brainiak.factoranalysis package

Factor analysis.

Submodules

brainiak.factoranalysis.htfa module

Hierarchical Topographical Factor Analysis (HTFA)

This implementation is based on the work in [Manning2014-1], [Manning2014-2], [AndersonMJ2016], and [Manning2018].

Manning2014-1

“Topographic factor analysis: a bayesian model for inferring brain networks from neural data”, J. R. Manning, R. Ranganath, K. A. Norman, and D. M. Blei. PLoS One, vol. 9, no. 5, 2014.

Manning2014-2

“Hierarchical topographic factor analysis”, Jeremy. R. Manning, R. Ranganath, W. Keung, N. B. Turk-Browne, J. D.Cohen, K. A. Norman, and D. M. Blei. Pattern Recognition in Neuroimaging, 2014 International Workshop on, June 2014.

Manning2018

“A Probabilistic Approach to Discovering Dynamic Full-brain Functional Connectivit Patterns”, J. R. Manning, X. Zhu, T.L. Willke, R. Ranganath, K. Stachenfeld, U. Hasson, D. M. Blei and K. A. Norman. Neuroimage, 2018. https://doi.org/10.1016/j.neuroimage.2018.01.071

AndersonMJ2016

“Enabling Factor Analysis on Thousand-Subject Neuroimaging Datasets”, Michael J. Anderson, Mihai Capotă, Javier S. Turek, Xia Zhu, Theodore L. Willke, Yida Wang, Po-Hsuan Chen, Jeremy R. Manning, Peter J. Ramadge, Kenneth A. Norman, IEEE International Conference on Big Data, 2016. https://doi.org/10.1109/BigData.2016.7840719

class brainiak.factoranalysis.htfa.HTFA(K, n_subj, max_global_iter=10, max_local_iter=10, threshold=0.01, nlss_method='trf', nlss_loss='soft_l1', jac='2-point', x_scale='jac', tr_solver=None, weight_method='rr', upper_ratio=1.8, lower_ratio=0.02, voxel_ratio=0.25, tr_ratio=0.1, max_voxel=5000, max_tr=500, comm=<mpi4py.MPI.Intracomm object>, verbose=False)

Bases: brainiak.factoranalysis.tfa.TFA

Hierarchical Topographical Factor Analysis (HTFA)

Given multi-subject data, HTFA factorizes data from each subject as a spatial factor F and a weight matrix W per subject. Also at top level, it estimates global template across subjects:

Parameters

  • K (int) – Number of factors to compute.

  • n_subj (int) – Total number of subjects in dataset.

  • max_global_iter (int, default: 10) – Number of global iterations to run the algorithm.

  • max_local_iter (int, default: 10) – Number of local iterations to run on each subject within each global interation.

  • threshold (float, default: 1.0) – Tolerance for terminate the parameter estimation

  • nlss_method ({'trf', 'dogbox', 'lm'}, default: 'trf') – Non-Linear Least Square (NLSS) algorithm used by scipy.least_suqares to perform minimization. More information at http://docs.scipy.org/doc/scipy-0.17.0/reference/generated/scipy.optimize.least_squares.html

  • nlss_loss (str or callable, default: 'linear') – Loss function used by scipy.least_squares. More information at http://docs.scipy.org/doc/scipy-0.17.0/reference/generated/scipy.optimize.least_squares.html

  • jac ({'2-point', '3-point', 'cs', callable}, default: '2-point') – Method of computing the Jacobian matrix. More information at http://docs.scipy.org/doc/scipy-0.17.0/reference/generated/scipy.optimize.least_squares.html

  • x_scale (float or array_like or 'jac', default: 1.0) – Characteristic scale of each variable for scipy.least_suqares. More information at http://docs.scipy.org/doc/scipy-0.17.0/reference/generated/scipy.optimize.least_squares.html

  • tr_solver ({None, 'exact', 'lsmr'}, default: None) – Method for solving trust-region subproblems, relevant only for ‘trf’ and ‘dogbox’ methods. More information at http://docs.scipy.org/doc/scipy-0.17.0/reference/generated/scipy.optimize.least_squares.html

  • weight_method ({'rr','ols'}, default: 'rr') – Method for estimating weight matrix W given X and F. ‘rr’ means ridge regression, ‘ols’ means ordinary least square.

  • upper_ratio (float, default: 1.8) – The upper bound of the ratio between factor’s width and brain diameter.

  • lower_ratio (float, default: 0.02) – The lower bound of the ratio between factor’s width and brain diameter.

