Robust classification in high dimensions based on the SIMCA method

Share:

Description

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.

Usage

1
2
3
4
5
6
RSimca(x, ...)
## Default S3 method:
RSimca(x, grouping, prior=proportions, k, kmax = ncol(x), 
    control="hubert", alpha, tol = 1.0e-4, trace=FALSE, ...)
## S3 method for class 'formula'
RSimca(formula, data = NULL, ..., subset, na.action)

Arguments

formula

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).

data

an optional data frame (or similar: see model.frame) containing the variables in the formula formula.

subset

an optional vector used to select rows (observations) of the data matrix x.

na.action

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.

x

a matrix or data frame containing the explanatory variables (training set).

grouping

grouping variable: a factor specifying the class for each observation.

prior

prior probabilities, default to the class proportions for the training set.

tol

tolerance

control

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)

alpha

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.

k

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 Σ_{j=1}^k l_j/Σ_{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.

kmax

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.

trace

whether to print intermediate results. Default is trace = FALSE

...

arguments passed to or from other methods.

Details

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).

Value

An S4 object of class RSimca-class which is a subclass of of the virtual class Simca-class.

Author(s)

Valentin Todorov valentin.todorov@chello.at

References

Vanden Branden K, Hubert M (2005) Robust classification in high dimensions based on the SIMCA method. Chemometrics and Intellegent Laboratory Systems 79:10–21

Examples

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
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 

Want to suggest features or report bugs for rdrr.io? Use the GitHub issue tracker.