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ReMPCA Smooth and Sparse Multivariate Functional Principal Component Analysis

ReMPCA.Rd

ReMPCA Smooth and Sparse Multivariate Functional Principal Component Analysis

Usage

ReMPCA(
  hd,
  centerhds = TRUE,
  num_pcs = 1,
  nfolds_u = 5,
  nfolds_v = NULL,
  thresh = 1e-10,
  maxit = 100,
  tuning_iter = 1,
  parallel = FALSE,
  weights = NULL,
  smoothness_type = "Second_order",
  sparse_tuning_type = "soft",
  tuning_order = "Sparsity",
  cv.pick = "1se",
  sparse_tuning_u = NULL,
  sparse_tuning_v = NULL,
  smooth_tuning_u = NULL,
  smooth_tuning_v = NULL
)

Arguments

hd

An hdClass object.

centerhds

A logical; if True, it demeans the data before calculating the principal components.

num_pcs

An integer. The number of principal components.

nfolds_u

An integer. It's used in cross validation approach for tuning the level of sparsity of rows.

nfolds_v

An integer vector of length p (the number of variables), where the i-th element specifies the number of cross-validation folds to use for the i-th variable. If not provided (NULL), a value of 5 will be assigned to all variables by default.

thresh

The convergence threshold in power algorithm.

maxit

Maximum number of iterations in power algorithm.

tuning_iter

Integer specifying the number of iterations to perform during the tuning process for conditional smoothing and sparsity parameters.

parallel

Logical; if TRUE, parallel computation is used to fit models across different sparsity parameter values. Users must register a parallel backend beforehand using packages such as doParallel, doMC, or similar.

weights

Optional numeric vector of scaling weights. If NULL, the function automatically computes weights based on the inverse square root of the average variance of each variable. If set to 0, no scaling is applied. If a numeric vector is provided, its length must match the number of variables, and each element is used to scale the corresponding variable. This is used to adjust for scale differences across variables in the hybrid data object.

smoothness_type

A character string specifying the method used in smoothing u and/or v, must be one of "Second_order" (default), "First_order" or "Indicator".

sparse_tuning_type

A character string specifying the sparse calculation method. Must be one of "soft" (default), "hard", or "SCAD".

tuning_order

A character string representing the tuning order. If set to 'Sparsity', sparsity parameters are tuned first, followed by smoothness. If set to 'Smoothness', the order is reversed.

cv.pick

A character string specifying the rule used to select the optimal tuning parameter during cross-validation for sparsity. If set to 'min', the tuning parameter corresponding to the minimum cross-validation error is chosen. If set to '1se' (the default), the 1-standard-error rule is applied, selecting the most regularized model whose error is within one standard error of the minimum.

sparse_tuning_u

Optional. Specifies the sparsity level(s) for rows:

  • A single non-negative integer for fixed sparsity.

  • A numeric vector of candidate values, to be selected via cross-validation (CV).

  • Set to 0 for no sparsity.

  • If NULL, the function defaults to the Sparsity_parameter attribute from the hdClass object.

sparse_tuning_v

Optional. A list of length p (number of variables), where the i-th element is either a numeric value or a vector specifying candidate sparsity levels for the i-th variable. If set to NULL, the function will default to using the Sparsity_parameter_col attribute from the input object of class hdClass.

smooth_tuning_u

Optional. Specifies smoothing parameter for rows:

  • A single number for fixed smoothness.

  • A numeric vector of candidate values, to be selected via generalized cross-validation (GCV).

  • Set to 0 for no smoothness

  • If NULL, the function defaults to the Smoothing_parameter attribute from the hdClass object.

smooth_tuning_v

Optional. A list of length p (number of variables), where the i-th element is either a numeric value or a vector specifying candidate smoothing parameters for the i-th variable. If set to NULL, the function will default to using the Smoothing_parameter_col attribute from the input object of class hdClass.

Value

ReconstructedData, PCFunctions, PCScores, OptimalAlphaV, OptimalAlphaU, OptimalGammaV, OptimalGammaU, GCVResultsV, GCVResultsU, CVResultsV, CVResultsU, VarianceExplained, variable_types