| Title: | Robust Angle Based Joint and Individual Variation Explained |
| Version: | 1.0 |
| Description: | A robust alternative to the aJIVE (angle based Joint and Individual Variation Explained) method (Feng et al 2018: <doi:10.1016/j.jmva.2018.03.008>) for the estimation of joint and individual components in the presence of outliers in multi-source data. It decomposes the multi-source data into joint, individual and residual (noise) contributions. The decomposition is robust to outliers and noise in the data. The method is illustrated in Ponzi et al (2021) <doi:10.48550/arXiv.2101.09110>. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| Depends: | R (≥ 3.1.0) |
| Suggests: | knitr, rmarkdown, testthat (≥ 2.1.0), cowplot, reshape2, dplyr |
| Imports: | ggplot2, doParallel, foreach |
| RoxygenNote: | 7.1.1 |
| NeedsCompilation: | no |
| Packaged: | 2021-01-28 12:53:49 UTC; ericapo |
| Author: | Erica Ponzi [aut, cre], Abhik Ghosh [aut] |
| Maintainer: | Erica Ponzi <erica.ponzi@medisin.uio.no> |
| Repository: | CRAN |
| Date/Publication: | 2021-02-04 15:20:05 UTC |
Robust Angle based Joint and Individual Variation Explained
Description
Computes the robust aJIVE decomposition with parallel computation.
Usage
Rajive(
blocks,
initial_signal_ranks,
full = TRUE,
n_wedin_samples = 1000,
n_rand_dir_samples = 1000,
joint_rank = NA
)
Arguments
blocks |
List. A list of the data matrices. |
initial_signal_ranks |
Vector. The initial signal rank estimates. |
full |
Boolean. Whether or not to store the full J, I, E matrices or just their SVDs (set to FALSE to save memory). |
n_wedin_samples |
Integer. Number of wedin bound samples to draw for each data matrix. |
n_rand_dir_samples |
Integer. Number of random direction bound samples to draw. |
joint_rank |
Integer or NA. User specified joint_rank. If NA will be estimated from data. |
Value
The aJIVE decomposition.
Examples
n <- 50
pks <- c(100, 80, 50)
Y <- ajive.data.sim(K =3, rankJ = 3, rankA = c(7, 6, 4), n = n,
pks = pks, dist.type = 1)
initial_signal_ranks <- c(7, 6, 4)
data.ajive <- list((Y$sim_data[[1]]), (Y$sim_data[[2]]), (Y$sim_data[[3]]))
ajive.results.robust <- Rajive(data.ajive, initial_signal_ranks)
Computes the robust SVD of a matrix
Description
Computes the robust SVD of a matrix
Usage
RobRSVD.all(data, nrank = min(dim(data)), svdinit = svd(data))
Arguments
data |
Matrix. X matrix. |
nrank |
Integer. Rank of SVD decomposition |
svdinit |
List. The standard SVD. |
Value
List. The SVD of X.
Simulation of data blocks
Description
Simulates blocks of data with joint and individual structures
Usage
ajive.data.sim(
K = 3,
rankJ = 2,
rankA = c(20, 15, 10),
n = 100,
pks,
dist.type = 1,
noise = 1
)
Arguments
K |
Integer. Number of data blocks. |
rankJ |
Integer. Joint rank. |
rankA |
Vector of Integers. Individual Ranks. |
n |
Integer. Number of data points. |
pks |
Vector of Integers. Number of variables in each block. |
dist.type |
Integer. 1 for normal, 2 for uniform, 3 for exponential |
noise |
Integer. Standard deviation in dist |
Value
Xsim a list of simulated data matrices and true rank values
Examples
n <- 20
p1 <- 10
p2 <- 8
p3 <- 5
JrankTrue <- 2
initial_signal_ranks <- c(5, 2, 2)
Y <- ajive.data.sim(K =3, rankJ = JrankTrue,
rankA = initial_signal_ranks,n = n,
pks = c(p1, p2, p3), dist.type = 1)
Decomposition Heatmaps
Description
Visualization of the RaJIVE decomposition, it shows heatmaps of the decomposition obtained by RaJIVE
Usage
data_heatmap(data, show_color_bar = TRUE, title = "", xlab = "", ylab = "")
Arguments
data |
List. The initial data blocks. |
show_color_bar |
Boolean. |
title |
Character. |
xlab |
Character. |
ylab |
Character |
Decomposition Heatmaps
Description
Visualization of the RaJIVE decomposition, it shows heatmaps of the decomposition obtained by RaJIVE
Usage
decomposition_heatmaps_robustH(blocks, jive_results_robust)
Arguments
blocks |
List. The initial data blocks. |
jive_results_robust |
List. The RaJIVE decomposition. |
Value
The heatmap of the decomposition
Examples
n <- 10
pks <- c(20, 10)
Y <- ajive.data.sim(K =2, rankJ = 2, rankA = c(7, 4), n = n,