  • voxel_ratio (float, default: 0.25) – The percentage of voxels to sample in each inner iteration.

  • tr_ratio (float, default: 0.1) – The percentage of trs to sample in each inner iteration.

  • max_voxel (int, default: 5000) – The maximum number of voxels to sample in each inner iteration.

  • max_tr (int, default: 500) – The maximum number of trs to sample in each inner iteration.

  • comm (Intracomm) – MPI communication group, default MPI.COMM_WORLD

  • verbose (boolean, default: False) – Verbose mode flag.

global_prior_

The global prior on mean and variance of centers and widths.

Type

1D array

global_posterior_

The global posterior on mean and variance of centers and widths.

Type

1D array

local_posterior_

Local posterior on centers and widths of subjects allocated to this process.

Type

1D array

local_weights_

Local posterior on weights allocated to this process.

Type

1D array

Notes

We recommend to use data in MNI space to better interpret global template

fit(X, R)
Compute Hierarchical Topographical Factor Analysis Model

[Manning2014-1][Manning2014-2]

Parameters

  • X (list of 2D arrays, element i has shape=[voxels_i, samples]) – Each element in the list contains the fMRI data of one subject.

  • R (list of 2D arrays, element i has shape=[n_voxel, n_dim]) – Each element in the list contains the scanner coordinate matrix of fMRI data of one subject.

Returns

Returns the instance itself.

Return type

HTFA

brainiak.factoranalysis.tfa module

Topographical Factor Analysis (TFA)

This implementation is based on the work in [Manning2014] and [AndersonM2016].

Manning2014

“Topographic factor analysis: a bayesian model for inferring brain networks from neural data”, J. R. Manning, R. Ranganath, K. A. Norman, and D. M. Blei.PLoS One, vol. 9, no. 5, 2014.

AndersonM2016

“Scaling Up Multi-Subject Neuroimaging Factor Analysis” Michael J. Anderson, Mihai Capota, Javier S. Turek, Xia Zhu, Theodore L. Willke, Yida Wang, Po-Hsuan Chen, Jeremy R. Manning, Peter J. Ramadge, and Kenneth A. Norman 2016.

class brainiak.factoranalysis.tfa.TFA(max_iter=10, threshold=1.0, K=50, nlss_method='trf', nlss_loss='soft_l1', jac='2-point', x_scale='jac', tr_solver=None, weight_method='rr', upper_ratio=1.8, lower_ratio=0.02, max_num_tr=500, max_num_voxel=5000, seed=100, verbose=False)

Bases: sklearn.base.BaseEstimator

Topographical Factor Analysis (TFA)

Given data from one subject, factorize it as a spatial factor F and a weight matrix W.

Parameters
local_posterior_

Local posterior on subject’s centers and widths

Type

1D array

F_

Latent factors of the subject

Type

2D array, in shape [n_voxel, K]

W_

Weight matrix of the subject

Type

2D array, in shape [K, n_tr]

fit(X, R, template_prior=None)

Topographical Factor Analysis (TFA)[Manning2014]

Parameters

  • X (2D array, in shape [n_voxel, n_sample]) – The fMRI data of one subject

  • R (2D array, in shape [n_voxel, n_dim]) – The voxel coordinate matrix of fMRI data

  • template_prior (None or 1D array) – The template prior as an extra constraint None when fitting TFA alone

get_bounds(R)

Calculate lower and upper bounds for centers and widths

Parameters

R (2D array, with shape [n_voxel, n_dim]) – The coordinate matrix of fMRI data from one subject

Returns

bounds – The lower and upper bounds on factor’s centers and widths.

Return type

2-tuple of array_like, default: None

get_centers(estimation)

Get estimation on centers

Parameters

estimation (1D arrary) – Either prior of posterior estimation

Returns

centers – Estimation on centers

Return type

2D array, in shape [K, n_dim]

get_centers_mean_cov(estimation)

Get estimation on the covariance of centers’ mean

Parameters

estimation (1D arrary) – Either prior of posterior estimation

Returns

centers_mean_cov – Estimation of the covariance of centers’ mean

Return type

2D array, in shape [K, cov_vec_size]

get_factors(unique_R, inds, centers, widths)

Calculate factors based on centers and widths

Parameters

  • unique_R (a list of array,) – Each element contains unique value in one dimension of scanner coordinate matrix R.

  • inds (a list of array,) – Each element contains the indices to reconstruct one dimension of original cooridnate matrix from the unique array.

