Description Usage Arguments Details Value Author(s) References See Also Examples
Performs a principal components analysis on the given data matrix that can contain missing values. If data are complete 'pca' uses Singular Value Decomposition, if there are some missing values, it uses the NIPALS algorithm.
1 2 3 4 5 6 7 8 9 10 11 12 13 
X 
a numeric matrix (or data frame) which provides the data for the principal components analysis. It can contain missing values. 
ncomp 
Integer, if data is complete 
center 
(Default=TRUE) Logical, whether the variables should be
shifted to be zero centered. Alternatively, a vector of length equal the
number of columns of 
scale 
(Default=FALSE) Logical indicating whether the variables should be
scaled to have unit variance before the analysis takes place. The default is

max.iter 
Integer, the maximum number of iterations in the NIPALS algorithm. 
tol 
Positive real, the tolerance used in the NIPALS algorithm. 
logratio 
(Default='none') one of ('none','CLR','ILR'). Specifies the log ratio transformation to deal with compositional values that may arise from specific normalisation in sequencing data. Default to 'none' 
ilr.offset 
(Default=0.001) When logratio is set to 'ILR', an offset must be input to avoid infinite value after the logratio transform. 
V 
Matrix used in the logratio transformation if provided. 
multilevel 
sample information for multilevel decomposition for repeated measurements. 
reconst 
(Default=TRUE) Logical. If matrix includes missing values, whether

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.
According to Filzmoser et al., a ILR log ratio transformation is more appropriate for PCA with compositional data. Both CLR and ILR are valid.
Logratio transform and multilevel analysis are performed sequentially as
internal preprocessing step, through logratio.transfo
and
withinVariation
respectively.
Logratio can only be applied if the data do not contain any 0 value (for count data, we thus advise the normalise raw data with a 1 offset). For ILR transformation and additional offset might be needed.
pca
returns a list with class "pca"
and "prcomp"
containing the following components:
call 
The function call. 
ncomp 
The number of principal components used. 
center 
The centering used. 
scale 
The scaling used. 
names 
List of row and column names of data. 
sdev 
The eigenvalues of the covariance/correlation matrix, though the calculation is actually done with the singular values of the data matrix or by using NIPALS. 
rotation 
The matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors). 
x 
The value of the rotated data (the centred (and scaled if requested) data multiplied by the rotation/loadings matrix), also called the principal components. 
var.tot 
Total variance in the data. 
loadings 
Same as 'rotation' to keep the mixOmics spirit 
variates 
Same as 'x' to keep the mixOmics spirit 
explained_variance 
Explained variance from the multivariate model, used for plotIndiv 
cum.var 
The cumulative explained variance for components. 
X 
The input data matrix. 
Florian Rohart, KimAnh Lê Cao, Ignacio González, Al J Abadi
On log ratio transformations: Filzmoser, P., Hron, K., Reimann, C.: Principal component analysis for compositional data with outliers. Environmetrics 20(6), 621632 (2009) Lê Cao K.A., Costello ME, Lakis VA, Bartolo, F,Chua XY, Brazeilles R, Rondeau P. MixMC: Multivariate insights into Microbial Communities. PLoS ONE, 11(8): e0160169 (2016). On multilevel decomposition: Westerhuis, J.A., van Velzen, E.J., Hoefsloot, H.C., Smilde, A.K.: Multivariate paired data analysis: multilevel plsda versus oplsda. Metabolomics 6(1), 119128 (2010) Liquet, B., Lê Cao, K.A., Hocini, H., Thiebaut, R.: A novel approach for biomarker selection and the integration of repeated measures experiments from two assays. BMC bioinformatics 13(1), 325 (2012)
nipals
, prcomp
, biplot
,
plotIndiv
, plotVar
and http://www.mixOmics.org
for more details.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  # example with missing values where NIPALS is applied
# 
data(multidrug)
pca.res < pca(multidrug$ABC.trans, ncomp = 4, scale = TRUE)
plot(pca.res)
print(pca.res)
biplot(pca.res, group = multidrug$cell.line$Class, legend.title = 'Class')
# samples representation
plotIndiv(pca.res, ind.names = multidrug$cell.line$Class,
group = as.numeric(as.factor(multidrug$cell.line$Class)))
# variable representation
plotVar(pca.res, cutoff = 0.7, pch = 16)
## Not run:
plotIndiv(pca.res, cex = 0.2,
col = as.numeric(as.factor(multidrug$cell.line$Class)),style="3d")
plotVar(pca.res, rad.in = 0.5, cex = 0.5,style="3d")
## End(Not run)
# example with multilevel decomposition and CLR log ratio transformation (ILR longer to run)
# 
data("diverse.16S")
pca.res = pca(X = diverse.16S$data.TSS, ncomp = 3,
logratio = 'CLR', multilevel = diverse.16S$sample)
plot(pca.res)
plotIndiv(pca.res, ind.names = FALSE, group = diverse.16S$bodysite, title = '16S diverse data',
legend = TRUE, legend.title = 'Bodysite')

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