def mds_withprocrust(a, t, **kwargs):
# data should already be in the needed scale -- we just care about
# rotation, shift, reflection
pm = ProcrusteanMapper(reflection=True,
scaling=False,
reduction=False,
oblique=False)
a_ = mdsf(a, **kwargs)
ds = dataset_wizard(a_, targets=t)
pm.train(ds)
return pm.forward(a_)
def hypalign(source, target, node, surfsel, projmat,mask):
slneighbors = surfsel[node]
if len(slneighbors) == 0:
return projmat
sl = []
sl = [source[:, slneighbors], target[:, slneighbors]]
hmapper = ProcrusteanMapper(space='commonspace')
refds = sl[1].copy()
commonspace = refds.samples
zscore(commonspace,chunks_attr=None)
ds_new = sl[0].copy()
ds_new.sa[hmapper.get_space()] = commonspace.astype(float)
hmapper.train(ds_new)
conproj = hmapper.proj
m, n = conproj.shape
index = np.array(slneighbors)
projmat[np.ix_(index,index)] += np.asarray(conproj)
return projmat
class Hyperalignment(ClassWithCollections):
"""Align the features across multiple datasets into a common feature space.
This is a three-level algorithm. In the first level, a series of input
datasets is projected into a common feature space using a configurable
mapper. The common space is initially defined by a chosen exemplar from the
list of input datasets, but is subsequently refined by iteratively combining
the common space with the projected input datasets.
In the second (optional) level, the original input datasets are again
aligned with (or projected into) the intermediate first-level common
space. Through a configurable number of iterations the common space is
further refined by repeated projections of the input datasets and
combination/aggregation of these projections into an updated common space.
In the third level, the input datasets are again aligned with the, now
final, common feature space. The output of this algorithm are trained
mappers (one for each input dataset) that transform the individual features
spaces into the common space.
Level 1 and 2 are performed by the ``train()`` method, and level 3 is
performed when the trained Hyperalignment instance is called with a list of
datasets. This dataset list may or may not be identical to the training
datasets.
The default values for the parameters of the algorithm (e.g. projection via
Procrustean transformation, common space aggregation by averaging) resemble
the setup reported in :ref:`Haxby et al., Neuron (2011) <HGC+11>` *A common,
high-dimensional model of the representational space in human ventral
temporal cortex.*
Examples
--------
>>> # get some example data
>>> from mvpa2.testing.datasets import datasets
>>> from mvpa2.misc.data_generators import random_affine_transformation
>>> ds4l = datasets['uni4large']
>>> # generate a number of distorted variants of this data
>>> dss = [random_affine_transformation(ds4l) for i in xrange(4)]
>>> ha = Hyperalignment()
>>> ha.train(dss)
>>> mappers = ha(dss)
>>> len(mappers)
4
"""
training_residual_errors = ConditionalAttribute(
enabled=False,
doc="""Residual error (norm of the difference between common space
and projected data) per each training dataset at each level. The
residuals are stored in a dataset with one row per level, and
one column per input dataset. The first row corresponds to the
error 1st-level of hyperalignment the remaining rows store the
residual errors for each 2nd-level iteration.""")
residual_errors = ConditionalAttribute(
enabled=False,
doc="""Residual error (norm of the difference between common space
and projected data) per each dataset. The residuals are stored
in a single-row dataset with one column per input dataset.""")
# XXX Who cares whether it was chosen, or specified? This should be just
# 'ref_ds'
chosen_ref_ds = ConditionalAttribute(
enabled=True,
doc="""Index of the input dataset used as 1st-level reference
dataset.""")
# Lets use built-in facilities to specify parameters which
# constructor should accept
# the ``space`` of the mapper determines where the algorithm places the
# common space definition in the datasets
alignment = Parameter(
ProcrusteanMapper(space='commonspace'),
# might provide allowedtype
# XXX Currently, there's no way to handle this with constraints
doc="""The multidimensional transformation mapper. If
`None` (default) an instance of
:class:`~mvpa2.mappers.procrustean.ProcrusteanMapper` is
used.""")
output_dim = Parameter(
None,
constraints=(EnsureInt() & EnsureRange(min=1) | EnsureNone()),
doc="""Output common space dimensionality. If None, datasets are aligned
to the features of the `ref_ds`. Otherwise, dimensionality reduction is
performed using SVD and only the top SVs are kept. To get all features in
SVD-aligned space, give output_dim>=nfeatures.
""")
alpha = Parameter(
1,
constraints=EnsureFloat() & EnsureRange(min=0, max=1),
doc="""Regularization parameter to traverse between (Shrinkage)-CCA
(canonical correlation analysis) and regular hyperalignment.
Setting alpha to 1 makes the algorithm identical to
hyperalignment and alpha of 0 makes it CCA. By default,
it is 1, therefore hyperalignment. """)
level2_niter = Parameter(1,
constraints=EnsureInt() & EnsureRange(min=0),
doc="Number of 2nd-level iterations.")
ref_ds = Parameter(
None,
constraints=(EnsureRange(min=0) & EnsureInt()
| EnsureNone()),
doc="""Index of a dataset to use as 1st-level common space
reference. If `None`, then the dataset with the maximum
number of features is used.""")
nproc = Parameter(
1,
constraints=EnsureInt(),
doc="""Number of processes to use to parallelize the last step of
alignment. If different from 1, it passes it as n_jobs to
`joblib.Parallel`. Requires joblib package.""")
zscore_all = Parameter(
False,
constraints='bool',
doc="""Flag to Z-score all datasets prior hyperalignment.
Turn it off if Z-scoring is not desired or was already performed.
If True, returned mappers are ChainMappers with the Z-scoring
prepended to the actual projection.""")
zscore_common = Parameter(
True,
constraints='bool',
doc="""Flag to Z-score the common space after each adjustment.
