tune.pca: Tune the number of principal components in PCA

In mixOmicsTeam/mixOmics: Omics Data Integration Project

Tune the number of principal components in PCA

Description

tune.pca can be used to quickly visualise the proportion of explained variance for a large number of principal components in PCA.

Usage

tune.pca(
  X,
  ncomp = NULL,
  center = TRUE,
  scale = TRUE,
  max.iter = 100,
  tol = 1e-09,
  logratio = c("none", "CLR", "ILR"),
  V = NULL,
  multilevel = NULL
)

Arguments

X	numeric matrix of predictors. NAs are allowed.
ncomp	integer, the number of components to initially analyse in tune.pca to choose a final ncomp for pca. If NULL, function sets ncomp = min(nrow(X), ncol(X))
center	a logical value indicating whether the variables should be shifted to be zero centered. Alternately, a vector of length equal the number of columns of X can be supplied. The value is passed to scale.
scale	a logical value indicating whether the variables should be scaled to have unit variance before the analysis takes place. The default is FALSE for consistency with prcomp function, but in general scaling is advisable. Alternatively, a vector of length equal the number of columns of X can be supplied. The value is passed to scale.
max.iter	Integer, the maximum number of iterations.
tol	Numeric, convergence tolerance criteria.
logratio	one of ('none','CLR','ILR'). Default to 'none'
V	Matrix used in the logratio transformation id provided.
multilevel	Design matrix for multilevel analysis (for repeated measurements).

Details

The calculation is done either by a singular value decomposition of the (possibly centered and scaled) data matrix, if the data is complete or by using the NIPALS algorithm if there is data missing. Unlike princomp, the print method for these objects prints the results in a nice format and the plot method produces a bar plot of the percentage of variance explaned by the principal components (PCs).

When using NIPALS (missing values), we make the assumption that the first (min(ncol(X), nrow(X)) principal components will account for 100 % of the explained variance.

Note that scale= TRUE cannot be used if there are zero or constant (for center = TRUE) variables.

Components are omitted if their standard deviations are less than or equal to comp.tol times the standard deviation of the first component. With the default null setting, no components are omitted. Other settings for comp.tol could be comp.tol = sqrt(.Machine$double.eps), which would omit essentially constant components, or comp.tol = 0.

logratio transform and multilevel analysis are performed sequentially as internal pre-processing step, through logratio.transfo and withinVariation respectively.

Value

tune.pca returns a list with class "tune.pca" containing the following components:

sdev	the square root of the eigenvalues of the covariance/correlation matrix, though the calculation is actually done with the singular values of the data matrix).
prop_expl_var	The proportion of explained variance accounted for by each principal component.
cum.var	the cumulative proportion of explained variance accounted for by the sequential accumulation of principal components is calculated using the sum of the proportion of explained variance

Author(s)

Ignacio González, Leigh Coonan, Kim-Anh Le Cao, Fangzhou Yao, Florian Rohart, Al J Abadi

See Also

nipals, biplot, plotIndiv, plotVar and http://www.mixOmics.org for more details.

Examples

# load data
data(liver.toxicity)

# run tuning
tune <- tune.pca(liver.toxicity$gene, center = TRUE, scale = TRUE)
plot(tune)

# set up multilevel dataset
repeat.indiv <- c(1, 2, 1, 2, 1, 2, 1, 2, 3, 3, 4, 3, 4, 3, 4, 4, 5, 6, 5, 5,
                  6, 5, 6, 7, 7, 8, 6, 7, 8, 7, 8, 8, 9, 10, 9, 10, 11, 9, 9,
                  10, 11, 12, 12, 10, 11, 12, 11, 12, 13, 14, 13, 14, 13, 14,
                  13, 14, 15, 16, 15, 16, 15, 16, 15, 16)
design <- data.frame(sample = repeat.indiv)

# run tuning
tune <- tune.pca(liver.toxicity$gene, center = TRUE, scale = TRUE, multilevel = design)
plot(tune)

mixOmicsTeam/mixOmics documentation built on Dec. 3, 2024, 11:15 p.m.