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brainiak/brainiak/funcalign/sssrm.py

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# Copyright 2016 Intel Corporation
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Semi-Supervised Shared Response Model (SS-SRM)
The implementations are based on the following publications:
.. [Turek2016] "A Semi-Supervised Method for Multi-Subject fMRI Functional
Alignment",
J. S. Turek, T. L. Willke, P.-H. Chen, P. J. Ramadge
IEEE International Conference on Acoustics, Speech and Signal Processing
(ICASSP), 2017, pp. 1098-1102.
https://doi.org/10.1109/ICASSP.2017.7952326
"""
# Authors: Javier Turek (Intel Labs), 2016
import logging
import numpy as np
from sklearn.base import BaseEstimator, TransformerMixin, ClassifierMixin
from sklearn.utils import assert_all_finite
from sklearn.utils.validation import NotFittedError
from sklearn.utils.multiclass import unique_labels
import theano
import theano.tensor as T
import theano.compile.sharedvalue as S
from pymanopt.manifolds import Euclidean
from pymanopt.manifolds import Product
from pymanopt.solvers import ConjugateGradient
from pymanopt import Problem
from pymanopt.manifolds import Stiefel
import pymanopt
import gc
from brainiak.utils import utils
from brainiak.funcalign import srm
__all__ = [
"SSSRM",
]
logger = logging.getLogger(__name__)
# FIXME workaround for Theano failure on macOS Conda builds
# https://travis-ci.org/github/brainiak/brainiak/jobs/689445834#L1414
# Inspired by workaround from PyMC3
# https://github.com/pymc-devs/pymc3/pull/3767
theano.config.gcc.cxxflags = "-Wno-c++11-narrowing"
# FIXME workaround for pymanopt only working with tensorflow 1.
# We don't use pymanopt+TF so we just let pymanopt pretend TF doesn't exist.
pymanopt.tools.autodiff._tensorflow.tf = None
class SSSRM(BaseEstimator, ClassifierMixin, TransformerMixin):
"""Semi-Supervised Shared Response Model (SS-SRM)
Given multi-subject data, factorize it as a shared response S among all
subjects and an orthogonal transform W per subject, using also labeled
data to train a Multinomial Logistic Regression (MLR) classifier (with
l2 regularization) in a semi-supervised manner:
.. math::
(1-\\alpha) Loss_{SRM}(W_i,S;X_i)
+ \\alpha/\\gamma Loss_{MLR}(\\theta, bias; {(W_i^T \\times Z_i, y_i})
+ R(\\theta)
:label: sssrm-eq
(see Equations (1) and (4) in [Turek2016]_).
Parameters
----------
n_iter : int, default: 10
Number of iterations to run the algorithm.
features : int, default: 50
Number of features to compute.
gamma : float, default: 1.0
Regularization parameter for the classifier.
alpha : float, default: 0.5
Balance parameter between the SRM term and the MLR term.
rand_seed : int, default: 0
Seed for initializing the random number generator.
Attributes
----------
w_ : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) for each subject.
s_ : array, shape=[features, samples]
The shared response.
theta_ : array, shape=[classes, features]
The MLR class plane parameters.
bias_ : array, shape=[classes]
The MLR class biases.
classes_ : array of int, shape=[classes]
Mapping table for each classes to original class label.
random_state_: `RandomState`
Random number generator initialized using rand_seed
Note
----
The number of voxels may be different between subjects. However, the
number of samples for the alignment data must be the same across
subjects. The number of labeled samples per subject can be different.
The Semi-Supervised Shared Response Model is approximated using the
Block-Coordinate Descent (BCD) algorithm proposed in [Turek2016]_.
This is a single node version.
"""
def __init__(self, n_iter=10, features=50, gamma=1.0, alpha=0.5,
rand_seed=0):
self.n_iter = n_iter
self.features = features
self.gamma = gamma
self.alpha = alpha
self.rand_seed = rand_seed
return
def fit(self, X, y, Z):
"""Compute the Semi-Supervised Shared Response Model
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, n_align]
Each element in the list contains the fMRI data for alignment of
one subject. There are n_align samples for each subject.
y : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the data samples
in Z.
Z : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject
for training the MLR classifier.
