Package 'multiCCA'

Compute Hopkins statistic for increasing numbers of components

Description

Computes the Hopkins statistic for representations based on increasing numbers of canonical components obtained from an MCCA model.

Usage

hopkins_vs_components(
  fit,
  blocks = NULL,
  max_comp = NULL,
  m = NULL,
  nrep = 50,
  seed = NULL
)

Arguments

fit	Fitted object of class mcca_fit.
blocks	Vector of block indices included in the representation. If NULL, all blocks are used.
max_comp	Maximum number of components to evaluate.
m	Number of sampled points used in the Hopkins statistic.
nrep	Number of repetitions used to estimate the statistic.
seed	Optional random seed.

Value

A data frame containing:

• components – number of components,

• hopkins – mean Hopkins statistic,

• sd – standard deviation across repetitions.

Examples

set.seed(1)

n <- 20
T_len <- 10

X <- list(
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 3), T_len, 3)),
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 2), T_len, 2))
)

fit <- mcca_fit(method = "kernel", X = X, ncomp = 3)

hopkins_vs_components(fit, max_comp = 2)

---

Fit multiple canonical correlation analysis

Description

Fits either kernel MCCA for repeated measures data or functional MCCA.

Usage

mcca_fit(
  method = c("kernel", "functional"),
  X,
  ncomp = 2,
  eps = 0.001,
  gamma = NULL,
  nbasis = 5,
  basis_type = "fourier",
  argvals = NULL
)

Arguments

method	Character string specifying the method to use. Either 'kernel' or 'functional'.
X	List of feature blocks. Each element X[[l]] is a list of matrices, where X[[l]][[i]] is a T x p_l matrix representing the observations for subject i in block l.
ncomp	Number of leading canonical components.
eps	Regularization parameter.
gamma	Gaussian kernel bandwidth for the kernel method.
nbasis	Number of basis functions for the functional method.
basis_type	Basis type for the functional method. Either 'fourier' or 'bspline'.
argvals	Optional time grid for the functional method.

Value

An object of class mcca_fit. The following S3 methods are available for this class:

• print() prints a short summary of the fitted model,

• summary() provides a more detailed summary of the model.

Examples

set.seed(1)

n <- 20
T_len <- 10

X <- list(lapply(seq_len(n), function(i) matrix(rnorm(T_len * 3), T_len, 3)),
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 2), T_len, 2)))

fit <- mcca_fit(method = 'kernel',
  X = X,
  ncomp = 2,
  eps = 1e-2)

print(fit)
summary(fit)

---

Grid search for tuning parameters in MCCA

Description

Performs a grid search over regularization and model parameters for kernel or functional multiple canonical correlation analysis.

Usage

mcca_grid_search(
  method = c("kernel", "functional"),
  X,
  eps_grid,
  gamma_grid = NULL,
  nbasis_grid = NULL,
  ncomp_eval = 2,
  criterion = c("first", "sumk"),
  basis_type = "fourier",
  argvals = NULL
)

Arguments

method	Character string specifying the method. Either 'kernel' or 'functional'.
X	List of feature blocks.
eps_grid	Vector of candidate regularization parameters.
gamma_grid	Vector of candidate kernel bandwidths (kernel method).
nbasis_grid	Vector of candidate numbers of basis functions (functional method).
ncomp_eval	Number of canonical components used in evaluation.
criterion	Criterion used to rank models: 'first' or 'sumk'.
basis_type	Basis type used in functional method: 'fourier' or 'bspline'.
argvals	Optional time grid for functional data.

Value

A list containing:

• results – data frame with grid search scores,

• best_fit – fitted MCCA model for the best parameter set,

• best_row – row of the grid corresponding to the best parameters.

Examples

set.seed(1)

n <- 20
T_len <- 10

X <- list(
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 3), T_len, 3)),
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 2), T_len, 2))
)

res <- mcca_grid_search(
  method = "kernel",
  X = X,
  eps_grid = c(1e-3, 1e-2),
  gamma_grid = c(0.1, 1),
  ncomp_eval = 2
)

res$best_row

---

Run the full MCCA analysis pipeline

Description

This function performs a complete analysis workflow for multiple canonical correlation analysis (MCCA). It fits either the kernel or functional MCCA model, computes the Hopkins statistic for increasing numbers of components, and produces diagnostic plots.

Usage

mcca_pipeline(
  method = c("kernel", "functional"),
  X,
  groups = NULL,
  labels = NULL,
  ncomp = 5,
  eps = 0.001,
  gamma = NULL,
  nbasis = 5,
  basis_type = "fourier",
  argvals = NULL,
  hopkins_blocks = NULL,
  hopkins_max_comp = NULL,
  hopkins_m = NULL,
  hopkins_nrep = 100,
  block_x = 1,
  block_y = 2,
  pair_comp = 1
)