This should be left enabled in most cases.""")
combiner1 = Parameter(
mean_xy, #
doc="""How to update common space in the 1st-level loop. This must
be a callable that takes two arguments. The first argument is
one of the input datasets after projection onto the 1st-level
common space. The second argument is the current 1st-level
common space. The 1st-level combiner is called iteratively for
each projected input dataset, except for the reference dataset.
By default the new common space is the average of the current
common space and the recently projected dataset.""")
level1_equal_weight = Parameter(
False,
constraints='bool',
doc="""Flag to force all datasets to have the same weight in the
level 1 iteration. False (default) means each time the new common
space is the average of the current common space and the newly
aligned dataset, and therefore earlier datasets have less weight."""
)
combiner2 = Parameter(
mean_axis0,
doc="""How to combine all individual spaces to common space. This
must be a callable that take a sequence of datasets as an argument.
The callable must return a single array. This combiner is called
once with all datasets after 1st-level projection to create an
updated common space, and is subsequently called again after each
2nd-level iteration.""")
joblib_backend = Parameter(
None,
constraints=EnsureChoice('multiprocessing', 'threading')
| EnsureNone(),
doc="""Backend to use for joblib when using nproc>1.
Options are 'multiprocessing' and 'threading'. Default is to use
'multiprocessing' unless run on OSX which have known issues with
joblib v0.10.3. If it is set to specific value here, then that will
be used at the risk of failure.""")
def __init__(self, **kwargs):
ClassWithCollections.__init__(self, **kwargs)
self.commonspace = None
# mapper to a low-dimensional subspace derived using SVD on training data
# Initializing here so that call can access it without passing after train.
# Moreover, it is similar to commonspace, in that, it is required for mapping
# new subjects
self._svd_mapper = None
@due.dcite(Doi('10.1016/j.neuron.2011.08.026'),
description="Hyperalignment of data to a common space",
tags=["implementation"])
def train(self, datasets):
"""Derive a common feature space from a series of datasets.
Parameters
----------
datasets : sequence of datasets
Returns
-------
A list of trained Mappers matching the number of input datasets.
"""
params = self.params # for quicker access ;)
ca = self.ca
# Check to make sure we get a list of datasets as input.
if not isinstance(datasets, (list, tuple, np.ndarray)):
raise TypeError("Input datasets should be a sequence "
"(of type list, tuple, or ndarray) of datasets.")
ndatasets = len(datasets)
nfeatures = [ds.nfeatures for ds in datasets]
alpha = params.alpha
residuals = None
if ca['training_residual_errors'].enabled:
residuals = np.zeros((1 + params.level2_niter, ndatasets))
ca.training_residual_errors = Dataset(
samples=residuals,
sa={
'levels':
['1'] + ['2:%i' % i for i in xrange(params.level2_niter)]
})
if __debug__:
debug('HPAL',
"Hyperalignment %s for %i datasets" % (self, ndatasets))
if params.ref_ds is None:
ref_ds = np.argmax(nfeatures)
else:
ref_ds = params.ref_ds
# Making sure that ref_ds is within range.
#Parameter() already checks for it being a non-negative integer
if ref_ds >= ndatasets:
raise ValueError, "Requested reference dataset %i is out of " \
"bounds. We have only %i datasets provided" \
% (ref_ds, ndatasets)
ca.chosen_ref_ds = ref_ds
# zscore all data sets
# ds = [ zscore(ds, chunks_attr=None) for ds in datasets]
# TODO since we are doing in-place zscoring create deep copies
# of the datasets with pruned targets and shallow copies of
# the collections (if they would come needed in the transformation)
# TODO: handle floats and non-floats differently to prevent
# waste of memory if there is no need (e.g. no z-scoring)
#otargets = [ds.sa.targets for ds in datasets]
datasets = [ds.copy(deep=False) for ds in datasets]
#datasets = [Dataset(ds.samples.astype(float), sa={'targets': [None] * len(ds)})
#datasets = [Dataset(ds.samples, sa={'targets': [None] * len(ds)})
# for ds in datasets]
if params.zscore_all:
if __debug__:
debug('HPAL', "Z-scoring all datasets")
for ids in xrange(len(datasets)):
zmapper = ZScoreMapper(chunks_attr=None)
zmapper.train(datasets[ids])
datasets[ids] = zmapper.forward(datasets[ids])
if alpha < 1:
datasets, wmappers = self._regularize(datasets, alpha)
# initial common space is the reference dataset
commonspace = datasets[ref_ds].samples
# the reference dataset might have been zscored already, don't do it
# twice
if params.zscore_common and not params.zscore_all:
if __debug__:
debug(
'HPAL_', "Creating copy of a commonspace and assuring "
"it is of a floating type")
commonspace = commonspace.astype(float)
zscore(commonspace, chunks_attr=None)
# If there is only one dataset in training phase, there is nothing to be done
# just use that data as the common space
if len(datasets) < 2:
self.commonspace = commonspace
else:
# create a mapper per dataset
# might prefer some other way to initialize... later
mappers = [deepcopy(params.alignment) for ds in datasets]
#
# Level 1 -- initial projection
#
lvl1_projdata = self._level1(datasets, commonspace, ref_ds,
mappers, residuals)
#
# Level 2 -- might iterate multiple times
#
# this is the final common space
self.commonspace = self._level2(datasets, lvl1_projdata, mappers,
residuals)
if params.output_dim is not None:
mappers = self._level3(datasets)
self._svd_mapper = SVDMapper()
self._svd_mapper.train(self._map_and_mean(datasets, mappers))
self._svd_mapper = StaticProjectionMapper(
proj=self._svd_mapper.proj[:, :params.output_dim])
def __call__(self, datasets):
"""Derive a common feature space from a series of datasets.
Parameters
----------
datasets : sequence of datasets
Returns
-------
A list of trained Mappers matching the number of input datasets.
"""
if self.commonspace is None:
self.train(datasets)
else:
# Check to make sure we get a list of datasets as input.
if not isinstance(datasets, (list, tuple, np.ndarray)):
raise TypeError(
"Input datasets should be a sequence "
"(of type list, tuple, or ndarray) of datasets.")
