Title:	Thresholded Ordered Sparse CCA
Version:	0.1.0
Description:	Performs Thresholded Ordered Sparse Canonical Correlation Analysis (CCA). For more details see Senar, N. (2024) <doi:10.1093/bioadv/vbae021> and Senar, N. et al. (2025) <doi:10.48550/arXiv.2503.15140>.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.3
Suggests:	ClusterR, RColorBrewer, cluster, knitr, rmarkdown, testthat (≥ 3.0.0)
Imports:	doParallel, foreach, parallel, forecast, ggplot2, lme4, scales, graphics, stats, utils, grDevices, mcompanion, EnvStats, MASS
Depends:	R (≥ 3.5)
VignetteBuilder:	knitr
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2025-11-05 11:53:54 UTC; PC
Author:	Nuria Senar [aut, cre]
Maintainer:	Nuria Senar <n.senarvilladeamigo@amsterdamumc.nl>
Repository:	CRAN
Date/Publication:	2025-11-07 13:40:02 UTC

Calculates cpev

Description

This function calculates cpev w.r.t. a chosen origin.

Usage

cpev.toscca(mat, weights)

Arguments

Value

Returns cpev values for the kth or 1:K components.

Performs eigen decomposition of a matrix in PS space.

Description

Performs eigen decomposition of a matrix in PS space.

Usage

fastEigen(A)

Arguments

Value

Matrix. Positive definite matrix.

Performs matrix residualisation over estimated canonical vectors by using the null space of the estimated canonical vector to construct a new matrix.

Description

Performs matrix residualisation over estimated canonical vectors by using the null space of the estimated canonical vector to construct a new matrix.

Usage

getCanSubspace(mat, vec)

Arguments

Details

For nxp matrix

\mathbf{A}

and pxk vector

\mathbf{\alpha}

, the canonical is compute as \mathbf{A}_{sub} = \mathbf{A}\mathbf{\alpha}(\mathbf{\alpha}^T\mathbf{\alpha})\mathbf{\alpha}^T.

Value

An nxk matrix.

Get location of required.

Description

Get location of required.

Usage

getWhich(data, fun)

Arguments

Value

Returns value matching function fun.

Examples

getWhich(rnorm(100), max)

Initialised the canonical vector for the iterative process based on positive eigen values. Then, SVD is performed on that PS matrix.

Description

Initialised the canonical vector for the iterative process based on positive eigen values. Then, SVD is performed on that PS matrix.

Usage

initialiseCanVar(A, B)

Arguments

Value

An pzp vector.

Examples

#sample size etc
N = 10
p = 25
q = 5
# noise
X0 = sapply(1:p, function(x) rnorm(N))
Y0 = sapply(1:q, function(x) rnorm(N))

colnames(X0) = paste0("x", 1:p)
colnames(Y0) = paste0("y", 1:q)

# signal
Z1 = rnorm(N,0,1)


#Some associations with the true signal
alpha = (6:10) / 10
beta  = -(2:3) / 10

loc_alpha = 1:length(alpha)
loc_beta  = 1:length(beta)

for(j in 1:length(alpha))
  X0[, loc_alpha[j]] =  alpha[j] * Z1 + rnorm(N,0,0.3)

for(j in 1:length(beta))
  Y0[, loc_beta[j]] =  beta[j] * Z1 + rnorm(N,0,0.3)
cv = initialiseCanVar(X0, Y0)

Calculates mode.

Description

Calculates mode.

Usage

modes(d)

Arguments

Plot heatmap of cv w.r.t. the penalty parameter perfotmance.

Description

This function plots cca for different thresholds

Usage

myHeatmap(
  mat,
  palette_values = mpalette,
  blue = NULL,
  xlab = "",
  ylab = "",
  show_axes = TRUE,
  show_labels = TRUE,
  K = NULL
)

Arguments

Value

No return value, called for plotting heatmap.

Examples

mat <- matrix(rexp(200, rate=.1), ncol=20)/200
myHeatmap(mat)

Plot slection stability for penalty parameter performance.

