generateModel1: Generate data from SLIDE model for two views.

In irinagain/SLIDE: Structural Learning and Integrative Decomposition of Multi-View Data

Description

Generates two matched datasets from SLIDE model with rank 2 for each type of structure (shared/individual).

Usage

generateModel1(
  n = 100,
  pvec = c(25, 25),
  cvec = c(1, 1),
  snr = 1,
  orthogonalV = T
)

Arguments

n	An integer specifying the number of matched samples, the default value is 100.
pvec	A vector of integer values p_1, p_2 corresponding to the number of measurements within each data view. The default value is pvec = c(25,25).
cvec	A vector of positive values c_1, c_2 corresponding to the scale of each view. The default value is cvec = c(1,1), that is both views have the same scale.
snr	A non-negative value specifying the ratio between the Frobenius norm of the signal matrix and the Frobenius norm of the noise matrix. This value determines the variance of the elements in the noise matrix. The default value is 1.
orthogonalV	A logical indicating whether the loading vectors should be generated orthogonal to each other, the default value is TRUE.

Details

Generates X_1 (n x p_1) and X_2 (n x p_2) according to the additive noise model

X_1 = Z_1 + E_1, X_2 = Z_2 + E_2,

where noise matrices E_1, E_2 have independent entries from normal distribution with mean zero, and standard deviations sigma1, sigma2 correspondingly, and

Z_1 = c_1 (U_1 D_0 W_{1,1}' + U_2 D_1 W_{1,2}')

Z_2 = c_2 (U_1 D_0 W_{2,1}' + U_3 D_2 W_{2,3}').

Here U=[U_1 U_2 U_3] (n x 6) is generated using uniform distribution on [0,1] with subsequent centering and orthonormalization, D_0 = diag(1.5, 1.3), D_1 = diag(1, 0.8), D_2 = diag(1, 0.7), and the loadings W = [W_1 W_2] (p_1 + p_2 X 6) with W_1 = [W_{1,1} W_{1,2} 0], W_2 = [W_{2,1} 0 W_{2,3}] are generated using uniform distribution on [0,1] with subsequent orthonormalization of W. The loadings matrix V in SLIDE model is generated by condensing c_1, c_2, D_0, D_1, D_2 and W.

Value

A list with the elements

X	A n x (p_1 + p_2) concatenated data matrix of views X_1, X_2.
pvec	The supplied values of pvec.
sigma1	The standard deviation of the elements of the noise matrix for the 1st dataset.
sigma2	The standard deviation of the elements of the noise matrix for the 2nd dataset.
U	The score matrix from the SLIDE model.
V	The loadings matrix from the SLIDE model.
cvec	The supplied values of cvec.
snr	The supplied value of snr.

Examples

data <- generateModel1(n = 50, pvec = c(50,75), snr = 2)
data <- generateModel1(n = 100, pvec = c(25,150), snr = 1)
data <- generateModel1(n = 100, pvec = c(25,25),cvec = c(0.5,1.5), snr = 1)

irinagain/SLIDE documentation built on Aug. 14, 2021, 2:56 p.m.