library(mixOmics) # import the mixOmics library
data(liver.toxicity) # extract the liver toxicity data
X <- liver.toxicity$gene # use the gene expression data as the X matrix
Y <- liver.toxicity$clinic # use the clinical data as the Y matrixpls.result <- pls(X, Y) # run the method
plotIndiv(pls.result) # plot the samples
plotVar(pls.result) # plot the variables?pls can be run to determine all default arguments of
this function:
ncomp = 2): The first two PLS
components are calculated,scale = TRUE): Each data set is scaled
(each variable has a variance of 1 to enable easier comparison) - data
are internally centered.mode = regression): A PLS regression mode is
performed.spls.result <- spls(X, Y, keepX = c(10, 20), keepY = c(3, 2)) # run the method
plotIndiv(spls.result) # plot the samples
plotVar(spls.result) # plot the variables
# extract the variables used to construct the first latent component
selectVar(spls.result, comp = 1)$X$name
# depict weight assigned to each of these variables
plotLoadings(spls.result, method = 'mean', contrib = 'max') ?spls can be run to determine the default arguments of
this function:
mode = regression): A PLS regression mode is
performed.keepx and keepY are not supplied, this
function will be equivalent to the pls() function as all
variables will be used.ncomp and scale
as the pls() function.Partial Least Squares, or Projection to Latent Structures, (PLS) [2, 3] is a robust, malleable multivariate projection-based method. It can be used to explore or explain the relationship between two continuous datasets. As with other projection methods, PLS seeks for linear combinations of the variables from each dataset in order to reduce the overall dimensionality of said data. The primary difference between PLS and CCA is that PLS maximises the covariance between the latent variables, rather than correlation. It is able to simultaneously model multiple response variables as well as handle noisy, correlated variables.
PLS is particularly efficient when P + Q > N, where P is the number of variables in the first dataset, Q is the number of variables in the second dataset and N is the number of samples in each. Hence, it is an extremely powerful algorithm when dealing with omics data, which commonly has high dimensionality and contains correlated variables.
While PLS is highly efficient, when operating on data of high dimensionality its interpretability suffers significantly. Sparse Partial Least Squares (sPLS) [4, 5] is the answer to this issue, such that it is able to perform simultaneous variable selection on both datasets. This is done by including the LASSO penalisation on loading vectors to reduce the number of original variables used when constructing latent variables.
Note: X and Y refer to the two omics datasets that PLS analyses.
There are two overarching types of PLS, which are:
There are four different modes that can be used for the sPLS
algorithm within the mixOmics package. This is inputted
through the mode parameter. The modes include:
mode = "regression"): X
and Y play asymmetric roles. Fits a linear relationship
between multiple responses in Y and multiple predictors
in X. Interchanging the roles of X and
Y (as predictors and responses) would result in
different latent variables. Useful when trying to explain the
relationship between the two datasets. Y is deflated
using information from X.mode = "canonical"): X and
Y play symmetric roles. While not mathematically
equivalent, the method is quite similar to CCA. It is appropriate to use
when there is no a priori relationship between
X and Y and as a replacement for CCA
in very high dimensional contexts (when variables selection is desired).
Y is deflated using information from
Y.mode = "invariant"): No matrix deflation
occurs to allow a Redundancy Analysis to be undergone.mode = "classic"): Similar to the ‘regression’
mode, but produces different loading vectors associated with the
Y matrix as different normalisations are used.
Equivalent to the PLS2 model proposed by Tenenhaus (1998) [1].Note that in all cases the first component will be identical as matrix deflation only occurs after the first component is produced. Each method utilises a different style of matrix deflation.