"""
logger.info('Starting SS-SRM')
# Check that the alpha value is in range (0.0,1.0)
if 0.0 >= self.alpha or self.alpha >= 1.0:
raise ValueError("Alpha parameter should be in range (0.0, 1.0)")
# Check that the regularizer value is positive
if 0.0 >= self.gamma:
raise ValueError("Gamma parameter should be positive.")
# Check the number of subjects
if len(X) <= 1 or len(y) <= 1 or len(Z) <= 1:
raise ValueError("There are not enough subjects in the input "
"data to train the model.")
if not (len(X) == len(y)) or not (len(X) == len(Z)):
raise ValueError("Different number of subjects in data.")
# Check for input data sizes
if X[0].shape[1] < self.features:
raise ValueError(
"There are not enough samples to train the model with "
"{0:d} features.".format(self.features))
# Check if all subjects have same number of TRs for alignment
# and if alignment and classification data have the same number of
# voxels per subject. Also check that there labels for all the classif.
# sample
number_trs = X[0].shape[1]
number_subjects = len(X)
for subject in range(number_subjects):
assert_all_finite(X[subject])
assert_all_finite(Z[subject])
if X[subject].shape[1] != number_trs:
raise ValueError("Different number of alignment samples "
"between subjects.")
if X[subject].shape[0] != Z[subject].shape[0]:
raise ValueError("Different number of voxels between alignment"
" and classification data (subject {0:d})"
".".format(subject))
if Z[subject].shape[1] != y[subject].size:
raise ValueError("Different number of samples and labels in "
"subject {0:d}.".format(subject))
# Map the classes to [0..C-1]
new_y = self._init_classes(y)
# Run SS-SRM
self.w_, self.s_, self.theta_, self.bias_ = self._sssrm(X, Z, new_y)
return self
def _init_classes(self, y):
"""Map all possible classes to the range [0,..,C-1]
Parameters
----------
y : list of arrays of int, each element has shape=[samples_i,]
Labels of the samples for each subject
Returns
-------
new_y : list of arrays of int, each element has shape=[samples_i,]
Mapped labels of the samples for each subject
Note
----
The mapping of the classes is saved in the attribute classes_.
"""
self.classes_ = unique_labels(utils.concatenate_not_none(y))
new_y = [None] * len(y)
for s in range(len(y)):
new_y[s] = np.digitize(y[s], self.classes_) - 1
return new_y
def transform(self, X, y=None):
"""Use the model to transform matrix to Shared Response space
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject
note that number of voxels and samples can vary across subjects.
y : not used as it only applies the mappings
Returns
-------
s : list of 2D arrays, element i has shape=[features_i, samples_i]
Shared responses from input data (X)
"""
# Check if the model exist
if hasattr(self, 'w_') is False:
raise NotFittedError("The model fit has not been run yet.")
# Check the number of subjects
if len(X) != len(self.w_):
raise ValueError("The number of subjects does not match the one"
" in the model.")
s = [None] * len(X)
for subject in range(len(X)):
s[subject] = self.w_[subject].T.dot(X[subject])
return s
def predict(self, X):
"""Classify the output for given data
Parameters
----------
X : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject
The number of voxels should be according to each subject at
the moment of training the model.
Returns
-------
p: list of arrays, element i has shape=[samples_i]
Predictions for each data sample.
"""
# Check if the model exist
if hasattr(self, 'w_') is False:
raise NotFittedError("The model fit has not been run yet.")
# Check the number of subjects
if len(X) != len(self.w_):
raise ValueError("The number of subjects does not match the one"
" in the model.")
X_shared = self.transform(X)
p = [None] * len(X_shared)
for subject in range(len(X_shared)):
sumexp, _, exponents = utils.sumexp_stable(
self.theta_.T.dot(X_shared[subject]) + self.bias_)
p[subject] = self.classes_[
(exponents / sumexp[np.newaxis, :]).argmax(axis=0)]
return p
def _sssrm(self, data_align, data_sup, labels):
"""Block-Coordinate Descent algorithm for fitting SS-SRM.
Parameters
----------
data_align : list of 2D arrays, element i has shape=[voxels_i, n_align]
Each element in the list contains the fMRI data for alignment of
one subject. There are n_align samples for each subject.
data_sup : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject for
the classification task.
labels : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the data samples
in data_sup.
Returns
-------
w : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
s : array, shape=[features, samples]
The shared response.
