smbpls: 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,
  ...
)

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.

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.
...: 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.

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.

Examples

Run this code

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")

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