Biology Reference
In-Depth Information
Partial Least Squares Regression
Projection to latent structures by means of
PLS is a regression-based method that has
proven its usefulness in various applications to
handle very large data tables with a limited
number of observations.
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A PLS model is based
on latent variables that are linear combinations
of the original manifest variables in X to build
a low-dimensional subspace. The Y information
is used to adjust the model by maximizing the
covariance between X and Y to capture the
Y-related variation in X.
Latent variables are computed sequentially in
a decomposition process that offers a good corre-
lation with the remaining unexplained fraction
of the response. The corresponding model
possesses a structure that summarizes the orig-
inal data matrix and has an intrinsic prediction
power. The contributions of the variables to the
model are then analyzed to assess their relevance
for the response prediction.
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The PLS frame-
work constitutes an attractive solution to provide
compact representations of correlated and noisy
variables and diagnostic tools for the detection
of biomarkers.
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When a discrete response has
to be predicted for classi
systematic variability related to an experimental
bias or to biological variations. The PLS method
and its extensions are broadly applied to
nd
common variation patterns in complex metabolo-
mics data.
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Decision Trees
Similarly to the HCA dendrogram, a decision
tree summarizes a MS data set in a treelike struc-
ture, but in that case each node corresponds to
a detected spectral feature and the leaves are
the observations. A quantitative or qualitative
response is predicted according to the values
characterizing each observation for the corre-
sponding variable when traversing the tree
from the root node. These logic-based algorithms
apply a divide-and-conquer strategy to model
the data set according to a hierarchy of tests.
The choice of the variable to test can be achieved
based on various criteria assessing its ability to
divide the remaining data subset. The most
informative is selected and the procedure is
repeated iteratively until a prediction is done
for each observation. The interpretation of the
predictive merit of individual variables is there-
fore straightforward. In their popular form,
a node corresponding to a single variable, deci-
sion trees are univariate, as in C4.5.
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Multivar-
iate alternatives have been proposed, such as
CART
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or algorithms based on logical opera-
tors
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or constructive induction.
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Decision trees ensemble strategies, such as the
Random Forests
cation purposes, such
as known groups of observations, the so-called
PLS discriminant analysis (PLS-DA) aims at the
maximum separation of the classes, that is,
the maximization of the between-groups covari-
ance matrix. PLS-DA was demonstrated as
a potent tool for the classi
cation of data from
metabolomics experiments.
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The orthogonal
PLS algorithm (O-PLS)
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and O2-PLS
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were
recently proposed to allow an easier interpret-
ability of the models by separating the
Y-predictive variability from the orthogonal
one. The predictive information is summarized
in the predictive component(s) and the corre-
sponding predictive scores and loading vectors
are therefore free from orthogonal variation.
Variation that is unrelated to the class response
is described in the orthogonal component(s).
The latter can be useful to highlight unexpected
, constitute other attractive
approaches. A large collection of individual deci-
sion trees based on random variable selection is
computed in parallel, based on a bootstrap
procedure, and a consensus model is obtained
from their aggregation.
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Kernel Methods
Kernel algorithms were developed to model
strong nonlinear relationships between indepen-
dent and dependent variables. In that perspec-
tive, the original data is transformed from the
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