"""
classes = self.classes_.size
# Initialization:
self.random_state_ = np.random.RandomState(self.rand_seed)
random_states = [
np.random.RandomState(self.random_state_.randint(2**32))
for i in range(len(data_align))]
# Set Wi's to a random orthogonal voxels by TRs
w, _ = srm._init_w_transforms(data_align, self.features, random_states)
# Initialize the shared response S
s = SSSRM._compute_shared_response(data_align, w)
# Initialize theta and bias
theta, bias = self._update_classifier(data_sup, labels, w, classes)
# calculate and print the objective function
if logger.isEnabledFor(logging.INFO):
objective = self._objective_function(data_align, data_sup, labels,
w, s, theta, bias)
logger.info('Objective function %f' % objective)
# Main loop:
for iteration in range(self.n_iter):
logger.info('Iteration %d' % (iteration + 1))
# Update the mappings Wi
w = self._update_w(data_align, data_sup, labels, w, s, theta, bias)
# Output the objective function
if logger.isEnabledFor(logging.INFO):
objective = self._objective_function(data_align, data_sup,
labels, w, s, theta, bias)
logger.info('Objective function after updating Wi %f'
% objective)
# Update the shared response S
s = SSSRM._compute_shared_response(data_align, w)
# Output the objective function
if logger.isEnabledFor(logging.INFO):
objective = self._objective_function(data_align, data_sup,
labels, w, s, theta, bias)
logger.info('Objective function after updating S %f'
% objective)
# Update the MLR classifier, theta and bias
theta, bias = self._update_classifier(data_sup, labels, w, classes)
# Output the objective function
if logger.isEnabledFor(logging.INFO):
objective = self._objective_function(data_align, data_sup,
labels, w, s, theta, bias)
logger.info('Objective function after updating MLR %f'
% objective)
return w, s, theta, bias
def _update_classifier(self, data, labels, w, classes):
"""Update the classifier parameters theta and bias
Parameters
----------
data : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject for
the classification task.
labels : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the data samples
in data_sup.
w : list of 2D array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
classes : int
The number of classes in the classifier.
Returns
-------
theta : array, shape=[features, classes]
The MLR parameter for the class planes.
bias : array shape=[classes,]
The MLR parameter for class biases.
"""
# Stack the data and labels for training the classifier
data_stacked, labels_stacked, weights = \
SSSRM._stack_list(data, labels, w)
features = w[0].shape[1]
total_samples = weights.size
data_th = S.shared(data_stacked.astype(theano.config.floatX))
val_ = S.shared(labels_stacked)
total_samples_S = S.shared(total_samples)
theta_th = T.matrix(name='theta', dtype=theano.config.floatX)
bias_th = T.col(name='bias', dtype=theano.config.floatX)
constf2 = S.shared(self.alpha / self.gamma, allow_downcast=True)
weights_th = S.shared(weights)
log_p_y_given_x = \
T.log(T.nnet.softmax((theta_th.T.dot(data_th.T)).T + bias_th.T))
f = -constf2 * T.sum((log_p_y_given_x[T.arange(total_samples_S), val_])
/ weights_th) + 0.5 * T.sum(theta_th ** 2)
manifold = Product((Euclidean(features, classes),
Euclidean(classes, 1)))
problem = Problem(manifold=manifold, cost=f, arg=[theta_th, bias_th],
verbosity=0)
solver = ConjugateGradient(mingradnorm=1e-6)
solution = solver.solve(problem)
theta = solution[0]
bias = solution[1]
del constf2
del theta_th
del bias_th
del data_th
del val_
del solver
del solution
return theta, bias
def _update_w(self, data_align, data_sup, labels, w, s, theta, bias):
"""
Parameters
----------
data_align : list of 2D arrays, element i has shape=[voxels_i, n_align]
Each element in the list contains the fMRI data for alignment of
one subject. There are n_align samples for each subject.
data_sup : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject for
the classification task.
labels : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the data samples
in data_sup.
w : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
s : array, shape=[features, samples]
The shared response.
theta : array, shape=[classes, features]
The MLR class plane parameters.
bias : array, shape=[classes]
The MLR class biases.
Returns
-------
w : list of 2D array, element i has shape=[voxels_i, features]
The updated orthogonal transforms (mappings).
