MBPCA: Multiblock Principal Components Analysis

Description

Performs MB-PCA on a set of quantitative blocks of variables.

Usage

MBPCA(
  X,
  block,
  name.block = NULL,
  ncomp = NULL,
  scale = TRUE,
  scale.block = TRUE
)

Value

Returns a list of the following elements:

optimalcrit: Numeric vector of the optimal value of the criterion (sum of saliences) obtained for each dimension.
saliences: Matrix of the specific weights of each block of variables on the global components, for each dimension.
T.g: Matrix of normed global components.
Scor.g: Matrix of global components (scores of individuals).
W.g: Matrix of global weights (normed) associated with deflated X.
Load.g: Matrix of global loadings (normed) = W.g in the specific context of MB-PCA.
Proj.g: Matrix of global projection (to compute scores from pretreated X) = W.g in the specific context of MB-PCA.
explained.X: Matrix of percentages of inertia explained in each block of variables.
cumexplained: Matrix giving the percentages, and cumulative percentages, of total inertia of X blocks explained by the global components.
Block: A list containing block components (T.b) and block weights (W.b)

Arguments

X: Dataset obtained by horizontally merging all the blocks of variables.
block: Vector indicating the number of variables in each block.
name.block: names of the blocks of variables (NULL by default).
ncomp: Number of dimensions to compute. By default (NULL), all the global components are extracted.
scale: Logical, if TRUE (by default) then variables are scaled to unit variance (all variables are centered anyway).
scale.block: Logical, if TRUE (by default) each block of variables is divided by the square root of its inertia (Frobenius norm).

References

S. Wold, S. Hellberg, T. Lundstedt, M. Sjostrom, H. Wold (1987). Hierarchical multiblock PLS and PC models for easier model interpretation and as an alternative to variable selection, in: Proc. Symp. On PLS Model Building: Theory and Application, Frankfurt am Main.

E. Tchandao Mangamana, V. Cariou, E. Vigneau, R. Glèlè Kakaï, E.M. Qannari (2019). Unsupervised multiblock data analysis: A unified approach and extensions, Chemometrics and Intelligent Laboratory Systems, 194, 103856.

Examples

Run this code

data(ham)
X=ham$X
block=ham$block
res.mbpca <- MBPCA(X,block, name.block=names(block))
summary(res.mbpca)
plot(res.mbpca)