# place datasets into a copy of the list since items
# will be reassigned
datasets = list(datasets)
params = self.params # for quicker access ;)
alpha = params.alpha # for letting me be lazy ;)
if params.zscore_all:
if __debug__:
debug('HPAL', "Z-scoring all datasets")
# zscore them once while storing corresponding ZScoreMapper's
# so we can assemble a comprehensive mapper at the end
# (together with procrustes)
zmappers = []
for ids in xrange(len(datasets)):
zmapper = ZScoreMapper(chunks_attr=None)
zmappers.append(zmapper)
zmapper.train(datasets[ids])
datasets[ids] = zmapper.forward(datasets[ids])
if alpha < 1:
datasets, wmappers = self._regularize(datasets, alpha)
#
# Level 3 -- final, from-scratch, alignment to final common space
#
mappers = self._level3(datasets)
# return trained mappers for projection from all datasets into the
# common space
if params.zscore_all:
# We need to construct new mappers which would chain
# zscore and then final transformation
if params.alpha < 1:
mappers = [
ChainMapper([zm, wm, m])
for zm, wm, m in zip(zmappers, wmappers, mappers)
]
else:
mappers = [
ChainMapper([zm, m]) for zm, m in zip(zmappers, mappers)
]
elif params.alpha < 1:
mappers = [
ChainMapper([wm, m]) for wm, m in zip(wmappers, mappers)
]
if params.output_dim is not None:
mappers = [ChainMapper([m, self._svd_mapper]) for m in mappers]
return mappers
def _regularize(self, datasets, alpha):
if __debug__:
debug('HPAL',
"Using regularized hyperalignment with alpha of %d" % alpha)
wmappers = []
for ids in xrange(len(datasets)):
U, S, Vh = np.linalg.svd(datasets[ids])
S = 1 / np.sqrt((1 - alpha) * np.square(S) + alpha)
S.resize(len(Vh))
S = np.matrix(np.diag(S))
W = np.matrix(Vh.T) * S * np.matrix(Vh)
wmapper = StaticProjectionMapper(proj=W, auto_train=False)
wmapper.train(datasets[ids])
wmappers.append(wmapper)
datasets[ids] = wmapper.forward(datasets[ids])
return datasets, wmappers
def _level1(self, datasets, commonspace, ref_ds, mappers, residuals):
params = self.params # for quicker access ;)
data_mapped = [ds.samples for ds in datasets]
counts = 1 # number of datasets used so far for generating commonspace
for i, (m, ds_new) in enumerate(zip(mappers, datasets)):
if __debug__:
debug('HPAL_', "Level 1: ds #%i" % i)
if i == ref_ds:
continue
# assign common space to ``space`` of the mapper, because this is
# where it will be looking for it
ds_new.sa[m.get_space()] = commonspace
# find transformation of this dataset into the current common space
m.train(ds_new)
# remove common space attribute again to save on memory when the
# common space is updated for the next iteration
del ds_new.sa[m.get_space()]
# project this dataset into the current common space
ds_ = m.forward(ds_new.samples)
if params.zscore_common:
zscore(ds_, chunks_attr=None)
# replace original dataset with mapped one -- only the reference
# dataset will remain unchanged
data_mapped[i] = ds_
# compute first-level residuals wrt to the initial common space
if residuals is not None:
residuals[0, i] = np.linalg.norm(ds_ - commonspace)
# Update the common space. This is an incremental update after
# processing each 1st-level dataset. Maybe there should be a flag
# to make a batch update after processing all 1st-level datasets
# to an identical 1st-level common space
# TODO: make just a function so we dont' waste space
if params.level1_equal_weight:
commonspace = params.combiner1(ds_,
commonspace,
weights=(float(counts), 1.0))
else:
commonspace = params.combiner1(ds_, commonspace)
counts += 1
if params.zscore_common:
zscore(commonspace, chunks_attr=None)
return data_mapped
def _level2(self, datasets, lvl1_data, mappers, residuals):
params = self.params # for quicker access ;)
data_mapped = lvl1_data
# aggregate all processed 1st-level datasets into a new 2nd-level
# common space
commonspace = params.combiner2(data_mapped)
# XXX Why is this commented out? Who knows what combiner2 is doing and
# whether it changes the distribution of the data
#if params.zscore_common:
#zscore(commonspace, chunks_attr=None)
ndatasets = len(datasets)
for loop in xrange(params.level2_niter):
# 2nd-level alignment starts from the original/unprojected datasets
# again
for i, (m, ds_new) in enumerate(zip(mappers, datasets)):
if __debug__:
debug('HPAL_',
"Level 2 (%i-th iteration): ds #%i" % (loop, i))
# Optimization speed up heuristic
# Slightly modify the common space towards other feature
# spaces and reduce influence of this feature space for the
# to-be-computed projection
temp_commonspace = (commonspace * ndatasets - data_mapped[i]) \
/ (ndatasets - 1)
if params.zscore_common:
zscore(temp_commonspace, chunks_attr=None)
# assign current common space
ds_new.sa[m.get_space()] = temp_commonspace
# retrain the mapper for this dataset
m.train(ds_new)
# remove common space attribute again to save on memory when the
# common space is updated for the next iteration
del ds_new.sa[m.get_space()]
# obtain the 2nd-level projection
ds_ = m.forward(ds_new.samples)
if params.zscore_common:
zscore(ds_, chunks_attr=None)
# store for 2nd-level combiner
data_mapped[i] = ds_
# compute residuals
if residuals is not None:
residuals[1 + loop, i] = np.linalg.norm(ds_ - commonspace)
commonspace = params.combiner2(data_mapped)
# and again
if params.zscore_common:
zscore(commonspace, chunks_attr=None)
# return the final common space
return commonspace
def _level3(self, datasets):
params = self.params # for quicker access ;)
# create a mapper per dataset
mappers = [deepcopy(params.alignment) for ds in datasets]
# key different from level-2; the common space is uniform
#temp_commonspace = commonspace
# Fixing nproc=0
if params.nproc == 0:
from mvpa2.base import warning
warning("nproc of 0 doesn't make sense. Setting nproc to 1.")