"""
subjects = len(data_align)
s_th = S.shared(s.astype(theano.config.floatX))
theta_th = S.shared(theta.T.astype(theano.config.floatX))
bias_th = S.shared(bias.T.astype(theano.config.floatX),
broadcastable=(True, False))
for subject in range(subjects):
logger.info('Subject Wi %d' % subject)
# Solve for subject i
# Create the theano function
w_th = T.matrix(name='W', dtype=theano.config.floatX)
data_srm_subject = \
S.shared(data_align[subject].astype(theano.config.floatX))
constf1 = \
S.shared((1 - self.alpha) * 0.5 / data_align[subject].shape[1],
allow_downcast=True)
f1 = constf1 * T.sum((data_srm_subject - w_th.dot(s_th))**2)
if data_sup[subject] is not None:
lr_samples_S = S.shared(data_sup[subject].shape[1])
data_sup_subject = \
S.shared(data_sup[subject].astype(theano.config.floatX))
labels_S = S.shared(labels[subject])
constf2 = S.shared(-self.alpha / self.gamma
/ data_sup[subject].shape[1],
allow_downcast=True)
log_p_y_given_x = T.log(T.nnet.softmax((theta_th.dot(
w_th.T.dot(data_sup_subject))).T + bias_th))
f2 = constf2 * T.sum(
log_p_y_given_x[T.arange(lr_samples_S), labels_S])
f = f1 + f2
else:
f = f1
# Define the problem and solve
f_subject = self._objective_function_subject(data_align[subject],
data_sup[subject],
labels[subject],
w[subject],
s, theta, bias)
minstep = np.amin(((10**-np.floor(np.log10(f_subject))), 1e-1))
manifold = Stiefel(w[subject].shape[0], w[subject].shape[1])
problem = Problem(manifold=manifold, cost=f, arg=w_th, verbosity=0)
solver = ConjugateGradient(mingradnorm=1e-2, minstepsize=minstep)
w[subject] = np.array(solver.solve(
problem, x=w[subject].astype(theano.config.floatX)))
if data_sup[subject] is not None:
del f2
del log_p_y_given_x
del data_sup_subject
del labels_S
del solver
del problem
del manifold
del f
del f1
del data_srm_subject
del w_th
del theta_th
del bias_th
del s_th
# Run garbage collector to avoid filling up the memory
gc.collect()
return w
@staticmethod
def _compute_shared_response(data, w):
""" Compute the shared response S
Parameters
----------
data : list of 2D arrays, element i has shape=[voxels_i, samples]
Each element in the list contains the fMRI data of one subject.
w : list of 2D arrays, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
Returns
-------
s : array, shape=[features, samples]
The shared response for the subjects data with the mappings in w.
"""
s = np.zeros((w[0].shape[1], data[0].shape[1]))
for m in range(len(w)):
s = s + w[m].T.dot(data[m])
s /= len(w)
return s
def _objective_function(self, data_align, data_sup, labels, w, s, theta,
bias):
"""Compute the objective function of the Semi-Supervised SRM
See :eq:`sssrm-eq`.
Parameters
----------
data_align : list of 2D arrays, element i has shape=[voxels_i, n_align]
Each element in the list contains the fMRI data for alignment of
one subject. There are n_align samples for each subject.
data_sup : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject for
the classification task.
labels : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the data samples
in data_sup.
w : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
s : array, shape=[features, samples]
The shared response.
theta : array, shape=[classes, features]
The MLR class plane parameters.
bias : array, shape=[classes]
The MLR class biases.
Returns
-------
f_val : float
The SS-SRM objective function evaluated based on the parameters to
this function.
"""
subjects = len(data_align)
# Compute the SRM loss
f_val = 0.0
for subject in range(subjects):
samples = data_align[subject].shape[1]
f_val += (1 - self.alpha) * (0.5 / samples) \
* np.linalg.norm(data_align[subject] - w[subject].dot(s),
'fro')**2
# Compute the MLR loss
f_val += self._loss_lr(data_sup, labels, w, theta, bias)
return f_val
def _objective_function_subject(self, data_align, data_sup, labels, w, s,
theta, bias):
"""Compute the objective function for one subject.
