Package 'BSPBSS'

Initial values

Description

Generate initial values, set up priors and perform kernel decomposition for the MCMC algorithm.

Usage

init_bspbss(
  X,
  coords,
  rescale = TRUE,
  center = FALSE,
  q = 2,
  dens = 0.5,
  ker_par = c(0.05, 20),
  num_eigen = 500,
  noise = 0
)

Arguments

X	Data matrix with n rows (sample) and p columns (voxel).
coords	Cordinate matrix with p rows (voxel) and d columns (dimension).
rescale	If TRUE, rows of X are rescaled to have unit variance.
center	If TRUE, rows of X are mean-centered.
q	Number of latent sources.
dens	The initial density level (between 0 and 1) of the latent sources.
ker_par	2-dimensional vector (a,b) with a>0, b>0, specifing the parameters in the modified exponetial squared kernel.
num_eigen	Number of eigen functions.
noise	Gaussian noise added to the initial latent sources, with mean 0 and standard deviation being noise * sd(S0), where sd(S0) is the standard deviation of the initial latent sources.

Value

List containing initial values, priors and eigen functions/eigen values of the kernel of the Gaussian process.

Examples

sim = sim_2Dimage(length = 30, sigma = 5e-4, n = 30, smooth = 6)
ini = init_bspbss(sim$X, sim$coords, q = 3, ker_par = c(0.1,50), num_eigen = 50)

---

levelplot for 2D images.

Description

The function plots 2D images for a data matrix.

Usage

levelplot2D(
  S,
  coords,
  lim = c(min(S), max(S)),
  xlim = c(0, max(coords[, 1])),
  ylim = c(0, max(coords[, 2])),
  color = bluered(100),
  layout = c(1, nrow(S)),
  file = NULL
)

Arguments

S	Data matrix with q rows (sample) and p colums (pixel).
coords	Coordinates matrix with p rows (pixel) and 2 columns (dimension), specifying the coordinates of the data points.
lim	2-dimensional numeric vector, specifying the limits for the data.
xlim	2-dimensional numeric vector, specifying the lower and upper limits of x.
ylim	2-dimensional numeric vector, specifying the lower and upper limits of y.
color	Colorbar.
layout	2-dimensional numeric vector, specifying the number of rows and number of columns for the layout of components.
file	Name of the file to be saved.

Value

No return value.

Examples

sim = sim_2Dimage(length = 30, sigma = 5e-4, n = 30, smooth = 6)
levelplot2D(sim$S,lim = c(-0.04,0.04), sim$coords)

---

MCMC algorithm for Bayesian spatial blind source separation with the thresholded Gaussian Process prior.

Description

Performan MCMC algorithm to draw samples from a Bayesian spatial blind source separation model.

Usage

mcmc_bspbss(
  X,
  init,
  prior,
  kernel,
  n.iter,
  n.burn_in,
  thin = 1,
  show_step,
  ep = 0.01,
  lr = 0.01,
  decay = 0.01,
  num_leapfrog = 5,
  subsample_n = 0.5,
  subsample_p = 0.5
)

Arguments

X	Data matrix with n rows (sample) and p columns (voxel).
init	List of initial values, see init_bspbss.
prior	List of priors, see init_bspbss.
kernel	List including eigenvalues and eigenfunctions of the kernel, see init_bspbss.
n.iter	Total iterations in MCMC.
n.burn_in	Number of burn-in.
thin	Thining interval.
show_step	Frequency for printing the current number of iterations.
ep	Approximation parameter.
lr	Per-batch learning rate in SGHMC.
decay	Decay parameter in SGHMC.
num_leapfrog	Number of leapfrog steps in SGHMC.
subsample_n	Mini-batch size of samples.
subsample_p	Mini-batch size of voxels.

Value

List containing MCMC samples of: A, b, sigma, and zeta.