pks = pks, dist.type = 1)
initial_signal_ranks <- c(7, 4)
data.ajive <- list((Y$sim_data[[1]]), (Y$sim_data[[2]]))
ajive.results.robust <- Rajive(data.ajive, initial_signal_ranks)
decomposition_heatmaps_robustH(data.ajive, ajive.results.robust)
Block Loadings
Description
Gets the block loadings from the Rajive decomposition
Usage
get_block_loadings(ajive_output, k, type)
Arguments
ajive_output |
List. The decomposition from Rajive |
k |
Integer. The index of the data block |
type |
Character. Joint or individual |
Value
The block loadings
Examples
n <- 10
pks <- c(20, 10)
Y <- ajive.data.sim(K =2, rankJ = 2, rankA = c(7, 4), n = n,
pks = pks, dist.type = 1)
initial_signal_ranks <- c(7, 4)
data.ajive <- list((Y$sim_data[[1]]), (Y$sim_data[[2]]))
ajive.results.robust <- Rajive(data.ajive, initial_signal_ranks)
get_block_loadings(ajive.results.robust, 2, 'joint')
Block Scores
Description
Gets the block scores from the Rajive decomposition
Usage
get_block_scores(ajive_output, k, type)
Arguments
ajive_output |
List. The decomposition from Rajive |
k |
Integer. The index of the data block |
type |
Character. Joint or individual |
Value
The block scores
Examples
n <- 10
pks <- c(20, 10)
Y <- ajive.data.sim(K =2, rankJ = 2, rankA = c(7, 4), n = n,
pks = pks, dist.type = 1)
initial_signal_ranks <- c(7, 4)
data.ajive <- list((Y$sim_data[[1]]), (Y$sim_data[[2]]))
ajive.results.robust <- Rajive(data.ajive, initial_signal_ranks)
get_block_scores(ajive.results.robust, 2, 'joint')
Computes the final JIVE decomposition.
Description
Computes X = J + I + E for a single data block and the respective SVDs.
Usage
get_final_decomposition_robustH(X, joint_scores, sv_threshold, full = TRUE)
Arguments
X |
Matrix. The original data matrix. |
joint_scores |
Matrix. The basis of the joint space (dimension n x joint_rank). |
sv_threshold |
Numeric vector. The singular value thresholds from the initial signal rank estimates. |
full |
Boolean. Do we compute the full J, I matrices or just svd |
Computes the individual matrix for a data block.
Description
Computes the individual matrix for a data block.
Usage
get_individual_decomposition_robustH(
X,
joint_scores,
sv_threshold,
full = TRUE
)
Arguments
X |
Matrix. The original data matrix. |
joint_scores |
Matrix. The basis of the joint space (dimension n x joint_rank). |
sv_threshold |
Numeric vector. The singular value thresholds from the initial signal rank estimates. |
full |
Boolean. Do we compute the full J, I matrices or just the SVD (set to FALSE to save memory). |
Individual Rank
Description
Gets the individual ranks from the Rajive decomposition
Usage
get_individual_rank(ajive_output, k)
Arguments
ajive_output |
List. The decomposition from Rajive |
k |
Integer. The index of the data block. |
Value
The individual ranks
Examples
n <- 10
pks <- c(20, 10)
Y <- ajive.data.sim(K =2, rankJ = 2, rankA = c(7, 4), n = n,
pks = pks, dist.type = 1)
initial_signal_ranks <- c(7, 4)
data.ajive <- list((Y$sim_data[[1]]), (Y$sim_data[[2]]))
ajive.results.robust <- Rajive(data.ajive, initial_signal_ranks)
get_individual_rank(ajive.results.robust, 2)
Computes the individual matrix for a data block
Description
Computes the individual matrix for a data block
Usage
get_joint_decomposition_robustH(X, joint_scores, full = TRUE)
Arguments
X |
Matrix. The original data matrix. |
joint_scores |
Matrix. The basis of the joint space (dimension n x joint_rank). |
full |
Boolean. Do we compute the full J, I matrices or just the SVD (set to FALSE to save memory). |
Joint Rank
Description
Gets the joint rank from the Rajive decomposition
Usage
get_joint_rank(ajive_output)
Arguments
ajive_output |
List. The decomposition from Rajive |
Value
The joint rank
Examples
n <- 10
pks <- c(20, 10)
Y <- ajive.data.sim(K =2, rankJ = 2, rankA = c(7, 4), n = n,
pks = pks, dist.type = 1)
initial_signal_ranks <- c(7, 4)
data.ajive <- list((Y$sim_data[[1]]), (Y$sim_data[[2]]))
ajive.results.robust <- Rajive(data.ajive, initial_signal_ranks)
get_joint_rank(ajive.results.robust)
Computes the joint scores.