params.nproc = 1
# Checking for joblib, if not, set nproc to 1
if params.nproc != 1:
from mvpa2.base import externals, warning
if not externals.exists('joblib'):
warning(
"Setting nproc different from 1 requires joblib package, which "
"does not seem to exist. Setting nproc to 1.")
params.nproc = 1
# start from original input datasets again
if params.nproc == 1:
residuals = []
for i, (m, ds_new) in enumerate(zip(mappers, datasets)):
if __debug__:
debug('HPAL_', "Level 3: ds #%i" % i)
m, residual = get_trained_mapper(
ds_new, self.commonspace, m,
self.ca['residual_errors'].enabled)
if self.ca['residual_errors'].enabled:
residuals.append(residual)
else:
if __debug__:
debug('HPAL_',
"Level 3: Using joblib with nproc = %d " % params.nproc)
verbose_level_parallel = 20 \
if (__debug__ and 'HPAL' in debug.active) else 0
from joblib import Parallel, delayed
import sys
# joblib's 'multiprocessing' backend has known issues of failure on OSX
# Tested with MacOS 10.12.13, python 2.7.13, joblib v0.10.3
if params.joblib_backend is None:
params.joblib_backend = 'threading' if sys.platform == 'darwin' \
else 'multiprocessing'
res = Parallel(n_jobs=params.nproc,
pre_dispatch=params.nproc,
backend=params.joblib_backend,
verbose=verbose_level_parallel)(
delayed(get_trained_mapper)(
ds, self.commonspace, mapper,
self.ca['residual_errors'].enabled)
for ds, mapper in zip(datasets, mappers))
mappers = [m for m, r in res]
if self.ca['residual_errors'].enabled:
residuals = [r for m, r in res]
if self.ca['residual_errors'].enabled:
self.ca.residual_errors = Dataset(
samples=np.array(residuals)[None, :])
return mappers
def _map_and_mean(self, datasets, mappers):
params = self.params
data_mapped = [[] for ds in datasets]
for i, (m, ds_new) in enumerate(zip(mappers, datasets)):
if __debug__:
debug('HPAL_', "Mapping training data for SVD: ds #%i" % i)
ds_ = m.forward(ds_new.samples)
# XXX should we zscore data before averaging and running SVD?
# zscore(ds_, chunks_attr=None)
data_mapped[i] = ds_
dss_mean = params.combiner2(data_mapped)
return dss_mean
def test_simple(self, oblique):
d_orig = datasets['uni2large'].samples
d_orig2 = datasets['uni4large'].samples
for sdim, nf_s, nf_t, full_test \
in (('Same 2D', 2, 2, True),
('Same 10D', 10, 10, True),
('2D -> 3D', 2, 3, True),
('3D -> 2D', 3, 2, False)):
# figure out some "random" rotation
d = max(nf_s, nf_t)
R = get_random_rotation(nf_s, nf_t, d_orig)
if nf_s == nf_t:
adR = np.abs(1.0 - np.linalg.det(R))
self.failUnless(adR < 1e-10,
"Determinant of rotation matrix should "
"be 1. Got it 1+%g" % adR)
self.failUnless(norm(np.dot(R, R.T)
- np.eye(R.shape[0])) < 1e-10)
for s, scaling in ((0.3, True), (1.0, False)):
pm = ProcrusteanMapper(scaling=scaling, oblique=oblique)
pm2 = ProcrusteanMapper(scaling=scaling, oblique=oblique)
t1, t2 = d_orig[23, 1], d_orig[22, 1]
# Create source/target data
d = d_orig[:, :nf_s]
d_s = d + t1
d_t = np.dot(s * d, R) + t2
# train bloody mapper(s)
ds = dataset_wizard(samples=d_s, targets=d_t)
pm.train(ds)
## not possible with new interface
#pm2.train(d_s, d_t)
## verify that both created the same transformation
#npm2proj = norm(pm.proj - pm2.proj)
#self.failUnless(npm2proj <= 1e-10,
# msg="Got transformation different by norm %g."
# " Had to be less than 1e-10" % npm2proj)
#self.failUnless(norm(pm._offset_in - pm2._offset_in) <= 1e-10)
#self.failUnless(norm(pm._offset_out - pm2._offset_out) <= 1e-10)
# do forward transformation on the same source data
d_s_f = pm.forward(d_s)
self.failUnlessEqual(d_s_f.shape, d_t.shape,
msg="Mapped shape should be identical to the d_t")
dsf = d_s_f - d_t
ndsf = norm(dsf)/norm(d_t)
if full_test:
dsR = norm(s*R - pm.proj)
if not oblique:
self.failUnless(dsR <= 1e-12,
msg="We should have got reconstructed rotation+scaling "
"perfectly. Now got d scale*R=%g" % dsR)
self.failUnless(np.abs(s - pm._scale) < 1e-12,
msg="We should have got reconstructed scale "
"perfectly. Now got %g for %g" % (pm._scale, s))
self.failUnless(ndsf <= 1e-12,
msg="%s: Failed to get to the target space correctly."
" normed error=%g" % (sdim, ndsf))
# Test if we get back
d_s_f_r = pm.reverse(d_s_f)
dsfr = d_s_f_r - d_s
ndsfr = norm(dsfr)/norm(d_s)
if full_test:
self.failUnless(ndsfr <= 1e-12,
msg="%s: Failed to reconstruct into source space correctly."
" normed error=%g" % (sdim, ndsfr))
class Hyperalignment(ClassWithCollections):
"""Align the features across multiple datasets into a common feature space.
