def bsa_dpmm(Fbeta, bf, gf0, sub, gfc, coord, dmax, thq, ths, g0,verbose=0):
"""
Estimation of the population level model of activation density using
dpmm and inference
Parameters
----------
Fbeta nipy.neurospin.graph.field.Field instance
an describing the spatial relationships
in the dataset. nbnodes = Fbeta.V
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
dmax float>0:
expected cluster std in the common space in units of coord
thq = 0.5 (float in the [0,1] interval)
p-value of the prevalence test
ths=0, float in the rannge [0,nsubj]
null hypothesis on region prevalence that is rejected during inference
g0 = 1.0 (float): constant value of the uniform density
over the (compact) volume of interest
verbose=0, verbosity mode
Returns
-------
crmap: array of shape (nnodes):
the resulting group-level labelling of the space
LR: a instance of sbf.Landmark_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
"""
nvox = coord.shape[0]
nsubj = len(bf)
crmap = -np.ones(nvox, np.int)
u = []
LR = None
p = np.zeros(nvox)
if len(sub)<1:
return crmap,LR,bf,p
sub = np.concatenate(sub).astype(np.int)
gfc = np.concatenate(gfc)
gf0 = np.concatenate(gf0)
# prepare the DPMM
g1 = g0
prior_precision = 1./(dmax*dmax)*np.ones((1,3), np.float)
dof = 100
spatial_coords = coord
burnin = 100
nis = 300
# nis = number of iterations to estimate p
nii = 100
# nii = number of iterations to estimate q
p,q = fc.fdp(gfc, 0.5, g0, g1, dof, prior_precision, 1-gf0,
sub, burnin, spatial_coords, nis, nii)
if verbose:
import matplotlib.pylab as mp
mp.figure()
mp.plot(1-gf0,q,'.')
h1,c1 = mp.histogram((1-gf0),bins=100)
h2,c2 = mp.histogram(q,bins=100)
mp.figure()
# We use c1[:len(h1)] to be independant of the change in np.hist
mp.bar(c1[:len(h1)],h1,width=0.005)
mp.bar(c2[:len(h2)]+0.003,h2,width=0.005,color='r')
print 'Number of candidate regions %i, regions found %i' % (
np.size(q), q.sum())
Fbeta.set_field(p)
idx,depth, major,label = Fbeta.custom_watershed(0,g0)
# append some information to the hroi in each subject
for s in range(nsubj):
bfs = bf[s]
if bfs!=None:
leaves = bfs.isleaf()
us = -np.ones(bfs.k).astype(np.int)
lq = np.zeros(bfs.k)
lq[leaves] = q[sub==s]
bfs.set_roi_feature('posterior_proba',lq)
lq = np.zeros(bfs.k)
lq[leaves] = 1-gf0[sub==s]
bfs.set_roi_feature('prior_proba',lq)
#idx = bfs.feature_argmax('activation')
#midx = [bfs.discrete_features['index'][k][idx[k]]
# for k in range(bfs.k)]
pos = bfs.roi_features['position']
midx = [np.argmin(np.sum((coord-pos[k])**2,1)) for k in range(bfs.k)]
j = label[np.array(midx)]
us[leaves] = j[leaves]
# when parent regions has similarly labelled children,
# include it also
us = bfs.propagate_upward(us)
bfs.set_roi_feature('label',us)
# derive the group-level landmarks
# with a threshold on the number of subjects
# that are represented in each one
LR,nl = infer_LR(bf, thq, ths,verbose=verbose)
# make a group-level map of the landmark position
crmap = -np.ones(np.shape(label))
if nl!=None:
aux = np.arange(label.max()+1)
aux[0:np.size(nl)] = nl
crmap[label>-1] = aux[label[label>-1]]
return crmap, LR, bf, p
def compute_BSA_ipmi(Fbeta,lbeta, coord,dmax, xyz, affine=np.eye(4),
shape=None, thq=0.5,
smin=5, ths=0, theta=3.0, g0=1.0, bdensity=0, verbose=0):
"""
Compute the Bayesian Structural Activation patterns
with approach described in IPMI'07 paper
