Multiple Factor Analysis (generic)

A generic front–end for **Multiple Factor Analysis** (MFA). Concrete methods should perform the estimation and return an object inheriting from class `mfa`.

Usage

mfa(data, preproc, ncomp = 2, normalization = "MFA", A = NULL, M = NULL, ...)

# S3 method for class 'list'
mfa(
  data,
  preproc = center(),
  ncomp = 2,
  normalization = c("MFA", "RV", "None", "Frob", "custom"),
  A = NULL,
  M = NULL,
  ...
)

# S3 method for class 'multiblock'
mfa(
  data,
  preproc = center(),
  ncomp = 2,
  normalization = c("MFA", "RV", "None", "Frob", "custom"),
  A = NULL,
  M = NULL,
  ...
)

Arguments

data

A data object for which a BaDA method is defined (see individual methods for details).

preproc

A preprocessing pipeline from the multivarious package. Defaults to `multivarious::center()` in the concrete methods.

ncomp

Integer; the number of discriminant components to compute.

normalization

Character string specifying the block‑weighting scheme (see [mfa.multiblock]).

A, M

Optional user‑supplied column/row weight matrices used when `normalization = "custom"`.

...

Additional arguments passed to the method.

Value

An object of class `mfa`.

Details

The mfa.list method applies the MFA algorithm to a list of data matrices or data frames. This method first converts the list to a multiblock object and then calls mfa.multiblock.

The mfa.multiblock method implements Multiple Factor Analysis for a collection of data blocks. This method handles data preprocessing, block normalization, and integration of multiple data tables that share the same observations.

Normalization options include:

• MFA: Scales each block by its first singular value (default)

• RV: Normalizes blocks based on RV matrix correlation

• None: No scaling applied

• Frob: Uses Frobenius norm for scaling

• custom: Uses custom weight matrices provided via A and M parameters

References

Abdi, H., Williams, L. J., & Valentin, D. (2013). *Multiple factor analysis: principal component analysis for multi‑table and multi‑block data sets*. **Wiley Interdisciplinary Reviews: Computational Statistics, 5**(2), 149–179.

Examples

# \donttest{
# Apply MFA to a list of matrices
X <- replicate(5, { matrix(rnorm(10*10), 10, 10) }, simplify=FALSE)
res <- mfa(X, ncomp=3, normalization="MFA")
#> Applying the same preprocessor definition independently to each block.
#> normalization type:MFA
#> Registered S3 method overwritten by 'genpca':
#>   method                   from        
#>   transfer.cross_projector multivarious
# }
# \donttest{
# Create 5 random matrices of the same size
X <- replicate(5, { matrix(rnorm(10*10), 10, 10) }, simplify=FALSE)

# Apply MFA with MFA normalization
res <- mfa(X, ncomp=3, normalization="MFA")
#> Applying the same preprocessor definition independently to each block.
#> normalization type:MFA

# Project a block onto the model
p <- multivarious::project_block(res, X[[1]], 1)

# Verify number of components
stopifnot(ncol(multivarious::scores(res)) == 3)

# Create a classifier
labs <- letters[1:10]
cfier <- multivarious::classifier(res, new_data=do.call(cbind, X), labels=labs)
pred <- predict(cfier, do.call(cbind, X)[1:2,])

# Create a classifier using a specific block
cfier2 <- multivarious::classifier(res, new_data=X[[2]], labels=labs,
                                  colind=res$block_indices[[2]])
pred2 <- predict(cfier2, X[[2]][1:2,])
# }