This is a three-level algorithm. In the first level, a series of input
datasets is projected into a common feature space using a configurable
mapper. The common space is initially defined by a chosen exemplar from the
list of input datasets, but is subsequently refined by iteratively combining
the common space with the projected input datasets.
In the second (optional) level, the original input datasets are again
aligned with (or projected into) the intermediate first-level common
space. Through a configurable number of iterations the common space is
further refined by repeated projections of the input datasets and
combination/aggregation of these projections into an updated common space.
In the third level, the input datasets are again aligned with the, now
final, common feature space. The output of this algorithm are trained
mappers (one for each input dataset) that transform the individual features
spaces into the common space.
Level 1 and 2 are performed by the ``train()`` method, and level 3 is
performed when the trained Hyperalignment instance is called with a list of
datasets. This dataset list may or may not be identical to the training
datasets.
The default values for the parameters of the algorithm (e.g. projection via
Procrustean transformation, common space aggregation by averaging) resemble
the setup reported in :ref:`Haxby et al., Neuron (2011) <HGC+11>` *A common,
high-dimensional model of the representational space in human ventral
temporal cortex.*
Examples
--------
>>> # get some example data
>>> from mvpa2.testing.datasets import datasets
>>> from mvpa2.misc.data_generators import random_affine_transformation
>>> ds4l = datasets['uni4large']
>>> # generate a number of distorted variants of this data
>>> dss = [random_affine_transformation(ds4l) for i in xrange(4)]
>>> ha = Hyperalignment()
>>> ha.train(dss)
>>> mappers = ha(dss)
>>> len(mappers)
4
"""
training_residual_errors = ConditionalAttribute(
enabled=False,
doc="""Residual error (norm of the difference between common space
and projected data) per each training dataset at each level. The
residuals are stored in a dataset with one row per level, and
one column per input dataset. The first row corresponds to the
error 1st-level of hyperalignment the remaining rows store the
residual errors for each 2nd-level iteration.""")
residual_errors = ConditionalAttribute(
enabled=False,
doc="""Residual error (norm of the difference between common space
and projected data) per each dataset. The residuals are stored
in a single-row dataset with one column per input dataset.""")
# XXX Who cares whether it was chosen, or specified? This should be just
# 'ref_ds'
choosen_ref_ds = ConditionalAttribute(
enabled=True,
doc="""Index of the input dataset used as 1st-level reference
dataset.""")
# Lets use built-in facilities to specify parameters which
# constructor should accept
# the ``space`` of the mapper determines where the algorithm places the
# common space definition in the datasets
alignment = Parameter(
ProcrusteanMapper(space='commonspace'), # might provide allowedtype
allowedtype='basestring',
doc="""The multidimensional transformation mapper. If
`None` (default) an instance of
:class:`~mvpa2.mappers.procrustean.ProcrusteanMapper` is
used.""")
alpha = Parameter(
1,
allowedtype='float32',
min=0,
max=1,
doc="""Regularization parameter to traverse between (Shrinkage)-CCA
(canonical correlation analysis) and regular hyperalignment.
Setting alpha to 1 makes the algorithm identical to
hyperalignment and alpha of 0 makes it CCA. By default,
it is 1, therefore hyperalignment. """)
level2_niter = Parameter(1,
allowedtype='int',
min=0,
doc="Number of 2nd-level iterations.")
ref_ds = Parameter(
None,
allowedtype='int',
min=0,
doc="""Index of a dataset to use as 1st-level common space
reference. If `None`, then the dataset with the maximum
number of features is used.""")
zscore_all = Parameter(
False,
allowedtype='bool',
doc="""Flag to Z-score all datasets prior hyperalignment.
Turn it off if Z-scoring is not desired or was already performed.
If True, returned mappers are ChainMappers with the Z-scoring
prepended to the actual projection.""")
zscore_common = Parameter(
True,
allowedtype='bool',
doc="""Flag to Z-score the common space after each adjustment.
This should be left enabled in most cases.""")
combiner1 = Parameter(
lambda x, y: 0.5 * (x + y), #
doc="""How to update common space in the 1st-level loop. This must
be a callable that takes two arguments. The first argument is
one of the input datasets after projection onto the 1st-level
common space. The second argument is the current 1st-level
common space. The 1st-level combiner is called iteratively for
each projected input dataset, except for the reference dataset.
By default the new common space is the average of the current
common space and the recently projected dataset.""")
combiner2 = Parameter(
lambda l: np.mean(l, axis=0),
doc="""How to combine all individual spaces to common space. This
must be a callable that take a sequence of datasets as an argument.
The callable must return a single array. This combiner is called
once with all datasets after 1st-level projection to create an
updated common space, and is subsequently called again after each
2nd-level iteration.""")
def __init__(self, **kwargs):
ClassWithCollections.__init__(self, **kwargs)
self.commonspace = None
def train(self, datasets):
"""Derive a common feature space from a series of datasets.
Parameters
----------
datasets : sequence of datasets
Returns
-------
A list of trained Mappers matching the number of input datasets.