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 is historically the first version,
but probably not the most optimal
It should not be changed for historical reason
"""
bf = []
gfc = []
gf0 = []
sub = []
gc = []
nbsubj = lbeta.shape[1]
nvox = lbeta.shape[0]
# intra-subject part: compute the blobs
# and assess their significance
for s in range(nbsubj):
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))
# find some way to avoid coordinate averaging
nroi.set_discrete_feature_from_index('activation',beta)
bfm = nroi.discrete_to_roi_features('activation','average')
nroi.set_discrete_feature_from_index('position',coord)
bfc = nroi.discrete_to_roi_features('position',
'cumulated_average')
gfc.append(bfc)
# get some prior on the significance of the regions
beta = np.reshape(beta,(nvox))
beta = beta[beta!=0]
# use a Gamma-Gaussian Mixture Model
bfp = en.Gamma_Gaussian_fit(beta,bfm,verbose)
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.float)
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)
# inference
valid = q>thq
if verbose>1:
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(nbsubj):
bfs = bf[s]
if bfs!=None:
valids = valid[sub==s]
valids = bfs.propagate_upward_and(valids)
bfs.clean(valids)
if bfs!=None:
bfs.merge_descending()
bfs.set_discrete_feature_from_index('position',coord)
bfs.discrete_to_roi_features('position','cumulated_average')
# compute probabilitsic correspondences across subjects
gc = _hierarchical_asso(bf,np.sqrt(2)*dmax)
if gc == []:
return crmap,AF,bf,p
# make hard clusters
# choose one solution...
#u = sbf.segment_graph_rd(gc,1)
u,cost = average_link_graph_segment(gc,0.2,gc.V*1.0/nbsubj)
q = 0
for s in range(nbsubj):
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
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
def compute_BSA_loo(Fbeta, lbeta, coord, dmax, xyz, affine=np.eye(4),
shape=None,
thq=0.5, smin=5, ths=0, theta=3.0, g0=1.0,
verbose=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
thq = 0.5 (float):
posterior significance threshold
should be in the [0,1] interval
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
verbose=0: verbosity mode
Results
-------
mll, float, the average cross-validated log-likelihood across subjects
ml0, float the log-likelihood of the model under a global null hypothesis
"""
nsubj = lbeta.shape[1]
nvox = lbeta.shape[0]
bf, gf0, sub, gfc = compute_individual_regions(Fbeta, lbeta, coord, dmax,
xyz, affine, shape, smin,
theta, verbose)
crmap = -np.ones(nvox, np.int)
LR = None
p = np.zeros(nvox)
if len(sub)<1:
return np.log(g0), np.log(g0)
sub = np.concatenate(sub).astype(np.int)
gfc = np.concatenate(gfc)
gf0 = np.concatenate(gf0)
# prepare the DPMM
g1 = g0
prior_precision = 1./(dmax*dmax)*np.ones((1,3), np.float)
dof = 100
burnin = 100
nis = 300
nii = 100
ll1 = []
ll0 = []
ll2 = []
for s in range(nsubj):
#
if np.sum(sub==s)>0:
spatial_coords = gfc[sub==s]
p, q = fc.fdp(gfc[sub!=s], 0.5, g0, g1, dof, prior_precision,
1-gf0[sub!=s], sub[sub!=s], burnin, spatial_coords,
nis, nii)
pp = gf0[sub==s]*g0 + p*(1-gf0[sub==s])
ll2.append(np.mean(np.log(pp)))
ll1.append(np.mean(np.log(p)))
ll0.append(np.mean(np.log(g0)))
ml0 = np.mean(np.array(ll0))
ml1 = np.mean(np.array(ll1))
mll = np.mean(np.array(ll2))
if verbose:
print 'average cross-validated log likelihood'
print 'null model: ', ml0,' alternative model: ', mll
return mll, ml0