Arguments

method	Character string specifying the method to use. Either 'kernel' or 'functional'.
X	List of feature blocks. Each element X[[l]] is a list of matrices, where X[[l]][[i]] is a ⁠T x p_l⁠ matrix representing the observations for subject i in block l.
groups	Optional grouping variable used for coloring points in plots.
labels	Optional vector of labels used to annotate points in plots.
ncomp	Number of canonical components to estimate.
eps	Regularization parameter used in the generalized eigenproblem.
gamma	Gaussian kernel bandwidth used in the kernel MCCA method.
nbasis	Number of basis functions used in the functional MCCA method.
basis_type	Basis type used in the functional method. Either 'fourier' or 'bspline'.
argvals	Optional time grid used for functional data smoothing.
hopkins_blocks	Vector of block indices used when computing the Hopkins statistic. If NULL, all blocks are used.
hopkins_max_comp	Maximum number of components used when computing the Hopkins statistic. If NULL, all available components are used.
hopkins_m	Number of sampled points used in the Hopkins statistic.
hopkins_nrep	Number of repetitions used when estimating the Hopkins statistic.
block_x	Index of the first block used in the pairwise component plot.
block_y	Index of the second block used in the pairwise component plot.
pair_comp	Index of the canonical component used in the pairwise plot.

Value

A list containing:

• fit – fitted MCCA model object.

• hopkins – data frame with Hopkins statistic values.

• pair_plot – ggplot object with pairwise component scatter plot.

• hopkins_plot – ggplot object showing Hopkins statistic versus number of components.

Examples

set.seed(1)

n <- 20
T_len <- 10

X <- list(
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 3), T_len, 3)),
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 2), T_len, 2))
)

groups <- sample(1:2, n, replace = TRUE)

res <- mcca_pipeline(
  method = 'kernel',
  X = X,
  groups = groups,
  ncomp = 3,
  eps = 1e-2
)

res$fit
head(res$hopkins)

---

Plot Hopkins statistic curve

Description

Plots the Hopkins statistic as a function of the number of canonical components.

Usage

plot_hopkins_curve(df, title = NULL)

Arguments

df	Data frame returned by hopkins_vs_components().
title	Optional plot title.

Value

A ggplot2 object.

Examples

set.seed(1)

n <- 20
T_len <- 10

X <- list(
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 3), T_len, 3)),
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 2), T_len, 2))
)

fit <- mcca_fit(method = "kernel", X = X, ncomp = 3)
H <- hopkins_vs_components(fit, max_comp = 2)

plot_hopkins_curve(H)

---

Plot canonical components for two blocks

Description

Creates a scatter plot comparing canonical components from two blocks.

Usage

plot_mcca_pair(
  fit_x,
  fit_y = NULL,
  block_x = 1,
  block_y = 2,
  comp = 1,
  groups = NULL,
  labels = NULL,
  title = NULL
)

Arguments

fit_x	Fitted object of class mcca_fit.
fit_y	Optional second MCCA object. If NULL, fit_x is used.
block_x	Block index for x-axis.
block_y	Block index for y-axis.
comp	Component index.
groups	Optional grouping variable.
labels	Optional point labels.
title	Optional plot title.

Value

A ggplot2 object.

Examples

set.seed(1)

n <- 20
T_len <- 10

X <- list(
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 3), T_len, 3)),
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 2), T_len, 2))
)

fit <- mcca_fit(method = "kernel", X = X, ncomp = 2)

plot_mcca_pair(fit)

---

Plot canonical components for a single block

Description

Creates a scatter plot of two canonical components obtained from an MCCA model for a selected block.

Usage

plot_mcca_scatter(
  fit,
  block = 1,
  comp_x = 1,
  comp_y = 2,
  groups = NULL,
  labels = NULL,
  add_ellipse = TRUE,
  point_size = 2.5,
  title = NULL
)

Arguments

fit	Object of class mcca_fit.
block	Block index.
comp_x	Component used on the x-axis.
comp_y	Component used on the y-axis.
groups	Optional grouping variable.
labels	Optional point labels.
add_ellipse	Logical; whether to draw group ellipses.
point_size	Size of plotted points.
title	Optional plot title.

Value

A ggplot2 object.

Examples

set.seed(1)

n <- 20
T_len <- 10

X <- list(
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 3), T_len, 3)),
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 2), T_len, 2))
)

fit <- mcca_fit(method = "kernel", X = X, ncomp = 2)

plot_mcca_scatter(fit)

---

Predict canonical component scores for new data

Description

Projects new observations onto canonical components obtained from a fitted MCCA model (kernel or functional).

Usage

## S3 method for class 'mcca_fit'
predict(object, newdata, ...)

Arguments

object	Object of class mcca_fit.
newdata	List of feature blocks with the same structure as used during model fitting.
...	Additional arguments (unused).

Value

List of matrices containing projected component scores for each block.

Examples

set.seed(1)

n <- 20
T_len <- 10

X <- list(
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 3), T_len, 3)),
  lapply(seq_len(n), function(i) matrix(rnorm(T_len * 2), T_len, 2))
)

fit <- mcca_fit(method = 'kernel', X = X, ncomp = 2)

predict(fit, X)

---

Summarize an MCCA model

Description

Provides a summary of a fitted MCCA model, including the number of blocks, sample size, regularization parameter, and generalized canonical correlations.

Usage

## S3 method for class 'mcca_fit'
summary(object, ...)

Arguments

object	An object of class mcca_fit.
...	Additional arguments (currently unused).

Value

An object of class summary.mcca_fit.

---