"""
params = self.params # for quicker access ;)
ca = self.ca
ndatasets = len(datasets)
nfeatures = [ds.nfeatures for ds in datasets]
alpha = params.alpha
residuals = None
if ca['training_residual_errors'].enabled:
residuals = np.zeros((1 + params.level2_niter, ndatasets))
ca.training_residual_errors = Dataset(
samples=residuals,
sa={
'levels':
['1'] + ['2:%i' % i for i in xrange(params.level2_niter)]
})
if __debug__:
debug('HPAL',
"Hyperalignment %s for %i datasets" % (self, ndatasets))
if params.ref_ds is None:
ref_ds = np.argmax(nfeatures)
else:
ref_ds = params.ref_ds
if ref_ds < 0 and ref_ds >= ndatasets:
raise ValueError, "Requested reference dataset %i is out of " \
"bounds. We have only %i datasets provided" \
% (ref_ds, ndatasets)
ca.choosen_ref_ds = ref_ds
# zscore all data sets
# ds = [ zscore(ds, chunks_attr=None) for ds in datasets]
# TODO since we are doing in-place zscoring create deep copies
# of the datasets with pruned targets and shallow copies of
# the collections (if they would come needed in the transformation)
# TODO: handle floats and non-floats differently to prevent
# waste of memory if there is no need (e.g. no z-scoring)
#otargets = [ds.sa.targets for ds in datasets]
datasets = [ds.copy(deep=False) for ds in datasets]
#datasets = [Dataset(ds.samples.astype(float), sa={'targets': [None] * len(ds)})
#datasets = [Dataset(ds.samples, sa={'targets': [None] * len(ds)})
# for ds in datasets]
if params.zscore_all:
if __debug__:
debug('HPAL', "Z-scoring all datasets")
for ids in xrange(len(datasets)):
zmapper = ZScoreMapper(chunks_attr=None)
zmapper.train(datasets[ids])
datasets[ids] = zmapper.forward(datasets[ids])
if alpha < 1:
datasets, wmappers = self._regularize(datasets, alpha)
# initial common space is the reference dataset
commonspace = datasets[ref_ds].samples
# the reference dataset might have been zscored already, don't do it
# twice
if params.zscore_common and not params.zscore_all:
if __debug__:
debug(
'HPAL_', "Creating copy of a commonspace and assuring "
"it is of a floating type")
commonspace = commonspace.astype(float)
zscore(commonspace, chunks_attr=None)
# create a mapper per dataset
# might prefer some other way to initialize... later
mappers = [deepcopy(params.alignment) for ds in datasets]
#
# Level 1 -- initial projection
#
lvl1_projdata = self._level1(datasets, commonspace, ref_ds, mappers,
residuals)
#
# Level 2 -- might iterate multiple times
#
# this is the final common space
self.commonspace = self._level2(datasets, lvl1_projdata, mappers,
residuals)
def __call__(self, datasets):
"""Derive a common feature space from a series of datasets.
Parameters
----------
datasets : sequence of datasets
Returns
-------
A list of trained Mappers matching the number of input datasets.
"""
if self.commonspace is None:
self.train(datasets)
# place datasets into a copy of the list since items
# will be reassigned
datasets = list(datasets)
params = self.params # for quicker access ;)
alpha = params.alpha # for letting me be lazy ;)
if params.zscore_all:
if __debug__:
debug('HPAL', "Z-scoring all datasets")
# zscore them once while storing corresponding ZScoreMapper's
# so we can assemble a comprehensive mapper at the end
# (together with procrustes)
zmappers = []
for ids in xrange(len(datasets)):
zmapper = ZScoreMapper(chunks_attr=None)
zmappers.append(zmapper)
zmapper.train(datasets[ids])
datasets[ids] = zmapper.forward(datasets[ids])
if alpha < 1:
datasets, wmappers = self._regularize(datasets, alpha)
#
# Level 3 -- final, from-scratch, alignment to final common space
#
mappers = self._level3(datasets)
# return trained mappers for projection from all datasets into the
# common space
if params.zscore_all:
# We need to construct new mappers which would chain
# zscore and then final transformation
if params.alpha < 1:
return [
ChainMapper([zm, wm, m])
for zm, wm, m in zip(zmappers, wmappers, mappers)
]
else:
return [
ChainMapper([zm, m]) for zm, m in zip(zmappers, mappers)
]
else:
if params.alpha < 1:
return [
ChainMapper([wm, m]) for wm, m in zip(wmappers, mappers)
]
else:
return mappers
def _regularize(self, datasets, alpha):
if __debug__:
debug('HPAL',
"Using regularized hyperalignment with alpha of %d" % alpha)
wmappers = []
for ids in xrange(len(datasets)):
U, S, Vh = np.linalg.svd(datasets[ids])
S = 1 / np.sqrt((1 - alpha) * np.square(S) + alpha)
S.resize(len(Vh))
S = np.matrix(np.diag(S))
W = np.matrix(Vh.T) * S * np.matrix(Vh)
wmapper = StaticProjectionMapper(proj=W)
wmappers.append(wmapper)
datasets[ids] = wmapper.forward(datasets[ids])
return datasets, wmappers
def _level1(self, datasets, commonspace, ref_ds, mappers, residuals):
params = self.params # for quicker access ;)
data_mapped = [ds.samples for ds in datasets]
for i, (m, ds_new) in enumerate(zip(mappers, datasets)):
if __debug__:
debug('HPAL_', "Level 1: ds #%i" % i)
if i == ref_ds:
continue
# assign common space to ``space`` of the mapper, because this is
# where it will be looking for it
ds_new.sa[m.get_space()] = commonspace
# find transformation of this dataset into the current common space
m.train(ds_new)
# remove common space attribute again to save on memory when the
# common space is updated for the next iteration
del ds_new.sa[m.get_space()]
# project this dataset into the current common space
ds_ = m.forward(ds_new.samples)
if params.zscore_common:
zscore(ds_, chunks_attr=None)
# replace original dataset with mapped one -- only the reference
# dataset will remain unchanged
data_mapped[i] = ds_