Description

This function plots cv for different thresholds

Usage

plt.selstab(
  object,
  X,
  Y,
  nonz_x,
  nonz_y,
  palette_values = mpalette,
  blue = TRUE,
  mm = TRUE,
  k = 1
)

Arguments

Value

No return value, called for selection stability pot.

Examples

# example code
#sample size etc
N = 10
p = 25
q = 5
# noise
X0 = sapply(1:p, function(x) rnorm(N))
Y0 = sapply(1:q, function(x) rnorm(N))

colnames(X0) = paste0("x", 1:p)
colnames(Y0) = paste0("y", 1:q)

# signal
Z1 = rnorm(N,0,10)


#Some associations with the true signal
alpha = (6:10) / 10
beta  = -(2:3) / 10

loc_alpha = 1:length(alpha)
loc_beta  = 1:length(beta)

for(j in 1:length(alpha))
  X0[, loc_alpha[j]] =  alpha[j] * Z1 + rnorm(N,0,0.03)

for(j in 1:length(beta))
  Y0[, loc_beta[j]] =  beta[j] * Z1 + rnorm(N,0,0.03)

# performa toscca
X = standardVar(X0)
Y = standardVar(Y0)
K = 2                                       # number of components to be estimated
nonz_x = c(2,5, 10, 20)                     # number of nonzero variables for X
nonz_y = c(2, 3, 4)                      # number of nonzero variables for Y
init   = "uniform"                          # type of initialisation
cca_toscca  = toscca(X, Y, nonz_x, nonz_y, K, alpha_init = init,
combination = TRUE, K=1, silent = TRUE, toPlot = FALSE)
plt <- plt.selstab(cca_toscca,X, Y, nonz_x = nonz_x, nonz_y = nonz_y, mm=FALSE)

Performs power method.

Description

Performs power method.

Usage

powerMethod(mat, vec, tol = 10^(-6), maxIter = 500, silent = TRUE)

Arguments

Value

List: vec: eigen vector; lambda: eigen value; t: total iterations.

Progress bar

Description

Shows progress of a process.

Usage

progressBar(end, round)

Arguments

Value

Display in consol of current status.

Performs matrix residualisation over estimated canonical vectors. There are three types: basic (subtracts scaled estimated latent variable from data), null (uses the null space of the estimated canonical vector to construct a new matrix) and LV (uses SVD to residualise).

Description

Performs matrix residualisation over estimated canonical vectors. There are three types: basic (subtracts scaled estimated latent variable from data), null (uses the null space of the estimated canonical vector to construct a new matrix) and LV (uses SVD to residualise).

Usage

residualisation(
  mat,
  vec,
  spaceMat = NULL,
  type = c("LV", "null", "basic"),
  na.allow = TRUE
)

Arguments

Value

Matrix.

Standardises matrices with multiple measurements per individual.

Description

This function stardadises matrices with multiple measurements w.r.t. a chosen origin.

Usage

scale_rm(mat, origin = NULL, centre = FALSE)

Arguments

Value

Returns scaled and/or centred values for repeated measurements.

Examples

#sample size etc
N = 10
p = 25
q = 5
# noise
X0 = sapply(1:p, function(x) rnorm(N))
Y0 = sapply(1:q, function(x) rnorm(N))

colnames(X0) = paste0("x", 1:p)
colnames(Y0) = paste0("y", 1:q)

# signal
Z1 = rnorm(N,0,1)


#Some associations with the true signal
alpha = (6:10) / 10
beta  = -(2:3) / 10

loc_alpha = 1:length(alpha)
loc_beta  = 1:length(beta)

for(j in 1:length(alpha))
  X0[, loc_alpha[j]] =  alpha[j] * Z1 + rnorm(N,0,0.3)

for(j in 1:length(beta))
  Y0[, loc_beta[j]] =  beta[j] * Z1 + rnorm(N,0,0.3)

X = standardVar(X0)
Y = standardVar(Y0)

Performs scalling for matrix residualisation based on calculated coefficients.

Description

Performs scalling for matrix residualisation based on calculated coefficients.

Usage

scaledResidualMat(A)

Arguments

Value

scaled matrix.

Stardardise a matrix

Description

This function stardardises a matrix or a vector and gives the option to centre or normalise (only vectors).