Description
Estimate the joint rank with the wedin bound, compute the signal scores SVD, double check each joint component.
Usage
get_joint_scores_robustH(
blocks,
block_svd,
initial_signal_ranks,
sv_thresholds,
n_wedin_samples = 1000,
n_rand_dir_samples = 1000,
joint_rank = NA
)
Arguments
blocks |
List. A list of the data matrices. |
block_svd |
List. The SVD of the data blocks. |
initial_signal_ranks |
Numeric vector. Initial signal ranks estimates. |
sv_thresholds |
Numeric vector. The singular value thresholds from the initial signal rank estimates. |
n_wedin_samples |
Integer. Number of wedin bound samples to draw for each data matrix. |
n_rand_dir_samples |
Integer. Number of random direction bound samples to draw. |
joint_rank |
Integer or NA. User specified joint_rank. If NA will be estimated from data. |
Estimate the wedin bound for a data matrix.
Description
Samples from the random direction bound. Returns on the scale of squared singular value.
Usage
get_random_direction_bound_robustH(n_obs, dims, num_samples = 1000)
Arguments
n_obs |
The number of observations. |
dims |
The number of features in each data matrix |
num_samples |
Integer. Number of vectors selected for resampling procedure. |
Value
rand_dir_samples
The singular value threshold.
Description
Computes the singular value threshold for the data matrix (half way between the rank and rank + 1 singluar value).
Usage
get_sv_threshold(singular_values, rank)
Arguments
singular_values |
Numeric. The singular values. |
rank |
Integer. The rank of the approximation. |
Computes the robust SVD of a matrix Using robRsvd
Description
Computes the robust SVD of a matrix Using robRsvd
Usage
get_svd_robustH(X, rank = NULL)
Arguments
X |
Matrix. X matrix. |
rank |
Integer. Rank of SVD decomposition |
Value
List. The SVD of X.
Gets the wedin bounds
Description
Gets the wedin bounds
Usage
get_wedin_bound_samples(X, SVD, signal_rank, num_samples = 1000)
Arguments
X |
Matrix. The data matrix. |
SVD |
List. The SVD decomposition of the matrix. List with entries 'u', 'd', and 'v'from the svd function. |
signal_rank |
Integer. |
num_samples |
Integer. Number of vectors selected for resampling procedure. |
Proportions of variance explained
Description
Gets the variance explained by each component of the Rajive decomposition
Usage
showVarExplained_robust(ajiveResults, blocks)
Arguments
ajiveResults |
List. The decomposition from Rajive |
blocks |
List. The initial data blocks |
Value
The proportion of variance explained by each component
Examples
n <- 10
pks <- c(20, 10)
Y <- ajive.data.sim(K =2, rankJ = 2, rankA = c(7, 4), n = n,
pks = pks, dist.type = 1)
initial_signal_ranks <- c(7, 4)
data.ajive <- list((Y$sim_data[[1]]), (Y$sim_data[[2]]))
ajive.results.robust <- Rajive(data.ajive, initial_signal_ranks)
showVarExplained_robust(ajive.results.robust, data.ajive)
Simulation of single data block from distribution
Description
Simulation of single data block from distribution
Usage
sim_dist(num, n, p)
Arguments
num |
Integer. Type of distribution. 1 for normal, 2 for uniform, 3 for exponential |
n |
Integer. Number of data points. |
p |
Integers. Number of variables in block. |
Reconstruces the original matrix from its robust SVD.
Description
Computes UDV^T to get the approximate (or full) X matrix.
Usage
svd_reconstruction(decomposition)
Arguments
decomposition |
List. List with entries 'u', 'd', and 'v'from the svd function. |
Value
Matrix. The original matrix.
Truncates a robust SVD.
Description
Removes columns from the U, D, V matrix computed form an SVD.
Usage
truncate_svd(decomposition, rank)
Arguments
decomposition |
List. List with entries 'u', 'd', and 'v'from the svd function. |
rank |
List. List with entries 'u', 'd', and 'v'from the svd function. |
Value
The trucated robust SVD of X.
Resampling procedure for the wedin bound
Description
Resampling procedure for the wedin bound
Usage
wedin_bound_resampling(X, perp_basis, right_vectors, num_samples = 1000)
Arguments
X |
Matrix. The data matrix. |
perp_basis |
Matrix. Either U_perp or V_perp: the remaining left/right singluar vectors of X after estimating the signal rank. |
right_vectors |
Boolean. Right multiplication or left multiplication. |
num_samples |
Integer. Number of vectors selected for resampling procedure. |