# compute first-level residuals wrt to the initial common space
if residuals is not None:
residuals[0, i] = np.linalg.norm(ds_ - commonspace)
# Update the common space. This is an incremental update after
# processing each 1st-level dataset. Maybe there should be a flag
# to make a batch update after processing all 1st-level datasets
# to an identical 1st-level common space
# TODO: make just a function so we dont' waste space
commonspace = params.combiner1(ds_, commonspace)
if params.zscore_common:
zscore(commonspace, chunks_attr=None)
return data_mapped
def _level2(self, datasets, lvl1_data, mappers, residuals):
params = self.params # for quicker access ;)
data_mapped = lvl1_data
# aggregate all processed 1st-level datasets into a new 2nd-level
# common space
commonspace = params.combiner2(data_mapped)
# XXX Why is this commented out? Who knows what combiner2 is doing and
# whether it changes the distribution of the data
#if params.zscore_common:
#zscore(commonspace, chunks_attr=None)
ndatasets = len(datasets)
for loop in xrange(params.level2_niter):
# 2nd-level alignment starts from the original/unprojected datasets
# again
for i, (m, ds_new) in enumerate(zip(mappers, datasets)):
if __debug__:
debug('HPAL_',
"Level 2 (%i-th iteration): ds #%i" % (loop, i))
# Optimization speed up heuristic
# Slightly modify the common space towards other feature
# spaces and reduce influence of this feature space for the
# to-be-computed projection
temp_commonspace = (commonspace * ndatasets - data_mapped[i]) \
/ (ndatasets - 1)
if params.zscore_common:
zscore(temp_commonspace, chunks_attr=None)
# assign current common space
ds_new.sa[m.get_space()] = temp_commonspace
# retrain the mapper for this dataset
m.train(ds_new)
# remove common space attribute again to save on memory when the
# common space is updated for the next iteration
del ds_new.sa[m.get_space()]
# obtain the 2nd-level projection
ds_ = m.forward(ds_new.samples)
if params.zscore_common:
zscore(ds_, chunks_attr=None)
# store for 2nd-level combiner
data_mapped[i] = ds_
# compute residuals
if residuals is not None:
residuals[1 + loop, i] = np.linalg.norm(ds_ - commonspace)
commonspace = params.combiner2(data_mapped)
# and again
if params.zscore_common:
zscore(commonspace, chunks_attr=None)
# return the final common space
return commonspace
def _level3(self, datasets):
params = self.params # for quicker access ;)
# create a mapper per dataset
mappers = [deepcopy(params.alignment) for ds in datasets]
# key different from level-2; the common space is uniform
#temp_commonspace = commonspace
residuals = None
if self.ca['residual_errors'].enabled:
residuals = np.zeros((1, len(datasets)))
self.ca.residual_errors = Dataset(samples=residuals)
# start from original input datasets again
for i, (m, ds_new) in enumerate(zip(mappers, datasets)):
if __debug__:
debug('HPAL_', "Level 3: ds #%i" % i)
# retrain mapper on final common space
ds_new.sa[m.get_space()] = self.commonspace
m.train(ds_new)
# remove common space attribute again to save on memory
del ds_new.sa[m.get_space()]
if residuals is not None:
# obtain final projection
data_mapped = m.forward(ds_new.samples)
residuals[0,
i] = np.linalg.norm(data_mapped - self.commonspace)
return mappers
def test_simple(self, svd, oblique):
d_orig = datasets['uni2large'].samples
d_orig2 = datasets['uni4large'].samples
for sdim, nf_s, nf_t, full_test \
in (('Same 2D', 2, 2, True),
('Same 10D', 10, 10, True),
('2D -> 3D', 2, 3, True),
('3D -> 2D', 3, 2, False)):
# figure out some "random" rotation
d = max(nf_s, nf_t)
R = get_random_rotation(nf_s, nf_t, d_orig)
if nf_s == nf_t:
adR = np.abs(1.0 - np.linalg.det(R))
self.assertTrue(
adR < 1e-10, "Determinant of rotation matrix should "
"be 1. Got it 1+%g" % adR)
self.assertTrue(
norm(np.dot(R, R.T) - np.eye(R.shape[0])) < 1e-10)
for s, scaling in ((0.3, True), (1.0, False)):
pm = ProcrusteanMapper(scaling=scaling,
oblique=oblique,
svd=svd)
# pm2 = ProcrusteanMapper(scaling=scaling, oblique=oblique)
t1, t2 = d_orig[23, 1], d_orig[22, 1]
# Create source/target data
d = d_orig[:, :nf_s]
d_s = d + t1
d_t = np.dot(s * d, R) + t2
# train bloody mapper(s)
ds = dataset_wizard(samples=d_s, targets=d_t)
pm.train(ds)
## not possible with new interface
#pm2.train(d_s, d_t)
## verify that both created the same transformation
#npm2proj = norm(pm.proj - pm2.proj)
#self.assertTrue(npm2proj <= 1e-10,
# msg="Got transformation different by norm %g."
# " Had to be less than 1e-10" % npm2proj)
#self.assertTrue(norm(pm._offset_in - pm2._offset_in) <= 1e-10)
#self.assertTrue(norm(pm._offset_out - pm2._offset_out) <= 1e-10)
# do forward transformation on the same source data
d_s_f = pm.forward(d_s)
self.assertEqual(
d_s_f.shape,
d_t.shape,
msg="Mapped shape should be identical to the d_t")
dsf = d_s_f - d_t
ndsf = norm(dsf) / norm(d_t)
if full_test:
dsR = norm(s * R - pm.proj)
if not oblique:
self.assertTrue(
dsR <= 1e-12,
msg=
"We should have got reconstructed rotation+scaling "
"perfectly. Now got d scale*R=%g" % dsR)
self.assertTrue(
np.abs(s - pm._scale) < 1e-12,
msg="We should have got reconstructed scale "
"perfectly. Now got %g for %g" % (pm._scale, s))
self.assertTrue(
ndsf <= 1e-12,
msg="%s: Failed to get to the target space correctly."
" normed error=%g" % (sdim, ndsf))
# Test if we get back
d_s_f_r = pm.reverse(d_s_f)
dsfr = d_s_f_r - d_s
ndsfr = norm(dsfr) / norm(d_s)
if full_test:
self.assertTrue(
ndsfr <= 1e-12,
msg=
"%s: Failed to reconstruct into source space correctly."