Usage

standardVar(mat, centre = TRUE, normalise = FALSE)

Arguments

Value

A matrix or vector with the preferred standardarisation

Examples

#sample size etc
N = 10
p = 25
q = 5
# noise
X0 = sapply(1:p, function(x) rnorm(N))
Y0 = sapply(1:q, function(x) rnorm(N))

colnames(X0) = paste0("x", 1:p)
colnames(Y0) = paste0("y", 1:q)

# signal
Z1 = rnorm(N,0,1)


#Some associations with the true signal
alpha = (6:10) / 10
beta  = -(2:3) / 10

loc_alpha = 1:length(alpha)
loc_beta  = 1:length(beta)

for(j in 1:length(alpha))
  X0[, loc_alpha[j]] =  alpha[j] * Z1 + rnorm(N,0,0.3)

for(j in 1:length(beta))
  Y0[, loc_beta[j]] =  beta[j] * Z1 + rnorm(N,0,0.3)

X = standardVar(X0)
Y = standardVar(Y0)

Computes permutatied cc fot TOSCCA-MM

Description

This function estimates sparse canonical vectors for permuted matrices with multiple measurements.

Usage

toscamm.perm(
  A,
  B,
  nonzero_a,
  nonzero_b,
  K = 1,
  folds = 1,
  toPlot = FALSE,
  draws = 1000,
  cancor,
  bootCCA = NULL,
  silent = TRUE,
  parallel_logic = TRUE,
  nuisanceVar = 0,
  testStatType = "CC",
  model = "lme",
  lmeformula = " ~ 0 + poly(time,3) + (1|id)",
  arformula = NULL,
  ncores = NULL
)

Arguments

Value

Permuted canonical correlation for ell K and p-values.

List with permuted correlations and p-values.

Examples

# example code

# dont run due to parallel processes
#sample size etc
N = 10
p = 25
q = 5
X0 = list()
Y0 = list()

#Some associations with the true signal
cwa = (6:10) / 10
cwb  = -(2:3) / 10

alpha = rep(0, p)
beta = rep(0, q)

loc_alpha = 1:length(alpha)
loc_beta  = 1:length(beta)

alpha[loc_alpha] = cwa
beta[loc_beta] = cwb

sg = matrix(c(1, 0.6, 0.3, rep(0, 2),
              0.6, 1, 0.6, 0.3, rep(0, 1),
              0.3, 0.6, 1, 0.6, 0.3,
              rep(0,1), 0.3, 0.6, 1, 0.6,
              rep(0,2), 0.3, 0.6, 1), ncol = 5)
for(i in 1:N)
{
  times = 1:5
  Zi1 = (sin(100*times))^times +   times * 0.65 +rnorm(1,0,0.95)
  Zi = cbind(Zi1)
  #Simulate data and add some noise
  X0i = sapply(1:p, function(a) MASS::mvrnorm(1, (Zi %*% t(alpha))[,a], Sigma = sg))
  Y0i = sapply(1:q, function(a) MASS::mvrnorm(1, (Zi %*% t(beta))[,a], Sigma = sg))

  colnames(X0i) = paste0("X", 1:ncol(X0i))
  colnames(Y0i) = paste0("Y", 1:ncol(Y0i))
  #Check the simulated cross correlation
  #image(cor(X0i, Y0i))

  #Remove some observations
  # p_observed = 1
  X0i = cbind(id=i, time=times, X0i)#[rbinom(length(times),1,p_observed)==1,]
  Y0i = cbind(id=i, time=times, Y0i)#[rbinom(length(times),1,p_observed)==1,]

  X0[[i]] = X0i
  Y0[[i]] = Y0i
}

X0 = do.call("rbind", X0)
Y0 = do.call("rbind", Y0)

X = data.frame(X0); Y = data.frame(Y0)
nonz_a = c(2, 5, 10, 20)
nonz_b =  c(2, 3, 4)

mod <- tosccamm(X, Y, folds = 2, nonzero_a = nonz_a, nonzero_b = nonz_b, silent = TRUE)
nza <- mod$nonzero_a
nzb <- mod$nonzero_b
cc  <- mod$cancor
perm_cc <- toscamm.perm(X,Y, nonzero_a=nza, nonzero_b=nzb,cancor=cc, ncores=2, draws = 10)

Sparse Canonical Correlation Analysis. Computation of CC via NIPALS with soft thresholding.