Examples

sim = sim_2Dimage(length = 30,
                  sigma = 5e-4,
                  n = 30,
                  smooth = 6)
ini = init_bspbss(sim$X, sim$coords,
                  q = 3,
                  ker_par = c(0.1,50),
                  num_eigen = 50)
res = mcmc_bspbss(ini$X,ini$init,
                  ini$prior,ini$kernel,
                  n.iter=200,n.burn_in=100,
                  thin=10,show_step=50)

---

Write a NIfTI file.

Description

This function saves a data matrix into a NIfTI file.

Usage

output_nii(X, nii, xgrid, file = NULL, std = TRUE, thres = 0)

Arguments

X	Data matrix with n rows (sample) and p colums (pixel).
nii	a reference NIfTI-class object, representing a image with p voxels.
xgrid	Cordinate matrix with p rows (voxel) and d columns (dimension).
file	The name of the file to be saved.
std	If TRUE, standarize each row of X.
thres	Quantile to threshold each row of X.

Value

NIfTI-class object.

---

Transforms NIfTI to matrix

Description

This function transforms a NIfTI-class object into a matrix.

Usage

pre_nii(nii, mask)

Arguments

nii	4D NIfTI-class object with dimensions x,y,z and t. Can be read from NIfTI file with readNIfTI function from the package oro.nifti.
mask	Mask variable, also in NIfTI format.

Value

List containing the data matrix with t rows and x*y*z colums (voxels), and the coordinates of the voxels.

---

Simulate image data using ICA

Description

The function simulates image data using a probabilistic ICA model whose latent components have specific spatial patterns.

Usage

sim_2Dimage(length = 20, n = 50, sigma = 0.002, smooth = 6)

Arguments

length	The length of the image.
n	sample size.
sigma	variance of the noise.
smooth	smoothness of the latent components.

Details

The observations are generated using probabilistic ICA:

$X_i(v) = \sum_{j=1}^q A_{i,j} S_j(v) + \epsilon_i(v) ,$

where $S_j, j=1,...,q$ are the latent components, $A_{i,j}$ is the mixing coeffecient and $\epsilon_i$ is the noise term. Specifically, the number of components in this function is $q = 3$, with each of them being a specific geometric shape. The mixing coefficient matrix is generated with a von Mises-Fisher distribution with the concentration parameter being zero, which means it is uniformly distributed on the sphere. $\epsilon_i$ is a i.i.d. Gaussian noise term with 0 mean and user-specified variance.

Value

List that contains the following terms:

X

Data matrix with n rows (sample) and p columns (pixel).

coords

Cordinate matrix with p rows (pixel) and d columns (dimension)

S

Latent components.

A

Mixing coefficent matrix.

snr

Signal-to-noise ratio.

Examples

sim = sim_2Dimage(length = 30, sigma = 5e-4, n = 30, smooth = 6)

---

Summarization of the MCMC result.

Description

The function summarizes the MCMC results obtained from mcmc_bspbss.

Usage

sum_mcmc_bspbss(res, X, kernel, start = 1, end = 100, select_prob = 0.8)

Arguments

res	List including MCMC samples, which can be obtained from function mcmc_bspbss
X	Original data matrix.
kernel	List including eigenvalues and eigenfunctions of the kernel, see init_bspbss.
start	Start point of the iterations being summarized.
end	End point of the iterations being summarized.
select_prob	Lower bound of the posterior inclusion probability required when summarizing the samples of latent sources.

Value

List that contains the following terms:

S

Estimated latent sources.

pip

Voxel-wise posterior inclusion probability for the latent sources.

A

Estimated mixing coefficent matrix.

zeta

Estimated zeta.

sigma

Estimated sigma.

logLik

Trace of log-likelihood.

Slist

MCMC samples of S.

Examples

sim = sim_2Dimage(length = 30, sigma = 5e-4, n = 30, smooth = 6)
ini = init_bspbss(sim$X, sim$coords, q = 3, ker_par = c(0.1,50), num_eigen = 50)
res = mcmc_bspbss(ini$X,ini$init,ini$prior,ini$kernel,n.iter=200,n.burn_in=100,thin=10,show_step=50)
res_sum = sum_mcmc_bspbss(res, ini$X, ini$kernel, start = 11, end = 20, select_p = 0.5)

---