" normed error=%g" % (sdim, ndsfr))
def test_reflection(self, rep=10):
for i in range(rep):
from mvpa2.testing.datasets import get_random_rotation
d = np.random.random((100, 2))
T = get_random_rotation(d.shape[1])
d2 = np.dot(d, T)
# scale it up a bit
d2 *= 1.2
# add a reflection by flipping the first dimension
d2[:, 0] *= -1
ds = dataset_wizard(samples=d, targets=d2)
norm0 = np.linalg.norm(d - d2)
mapper = ProcrusteanMapper(scaling=False, reflection=False)
mapper.train(ds)
norm1 = np.linalg.norm(d2 - mapper.forward(ds).samples)
eps = 1e-7
self.assertLess(norm1, norm0 + eps,
msg='Procrustes should reduce difference, '
'but %f > %f' % (norm1, norm0))
mapper = ProcrusteanMapper(scaling=True, reflection=False)
mapper.train(ds)
norm2 = np.linalg.norm(d2 - mapper.forward(ds).samples)
self.assertLess(norm2, norm1 + eps,
msg='Procrustes with scaling should work better, '
'but %f > %f' % (norm2, norm1))
mapper = ProcrusteanMapper(scaling=False, reflection=True)
mapper.train(ds)
norm3 = np.linalg.norm(d2 - mapper.forward(ds).samples)
self.assertLess(norm3, norm1 + eps,
msg='Procrustes with reflection should work better, '
'but %f > %f' % (norm3, norm1))
mapper = ProcrusteanMapper(scaling=True, reflection=True)
mapper.train(ds)
norm4 = np.linalg.norm(d2 - mapper.forward(ds).samples)
self.assertLess(norm4, norm3 + eps,
msg='Procrustes with scaling should work better, '
'but %f > %f' % (norm4, norm3))
self.assertLess(norm4, norm2 + eps,
msg='Procrustes with reflection should work better, '
'but %f > %f' % (norm4, norm2))
def run(args):
print(args.data)
dss = [arg2ds(d)[:, :100] for d in args.data]
verbose(1, "Loaded %i input datasets" % len(dss))
if __debug__:
for i, ds in enumerate(dss):
debug('CMDLINE', "dataset %i: %s" % (i, str(ds)))
# TODO at this point more check could be done, e.g. ref_ds > len(dss)
# assemble parameters
params = dict([(param, getattr(args, param))
for param in _supported_parameters])
if __debug__:
debug('CMDLINE', "configured parameters: '%s'" % params)
# assemble CAs
enabled_ca = [ca for ca in _supported_cas if getattr(args, ca)]
if __debug__:
debug('CMDLINE', "enabled conditional attributes: '%s'" % enabled_ca)
hyper = Hyperalignment(enable_ca=enabled_ca,
alignment=ProcrusteanMapper(svd='dgesvd',
space='commonspace'),
**params)
verbose(1, "Running hyperalignment")
promappers = hyper(dss)
verbose(2, "Alignment reference is dataset %i" % hyper.ca.chosen_ref_ds)
verbose(1, "Writing output")
# save on memory and remove the training data
del dss
if args.commonspace:
if __debug__:
debug('CMDLINE', "write commonspace as hdf5")
h5save('%s%s.hdf5' % (args.output_prefix,
_output_specs['commonspace']['output_suffix']),
hyper.commonspace,
compression=args.hdf5_compression)
for ca in _supported_cas:
if __debug__:
debug('CMDLINE', "check conditional attribute: '%s'" % ca)
if getattr(args, ca):
if __debug__:
debug('CMDLINE', "store conditional attribute: '%s'" % ca)
np.savetxt(
'%s%s' %
(args.output_prefix, _supported_cas[ca]['output_suffix']),
hyper.ca[ca].value.samples)
if args.store_transformation:
for i, pm in enumerate(promappers):
if __debug__:
debug('CMDLINE', "store mapper %i: %s" % (i, str(pm)))
h5save('%s%s.hdf5' % (args.output_prefix, '_map%.3i' % i),
pm,
compression=args.hdf5_compression)
if args.transform:
tdss, dss = _transform_dss(args.transform, promappers, args)
del dss
verbose(1, "Store transformed datasets")
for i, td in enumerate(tdss):
if __debug__:
debug('CMDLINE',
"store transformed data %i: %s" % (i, str(td)))
h5save('%s%s.hdf5' % (args.output_prefix, '_transformed%.3i' % i),
td,
compression=args.hdf5_compression)
def test_reflection(self, rep=10):
for i in range(rep):
from mvpa2.testing.datasets import get_random_rotation
d = np.random.random((100, 2))
T = get_random_rotation(d.shape[1])
d2 = np.dot(d, T)
# scale it up a bit
d2 *= 1.2
# add a reflection by flipping the first dimension
d2[:, 0] *= -1
ds = dataset_wizard(samples=d, targets=d2)
norm0 = np.linalg.norm(d - d2)
mapper = ProcrusteanMapper(scaling=False, reflection=False)
mapper.train(ds)
norm1 = np.linalg.norm(d2 - mapper.forward(ds).samples)
eps = 1e-7
self.assertLess(norm1,
norm0 + eps,
msg='Procrustes should reduce difference, '
'but %f > %f' % (norm1, norm0))
mapper = ProcrusteanMapper(scaling=True, reflection=False)
mapper.train(ds)
norm2 = np.linalg.norm(d2 - mapper.forward(ds).samples)
self.assertLess(norm2,
norm1 + eps,
msg='Procrustes with scaling should work better, '
'but %f > %f' % (norm2, norm1))
mapper = ProcrusteanMapper(scaling=False, reflection=True)
mapper.train(ds)
norm3 = np.linalg.norm(d2 - mapper.forward(ds).samples)
self.assertLess(
norm3,
norm1 + eps,
msg='Procrustes with reflection should work better, '
'but %f > %f' % (norm3, norm1))
mapper = ProcrusteanMapper(scaling=True, reflection=True)
mapper.train(ds)
norm4 = np.linalg.norm(d2 - mapper.forward(ds).samples)
self.assertLess(norm4,
norm3 + eps,
msg='Procrustes with scaling should work better, '
'but %f > %f' % (norm4, norm3))
self.assertLess(
norm4,
norm2 + eps,
msg='Procrustes with reflection should work better, '
'but %f > %f' % (norm4, norm2))
