smbpls {multiblock}

Sparse Multiblock Partial Least Squares - sMB-PLS

Description

sMB-PLS is an adaptation of MB-PLS (mbpls) that enforces sparseness in loading weights when computing PLS components in the global model.

Usage

smbpls(
  formula,
  data,
  subset,
  na.action,
  X = NULL,
  Y = NULL,
  ncomp = 1,
  scale = FALSE,
  shrink = NULL,
  truncation = NULL,
  trunc.width = 0.95,
  blockScale = c("sqrtnvar", "ssq", "none"),
  ...
)

Arguments

formula

Model formula accepting a single response (block) and predictor block names separated by + signs.

data

The data set to analyse.

subset

Expression for subsetting the data before modelling.

na.action

How to handle NAs (no action implemented).

X

list of input blocks. If X is supplied, the formula interface is skipped.

Y

matrix of responses.

ncomp

integer number of PLS components.

scale

logical for autoscaling inputs (default = FALSE).

shrink

numeric scalar indicating degree of L1-shrinkage/Soft-Thresholding (optional), 0 <= shrink < 1.

truncation

character indicating type of truncation (optional) "Lenth" uses asymmetric confidence intervals to determine outlying loading weights. "quantile" uses a quantile plot approach to determining outliers.

trunc.width

numeric indicating confidence of "Lenth type" confidence interval or quantile in "quantile plot" approach. Default = 0.95.

blockScale

Either a character indicating type of block scaling or a numeric vector of block weights (see Details).

...

additional arguments to pls::plsr.

Details

Two versions of sparseness are supplied: Soft-Threshold PLS, also known as Sparse PLS, and Truncation PLS. The former uses L1 shrinkage of loading weights, while the latter comes in two flavours, both estimating inliers and outliers. The "Lenth" method uses asymmetric confidence intervals around the median of a loading weigh vector to estimate inliers. The "quantile" method uses a quantile plot approach to estimate outliers as deviations from the estimated quantile line. As with ordinary MB-PLS scaled input blocks (1/sqrt(ncol)) are used.

Block weighting is performed after scaling all variables and is by default "sqrtnvar": 1/sqrt(ncol(X[[i]])) in each block. Alternatives are "ssq": 1/norm(X[[i]], "F")^2 and "none": 1/1. Finally, if a numeric vector is supplied, it will be used to scale the blocks after "ssq" scaling, i.e., Z[[i]] = X[[i]] / norm(X[[i]], "F")^2 * blockScale[i].

Value

multiblock, mvr object with super-scores, super-loadings, block-scores and block-loading, and the underlying mvr (PLS) object for the super model, with all its result and plot possibilities. Relevant plotting functions: multiblock_plots and result functions: multiblock_results.

References

• Sæbø, S.; Almøy, T.; Aarøe, J. & Aastveit, A. ST-PLS: a multi-directional nearest shrunken centroid type classifier via PLS Journal of Chemometrics: A Journal of the Chemometrics Society, Wiley Online Library, 2008, 22, 54-62.

• Lê Cao, K.; Rossouw, D.; Robert-Granié, C. & Besse, P. A sparse PLS for variable selection when integrating omics data Statistical applications in genetics and molecular biology, 2008, 7.

• Liland, K.; Høy, M.; Martens, H. & Sæbø, S. Distribution based truncation for variable selection in subspace methods for multivariate regression Chemometrics and Intelligent Laboratory Systems, 2013, 122, 103-111.

• Karaman, I.; Nørskov, N.; Yde, C.; Hedemann, M.; Knudsen, K. & Kohler, A. Sparse multi-block PLSR for biomarker discovery when integrating data from LC–MS and NMR metabolomics Metabolomics, 2015, 11, 367-379.

See Also

Overviews of available methods, multiblock, and methods organised by main structure: basic, unsupervised, asca, supervised and complex.

Examples

data(potato)

# Truncation MB-PLS 
# Loading weights inside 60% confidence intervals around the median are set to 0.
tmb <- smbpls(Sensory ~ Chemical+Compression, data=potato, ncomp = 5, 
              truncation = "Lenth", trunc.width = 0.6)
              
# Alternative XY-interface
tmb.XY <- smbpls(X=potato[c('Chemical','Compression')], Y=potato[['Sensory']], ncomp = 5, 
              truncation = "Lenth", trunc.width = 0.6)
identical(tmb, tmb.XY)
scoreplot(tmb, labels="names") # Exploiting mvr object structure from pls package
loadingweightplot(tmb, labels="names")

# Soft-Threshold / Sparse MB-PLS 
# Loading weights are subtracted by 60% of maximum value.
smb <- smbpls(X=potato[c('Chemical','Compression')], Y=potato[['Sensory']], 
              ncomp = 5, shrink = 0.6)
print(smb)
scoreplot(smb, labels="names") # Exploiting mvr object structure from pls package
loadingweightplot(smb, labels="names")

# Emphasis may be different for blocks
smb <- smbpls(X=potato[c('Chemical','Compression')], Y=potato[['Sensory']], 
              ncomp = 5, shrink = 0.6, blockScale = c(1, 10))