RSimca performs a robust version of the SIMCA method. This method classifies a data matrix x with a known group structure. To reduce the dimension on each group a robust PCA analysis is performed. Afterwards a classification rule is developped to determine the assignment of new observations.
RSimca(x, ...)
# S3 method for default
RSimca(x, grouping, prior=proportions, k, kmax = ncol(x),
control="hubert", alpha, tol = 1.0e-4, trace=FALSE, ...)
# S3 method for formula
RSimca(formula, data = NULL, ..., subset, na.action)An S4 object of class RSimca-class which is a subclass of of the
virtual class Simca-class.
a formula of the form y~x, it describes the response
and the predictors. The formula can be more complicated, such as
y~log(x)+z etc (see formula for more details).
The response should
be a factor representing the response variable, or any vector
that can be coerced to such (such as a logical variable).
an optional data frame (or similar: see
model.frame) containing the variables in the
formula formula.
an optional vector used to select rows (observations) of the
data matrix x.
a function which indicates what should happen
when the data contain NAs. The default is set by
the na.action setting of options, and is
na.fail if that is unset. The default is na.omit.
a matrix or data frame containing the explanatory variables (training set).
grouping variable: a factor specifying the class for each observation.
prior probabilities, default to the class proportions for the training set.
tolerance
a control object (S4) for specifying one of the available PCA estimation methods and containing estimation options. The class of this object defines which estimator will be used. Alternatively a character string can be specified which names the estimator - one of auto, hubert, locantore, grid, proj. If 'auto' is specified or the argument is missing, the function will select the estimator (see below for details)
this parameter measures the fraction of outliers the algorithm should resist. In MCD alpha controls the size of the subsets over which the determinant is minimized, i.e. alpha*n observations are used for computing the determinant. Allowed values are between 0.5 and 1 and the default is 0.5.
number of principal components to compute. If k is missing,
or k = 0, the algorithm itself will determine the number of
components by finding such k that \(l_k/l_1 >= 10.E-3\) and
\(\Sigma_{j=1}^k l_j/\Sigma_{j=1}^r l_j >= 0.8\).
It is preferable to investigate the scree plot in order to choose the number
of components and then run again. Default is k=0.
maximal number of principal components to compute.
Default is kmax=10. If k is provided, kmax
does not need to be specified, unless k is larger than 10.
whether to print intermediate results. Default is trace = FALSE
arguments passed to or from other methods.
Valentin Todorov valentin.todorov@chello.at
RSimca, serving as a constructor for objects of class RSimca-class
is a generic function with "formula" and "default" methods.
SIMCA is a two phase procedure consisting of PCA performed on each group
separately for dimension reduction followed by classification rules built
in the lower dimensional space (note that the dimension in
each group can be different). Instead of classical PCA robust alternatives will be used.
Any of the robust PCA methods available in package Pca-class
can be used through the argument control.
In original SIMCA new observations are
classified by means of their deviations from the different PCA models.
Here the classification rules will be obtained using two popular distances arising from PCA -
orthogonal distances (OD) and score distances (SD). For the definition of these distances,
the definition of the cutoff values and the standartization of the distances see
Vanden Branden K, Hubert M (2005) and Todorov and Filzmoser (2009).
Vanden Branden K, Hubert M (2005) Robust classification in high dimensions based on the SIMCA method. Chemometrics and Intellegent Laboratory Systems 79:10--21
Todorov V & Filzmoser P (2014), Software Tools for Robust Analysis of High-Dimensional Data. Austrian Journal of Statistics, 43(4), 255--266, tools:::Rd_expr_doi("10.17713/ajs.v43i4.44").
data(pottery)
dim(pottery) # 27 observations in 2 classes, 6 variables
head(pottery)
## Build the SIMCA model. Use RSimca for a robust version
rs <- RSimca(origin~., data=pottery)
rs
summary(rs)
## generate a sample from the pottery data set -
## this will be the "new" data to be predicted
smpl <- sample(1:nrow(pottery), 5)
test <- pottery[smpl, -7] # extract the test sample. Remove the last (grouping) variable
print(test)
## predict new data
pr <- predict(rs, newdata=test)
pr@classification
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