.. math:: (1-C)*Loss_{SRM}_i(W_i,S;X_i)
.. math:: + C/\\gamma * Loss_{MLR_i}(\\theta, bias; {(W_i^T*Z_i, y_i})
.. math:: + R(\\theta)
Parameters
----------
data_align : 2D array, shape=[voxels_i, samples_align]
Contains the fMRI data for alignment of subject i.
data_sup : 2D array, shape=[voxels_i, samples_i]
Contains the fMRI data of one subject for the classification task.
labels : array of int, shape=[samples_i]
The labels for the data samples in data_sup.
w : array, shape=[voxels_i, features]
The orthogonal transform (mapping) :math:`W_i` for subject i.
s : array, shape=[features, samples]
The shared response.
theta : array, shape=[classes, features]
The MLR class plane parameters.
bias : array, shape=[classes]
The MLR class biases.
Returns
-------
f_val : float
The SS-SRM objective function for subject i evaluated on the
parameters to this function.
"""
# Compute the SRM loss
f_val = 0.0
samples = data_align.shape[1]
f_val += (1 - self.alpha) * (0.5 / samples) \
* np.linalg.norm(data_align - w.dot(s), 'fro')**2
# Compute the MLR loss
f_val += self._loss_lr_subject(data_sup, labels, w, theta, bias)
return f_val
def _loss_lr_subject(self, data, labels, w, theta, bias):
"""Compute the Loss MLR for a single subject (without regularization)
Parameters
----------
data : array, shape=[voxels, samples]
The fMRI data of subject i for the classification task.
labels : array of int, shape=[samples]
The labels for the data samples in data.
w : array, shape=[voxels, features]
The orthogonal transform (mapping) :math:`W_i` for subject i.
theta : array, shape=[classes, features]
The MLR class plane parameters.
bias : array, shape=[classes]
The MLR class biases.
Returns
-------
loss : float
The loss MLR for the subject
"""
if data is None:
return 0.0
samples = data.shape[1]
thetaT_wi_zi_plus_bias = theta.T.dot(w.T.dot(data)) + bias
sum_exp, max_value, _ = utils.sumexp_stable(thetaT_wi_zi_plus_bias)
sum_exp_values = np.log(sum_exp) + max_value
aux = 0.0
for sample in range(samples):
label = labels[sample]
aux += thetaT_wi_zi_plus_bias[label, sample]
return self.alpha / samples / self.gamma * (sum_exp_values.sum() - aux)
def _loss_lr(self, data, labels, w, theta, bias):
"""Compute the Loss MLR (with the regularization)
Parameters
----------
data : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject for
the classification task.
labels : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the samples in
data.
w : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
theta : array, shape=[classes, features]
The MLR class plane parameters.
bias : array, shape=[classes]
The MLR class biases.
Returns
-------
loss : float
The loss MLR for the SS-SRM model
"""
subjects = len(data)
loss = 0.0
for subject in range(subjects):
if labels[subject] is not None:
loss += self._loss_lr_subject(data[subject], labels[subject],
w[subject], theta, bias)
return loss + 0.5 * np.linalg.norm(theta, 'fro')**2
@staticmethod
def _stack_list(data, data_labels, w):
"""Construct a numpy array by stacking arrays in a list
Parameter
----------
data : list of 2D arrays, element i has shape=[voxels_i, samples_i]
Each element in the list contains the fMRI data of one subject for
the classification task.
data_labels : list of arrays of int, element i has shape=[samples_i]
Each element in the list contains the labels for the samples in
data.
w : list of array, element i has shape=[voxels_i, features]
The orthogonal transforms (mappings) :math:`W_i` for each subject.
Returns
-------
data_stacked : 2D array, shape=[samples, features]
The data samples from all subjects are stacked into a single
2D array, where "samples" is the sum of samples_i.
labels_stacked : array, shape=[samples,]
The labels from all subjects are stacked into a single
array, where "samples" is the sum of samples_i.
weights : array, shape=[samples,]
The number of samples of the subject that are related to that
sample. They become a weight per sample in the MLR loss.
"""
labels_stacked = utils.concatenate_not_none(data_labels)
weights = np.empty((labels_stacked.size,))
data_shared = [None] * len(data)
curr_samples = 0
for s in range(len(data)):
if data[s] is not None:
subject_samples = data[s].shape[1]
curr_samples_end = curr_samples + subject_samples
weights[curr_samples:curr_samples_end] = subject_samples
data_shared[s] = w[s].T.dot(data[s])
curr_samples += data[s].shape[1]
data_stacked = utils.concatenate_not_none(data_shared, axis=1).T
return data_stacked, labels_stacked, weights