 3, 5)
pl.imshow(gam_gaus_pp[..., 1], cmap=pl.cm.hot)
pl.title('Gamma-Gaussian mixture,\n second component posterior proba.')
pl.colorbar()
pl.subplot(3, 3, 6)
pl.imshow(gam_gaus_pp[..., 2], cmap=pl.cm.hot)
pl.title('Gamma-Gaussian mixture,\n third component posterior proba.')
pl.colorbar()
################################################################################
# fit Beta's histogram with a mixture of Gaussians
alpha = 0.01
gaus_mix_pp = en.three_classes_GMM_fit(Beta, None,
alpha, prior_strength=100)
gaus_mix_pp = np.reshape(gaus_mix_pp, (dimx, dimy, 3))
pl.figure(fig.number)
pl.subplot(3, 3, 7)
pl.imshow(gaus_mix_pp[..., 0], cmap=pl.cm.hot)
pl.title('Gaussian mixture,\n first component posterior proba.')
pl.colorbar()
pl.subplot(3, 3, 8)
pl.imshow(gaus_mix_pp[..., 1], cmap=pl.cm.hot)
pl.title('Gaussian mixture,\n second component posterior proba.')
pl.colorbar()
pl.subplot(3, 3, 9)
pl.imshow(gaus_mix_pp[..., 2], cmap=pl.cm.hot)
pl.title('Gamma-Gaussian mixture,\n third component posterior proba.')
def compute_BSA_dev (Fbeta, lbeta, coord, dmax, xyz, affine=np.eye(4),
shape=None, thq=0.9,smin=5, ths=0, theta=3.0, g0=1.0,
bdensity=0, verbose=0):
"""
Compute the Bayesian Structural Activation paterns
Parameters
----------
Fbeta : nipy.neurospin.graph.field.Field instance
an describing the spatial relationships
in the dataset. nbnodes = Fbeta.V
lbeta: an array of shape (nbnodes, subjects):
the multi-subject statistical maps
coord array of shape (nnodes,3):
spatial coordinates of the nodes
xyz array of shape (nnodes,3):
the grid coordinates of the field
affine=np.eye(4), array of shape(4,4)
coordinate-defining affine transformation
shape=None, tuple of length 3 defining the size of the grid
implicit to the discrete ROI definition
thq = 0.5 (float): posterior significance threshold should be in [0,1]
smin = 5 (int): minimal size of the regions to validate them
theta = 3.0 (float): first level threshold
g0 = 1.0 (float): constant values of the uniform density
over the (compact) volume of interest
bdensity=0 if bdensity=1, the variable p in ouput
contains the likelihood of the data under H1
on the set of input nodes
verbose=0 : verbosity mode
Results
-------
crmap: array of shape (nnodes):
the resulting group-level labelling of the space
LR: a instance of sbf.Landmrak_regions that describes the ROIs found
in inter-subject inference
If no such thing can be defined LR is set to None
bf: List of nipy.neurospin.spatial_models.hroi.Nroi instances
representing individual ROIs
p: array of shape (nnodes):
likelihood of the data under H1 over some sampling grid
Note
----
This version is probably the best one to date
the intra subject Gamma-Gaussian MM has been replaces by a Gaussian MM
which is probably mroe robust
"""
bf = []
gfc = []
gf0 = []
sub = []
gc = []
nsubj = lbeta.shape[1]
nvox = lbeta.shape[0]
# intra-subject analysis: get the blobs,
# with their position and their significance
for s in range(nsubj):
# description in terms of blobs
beta = np.reshape(lbeta[:,s],(nvox,1))
Fbeta.set_field(beta)
nroi = hroi.NROI_from_field(Fbeta, affine, shape, xyz, refdim=0,
th=theta,smin=smin)
bf.append(nroi)
if nroi!=None:
sub.append(s*np.ones(nroi.k))
nroi.set_discrete_feature_from_index('activation',beta)
bfm = nroi.discrete_to_roi_features('activation','average')
# compute the region position
nroi.set_discrete_feature_from_index('position',coord)
bfc = nroi.discrete_to_roi_features('position',
'cumulated_average')
gfc.append(bfc)
# compute the prior proba of being null
beta = np.squeeze(beta)
beta = beta[beta!=0]
alpha = 0.01
prior_strength = 100
fixed_scale = True
bfp = en.three_classes_GMM_fit(beta, bfm, alpha,
prior_strength,verbose,fixed_scale)
bf0 = bfp[:,1]
gf0.append(bf0)
crmap = -np.ones(nvox, np.int)
u = []
AF = []
p = np.zeros(nvox)
if len(sub)<1:
return crmap,AF,bf,u,p
# inter-subject analysis
# use the DPMM (core part)
sub = np.concatenate(sub).astype(np.int)
gfc = np.concatenate(gfc)
gf0 = np.concatenate(gf0)
p = np.zeros(np.size(nvox))
g1 = g0
dof = 0
prior_precision = 1./(dmax*dmax)*np.ones((1,3), np.int)
if bdensity:
spatial_coords = coord
else:
spatial_coords = gfc
p,q = fc.fdp(gfc, 0.5, g0, g1, dof,prior_precision, 1-gf0,
sub, 100, spatial_coords,10,1000)
valid = q>thq
if verbose:
import matplotlib.pylab as mp
mp.figure()
mp.plot(1-gf0,q,'.')
print np.sum(valid),np.size(valid)
# remove non-significant regions
for s in range(nsubj):
bfs = bf[s]
if bfs!=None:
valids = valid[sub==s]
valids = bfs.propagate_upward_and(valids)
bfs.clean(valids)
bfs.merge_descending()
# re-compute the region position
bfs.set_discrete_feature_from_index('position',coord)
bfc = bfs.discrete_to_roi_features('position',
'cumulated_average')
# Alan's choice
#beta = np.reshape(lbeta[:,s],(nvox,1))
#bfsc = coord[bfs.feature_argmax(beta)]
#bfs.set_roi_feature(bfsc,'position')
# compute a model of between-regions associations
gc = _hierarchical_asso(bf,np.sqrt(2)*dmax)
# Infer the group-level clusters
if gc == []:
return crmap,AF,bf,p
# either replicator dynamics or agglomerative clustering
#u = sbf.segment_graph_rd(gc,1)
u,cost = average_link_graph_segment(gc,0.1,gc.V*1.0/nsubj)
q = 0
for s in range(nsubj):
if bf[s]!=None:
bf[s].set_roi_feature('label',u[q:q+bf[s].k])
q += bf[s].k
LR,mlabel = sbf.build_LR(bf,ths)
if LR!=None:
crmap = LR.map_label(coord,pval = 0.95,dmax=dmax)
return crmap,LR,bf,p