  • centers (2D array, with shape [K, n_dim]) – The centers of factors.

  • widths (1D array, with shape [K, 1]) – The widths of factors.

Returns

F – The latent factors from fMRI data.

Return type

2D array, with shape [n_voxel,self.K]

get_map_offset()

Compute offset of prior/posterior

Returns

map_offest – The offset to different fields in prior/posterior

Return type

1D array

get_template(R)

Compute a template on latent factors

Parameters

R (2D array, in format [n_voxel, n_dim]) – The scanner coordinate matrix of one subject’s fMRI data

Returns

  • template_prior (1D array) – The template prior.

  • template_centers_cov (2D array, in shape [n_dim, n_dim]) – The template on centers’ covariance.

  • template_widths_var (float) – The template on widths’ variance

get_unique_R(R)

Get unique vlaues from coordinate matrix

Parameters

R (2D array) – The coordinate matrix of a subject’s fMRI data

Returns

  • unique_R (a list of array,) – Each element contains unique value in one dimension of coordinate matrix R.

  • inds (a list of array,) – Each element contains the indices to reconstruct one dimension of original cooridnate matrix from the unique array.

get_weights(data, F)

Calculate weight matrix based on fMRI data and factors

Parameters

  • data (2D array, with shape [n_voxel, n_tr]) – fMRI data from one subject

  • F (2D array, with shape [n_voxel,self.K]) – The latent factors from fMRI data.

Returns

W – The weight matrix from fMRI data.

Return type

2D array, with shape [K, n_tr]

get_widths(estimation)

Get estimation on widths

Parameters

estimation (1D arrary) – Either prior of posterior estimation

Returns

fields – Estimation of widths

Return type

2D array, in shape [K, 1]

get_widths_mean_var(estimation)

Get estimation on the variance of widths’ mean

Parameters

estimation (1D arrary) – Either prior of posterior estimation

Returns

widths_mean_var – Estimation on variance of widths’ mean

Return type

2D array, in shape [K, 1]

init_centers_widths(R)

Initialize prior of centers and widths

Returns

  • centers (2D array, with shape [K, n_dim]) – Prior of factors’ centers.

  • widths (1D array, with shape [K, 1]) – Prior of factors’ widths.

init_prior(R)

initialize prior for the subject

Returns

Returns the instance itself.

Return type

TFA

set_K(K)

set K for the subject

Parameters

K (integer) – Number of latent factor.

Returns

Returns the instance itself.

Return type

TFA

set_centers(estimation, centers)

Set estimation on centers

Parameters

  • estimation (1D arrary) – Either prior or posterior estimation

  • centers (2D array, in shape [K, n_dim]) – Estimation on centers

set_centers_mean_cov(estimation, centers_mean_cov)

Set estimation on centers

Parameters

  • estimation (1D arrary) – Either prior of posterior estimation

  • centers (2D array, in shape [K, n_dim]) – Estimation on centers

set_prior(prior)

set prior for the subject

Parameters

prior (1D array, with K*(n_dim+1) elements) – Subject prior of centers and widths.

Returns

Returns the instance itself.

Return type

TFA

set_seed(seed)

set seed for the subject

Parameters

seed (int) – Seed for subsampling voxels and trs

Returns

Returns the instance itself.

Return type

TFA

set_widths(estimation, widths)

Set estimation on widths

Parameters

  • estimation (1D arrary) – Either prior of posterior estimation

  • widths (2D array, in shape [K, 1]) – Estimation on widths

set_widths_mean_var(estimation, widths_mean_var)

Set estimation on centers

Parameters

  • estimation (1D arrary) – Either prior of posterior estimation

  • centers (2D array, in shape [K, n_dim]) – Estimation on centers

brainiak.factoranalysis.tfa_extension module

brainiak.factoranalysis.tfa_extension.factor(arg0: numpy.ndarray[float64], arg1: numpy.ndarray[float64], arg2: numpy.ndarray[float64], arg3: numpy.ndarray[float64], arg4: numpy.ndarray[float64], arg5: numpy.ndarray[float64], arg6: numpy.ndarray[int64], arg7: numpy.ndarray[int64], arg8: numpy.ndarray[int64]) → None

Calculate factor matrix

brainiak.factoranalysis.tfa_extension.recon(arg0: numpy.ndarray[float64], arg1: numpy.ndarray[float64], arg2: numpy.ndarray[float64], arg3: numpy.ndarray[float64], arg4: numpy.ndarray[float64]) → None

Reconstruct data