Description

Sparse Canonical Correlation Analysis. Computation of CC via NIPALS with soft thresholding.

Usage

toscca(
  A,
  B,
  nonzero_a,
  nonzero_b,
  K = 1,
  alpha_init = c("eigen", "random", "uniform"),
  folds = 1,
  silent = FALSE,
  toPlot = TRUE,
  typeResid = "basic",
  combination = FALSE,
  parallel_logic = FALSE
)

Arguments

Value

a list with the following elements:

List with estimated toscca parameters.

Examples

#sample size etc
N = 10
p = 25
q = 5
# noise
X0 = sapply(1:p, function(x) rnorm(N))
Y0 = sapply(1:q, function(x) rnorm(N))

colnames(X0) = paste0("x", 1:p)
colnames(Y0) = paste0("y", 1:q)

# signal
Z1 = rnorm(N,0,1)


#Some associations with the true signal
alpha = (6:10) / 10
beta  = -(2:3) / 10

loc_alpha = 1:length(alpha)
loc_beta  = 1:length(beta)

for(j in 1:length(alpha))
  X0[, loc_alpha[j]] =  alpha[j] * Z1 + rnorm(N,0,0.3)

for(j in 1:length(beta))
  Y0[, loc_beta[j]] =  beta[j] * Z1 + rnorm(N,0,0.3)

X = standardVar(X0)
Y = standardVar(Y0)
K = 2                                       # number of components to be estimated
nonz_x = c(2,5, 10, 20)                     # number of nonzero variables for X
nonz_y = c(2, 3, 4)                      # number of nonzero variables for Y
init   = "uniform"                          # type of initialisation
cca_toscca  = toscca(X, Y, nonz_x, nonz_y, K, alpha_init = init, silent = TRUE, toPlot = FALSE)

Sparse Canonical Correlation Analysis. Computation of CC via NIPALS with soft thresholding.

Description

Sparse Canonical Correlation Analysis. Computation of CC via NIPALS with soft thresholding.

Usage

toscca.core(
  alphaInit,
  A,
  B,
  nonzero_a,
  nonzero_b,
  iter = 20,
  tol = 10^(-6),
  silent = FALSE
)

Arguments

Value

a list with the following elements:

Sparse Canonical Correlation Analysis. Computation of CC via NIPALS with soft thresholding.

Description

Sparse Canonical Correlation Analysis. Computation of CC via NIPALS with soft thresholding.

Usage

toscca.folds(
  A,
  B,
  nonzero_a,
  nonzero_b,
  alpha_init,
  folds = 1,
  parallel_logic = FALSE,
  silent = FALSE,
  toPlot = TRUE,
  ATest_res = NULL,
  BTest_res = NULL
)

Arguments

Value

a list with the following elements:

Get latent variables

Description

Gets latent variables from data and estimates.

Usage

toscca.lv(data, alpha, beta)

Arguments

Permutation testing for toscca

Description

This function performs permutation testing on CC estimates.

Usage

toscca.perm(
  A,
  B,
  nonzero_a,
  nonzero_b,
  K,
  alpha_init = c("eigen", "random", "uniform"),
  folds = 1,
  toPlot = FALSE,
  draws = 20,
  cancor,
  silent = TRUE,
  parallel_logic = TRUE,
  nuisanceVar = 0,
  testStatType = "CC",
  ncores = NULL
)

Arguments

Details

For a exploratory analysis nonzero_a and nonzero_b can be vectors. The algorithm will then search for the best combination of sparsity choice nonzero_a and nonzero_b for each component.

Value

Matrix with permutation estimates.

List with permuted correlations and p-values.

