moma_sfpca: Sparse and functional PCA
In DataSlingers/MoMA: MoMA - Modern Multivariate Analysis in R

Description Usage Arguments Value Functions

moma_sfpca creates an SFPCA R6 object and returns it.

moma_spca is a function for performing one-way sparse PCA.

moma_twspca is a function for performing two-way sparse PCA.

moma_fpca is a function for performing one-way functional PCA.

moma_twfpca is a function for performing two-way functional PCA.

moma_sfpca(X, ..., center = TRUE, scale = FALSE,
  u_sparse = moma_empty(), v_sparse = moma_lasso(),
  u_smooth = moma_smoothness(), v_smooth = moma_smoothness(),
  pg_settings = moma_pg_settings(), max_bic_iter = 5, rank = 1,
  deflation_scheme = "PCA_Hotelling")

moma_spca(X, ..., center = TRUE, scale = FALSE,
  u_sparse = moma_empty(), v_sparse = moma_lasso(),
  pg_settings = moma_pg_settings(), max_bic_iter = 5, rank = 1,
  deflation_scheme = "PCA_Hotelling")

moma_twspca(X, ..., center = TRUE, scale = FALSE,
  u_sparse = moma_lasso(), v_sparse = moma_lasso(),
  pg_settings = moma_pg_settings(), max_bic_iter = 5, rank = 1,
  deflation_scheme = "PCA_Hotelling")

moma_fpca(X, ..., center = TRUE, scale = FALSE,
  u_smooth = moma_smoothness(), v_smooth = moma_smoothness(),
  pg_settings = moma_pg_settings(), max_bic_iter = 5, rank = 1,
  deflation_scheme = "PCA_Hotelling")

moma_twfpca(X, ..., center = TRUE, scale = FALSE,
  u_smooth = moma_smoothness(), v_smooth = moma_smoothness(),
  pg_settings = moma_pg_settings(), max_bic_iter = 5, rank = 1,
  deflation_scheme = "PCA_Hotelling")

`X`	A data matrix, each row representing a sample, and each column a feature.
`...`	Force users to specify arguments by names.
`center`	A logical value indicating whether the variables should be shifted to be zero centered. Defaults to `TRUE`.
`scale`	A logical value indicating whether the variables should be scaled to have unit variance. Defaults to `FALSE`.
`u_sparse, v_sparse`	An object of class inheriting from "`moma_sparsity_type`". Most conveniently specified by functions described in `moma_sparsity_options`. It specifies the type of sparsity-inducing penalty function used in the model. Note that for `moma_spca`, these two parameters must not be specified at the same time. For `moma_fpca` and `moma_twfpca`, they must not be specified.
`u_smooth, v_smooth`	An object of class inheriting from "`moma_smoothness_type`". Most conveniently specified by functions described in `moma_smoothness`. It specifies the type of smoothness terms used in the model. Note that for `moma_fpca`, these two parameters must not be specified at the same time. For `moma_spca` and `moma_twspca`, they must not be specified.
`pg_settings`	An object of class inheriting from "`moma_pg_settings`". Most conviently specified by functions described in `moma_pg_settings`. It specifies the type of algorithm used to solve the problem, acceptable level of precision, and the maximum number of iterations allowed.
`max_bic_iter`	A positive integer. Defaults to 5. The maximum number of iterations allowed in nested greedy BIC selection scheme.
`rank`	A positive integer. Defaults to 1. The maximal rank, i.e., maximal number of principal components to be used.
`deflation_scheme`	A string specifying the deflation scheme. It should be one of `"PCA_Hotelling", "PCA_Schur_Complement", "PCA_Projection"`. In the discussion below, let u,v be the normalized vectors obtained by scaling the penalized singular vectors. When `deflation_scheme = "Hotelling_deflation"` is specified, the following deflation scheme is used. \boldsymbol{X}_{t} :=\boldsymbol{X}_{t-1}-d_{t} \boldsymbol{u}_{t} \boldsymbol{v}_{t}^{T}, where d_{t}=\boldsymbol{u}_{t}^{T} \boldsymbol{X}_{t-1} \boldsymbol{v}_{t}. When `deflation_scheme = "PCA_Schur_Complement"` is specified, the following deflation scheme is used: \boldsymbol{X}_{t} :=≤ft(\boldsymbol{I}_{n}- \boldsymbol{u}_{t} \boldsymbol{u}_{t}^{T}\right) \boldsymbol{X}_{t-1} ≤ft(\boldsymbol{I}_{p}-\boldsymbol{v}_{t} \boldsymbol{v}_{t}^{T}\right). When `deflation_scheme = "PCA_Projection"` is specified, the following deflation scheme is used: \boldsymbol{X}_{t} :=\boldsymbol{X}_{t-1}-\frac{\boldsymbol{X}_{t-1} \boldsymbol{v}_{t} \boldsymbol{u}_{t}^{T} \boldsymbol{X}_{t-1}}{\boldsymbol{u}_{t}^{T} \boldsymbol{X}_{t-1} \boldsymbol{v}_{t}}.