Examples

#sample size etc
N = 10
p = 25
q = 5
# noise
X0 = sapply(1:p, function(x) rnorm(N))
Y0 = sapply(1:q, function(x) rnorm(N))

colnames(X0) = paste0("x", 1:p)
colnames(Y0) = paste0("y", 1:q)

# signal
Z1 = rnorm(N,0,1)


#Some associations with the true signal
alpha = (6:10) / 10
beta  = -(2:3) / 10

loc_alpha = 1:length(alpha)
loc_beta  = 1:length(beta)

for(j in 1:length(alpha))
  X0[, loc_alpha[j]] =  alpha[j] * Z1 + rnorm(N,0,0.3)

for(j in 1:length(beta))
  Y0[, loc_beta[j]] =  beta[j] * Z1 + rnorm(N,0,0.3)

X = standardVar(X0)
Y = standardVar(Y0)
K = 2                                       # number of components to be estimated
nonz_x = c(2,5, 10, 20)                     # number of nonzero variables for X
nonz_y = c(1, 2, 3, 4)                      # number of nonzero variables for Y
init   = "uniform"                          # type of initialisation
cca_toscca  = toscca(X, Y, nonz_x, nonz_y, K, alpha_init = init, silent = TRUE, toPlot = FALSE)

#dont run due to parallelisation.
cc = cca_toscca$cancor
perm_toscca = toscca.perm(X, Y, nonz_x, nonz_y, K = K, init, draws = 10, cancor = cc, ncores = 2)

Get the estatistic for the permutations.

Description

Get the estatistic for the permutations.

Usage

toscca.tStat(cancor, A, B, C = 0, type = c("CC", "Wilks", "Roy"))

Arguments

Value

Statistic

Computes TOSCCA-MM

Description

This function estimates sparse canonical vectors for matrices with multiple measurements and the trajectories of the latent variables.

Usage

tosccamm(
  A,
  B,
  nonzero_a,
  nonzero_b,
  folds = 1,
  parallel_logic = FALSE,
  silent = FALSE,
  ATest_res = NULL,
  BTest_res = NULL,
  model = "lme",
  lmeformula = " ~ -1 + time + (1|id)",
  arformula = c(1, 0, 0)
)

Arguments

Value

Canonical vectors for k components.

List with estimated tosccamm parameters.

Examples

# example code
#sample size etc
N = 10
p = 25
q = 5
X0 = list()
Y0 = list()

#Some associations with the true signal
cwa = (6:10) / 10
cwb  = -(2:3) / 10

alpha = rep(0, p)
beta = rep(0, q)

loc_alpha = 1:length(alpha)
loc_beta  = 1:length(beta)

alpha[loc_alpha] = cwa
beta[loc_beta] = cwb

sg = matrix(c(1, 0.6, 0.3, rep(0, 2),
              0.6, 1, 0.6, 0.3, rep(0, 1),
              0.3, 0.6, 1, 0.6, 0.3,
              rep(0,1), 0.3, 0.6, 1, 0.6,
              rep(0,2), 0.3, 0.6, 1), ncol = 5)
for(i in 1:N)
{
  times = 1:5
  Zi1 = (sin(100*times))^times +   times * 0.65 +rnorm(1,0,0.95)
  Zi = cbind(Zi1)
  #Simulate data and add some noise
  X0i = sapply(1:p, function(a) MASS::mvrnorm(1, (Zi %*% t(alpha))[,a], Sigma = sg))
  Y0i = sapply(1:q, function(a) MASS::mvrnorm(1, (Zi %*% t(beta))[,a], Sigma = sg))

  colnames(X0i) = paste0("X", 1:ncol(X0i))
  colnames(Y0i) = paste0("Y", 1:ncol(Y0i))
  #Check the simulated cross correlation
  #image(cor(X0i, Y0i))

  #Remove some observations
  # p_observed = 1
  X0i = cbind(id=i, time=times, X0i)#[rbinom(length(times),1,p_observed)==1,]
  Y0i = cbind(id=i, time=times, Y0i)#[rbinom(length(times),1,p_observed)==1,]

  X0[[i]] = X0i
  Y0[[i]] = Y0i
}

X0 = do.call("rbind", X0)
Y0 = do.call("rbind", Y0)

X = data.frame(X0); Y = data.frame(Y0)
nonz_a = c(2, 5, 10, 20)
nonz_b =  c(2, 3, 4)

mod <- tosccamm(X, Y, folds = 2, nonzero_a = nonz_a, nonzero_b = nonz_b, silent = TRUE)