estim_ncpPCA: Estimate the number of dimensions for the Principal Component Analysis by cross-validation

Description

Estimate the number of dimensions for the Principal Component Analysis by cross-validation

Usage

estim_ncpPCA(X, ncp.min = 0, ncp.max = 5, method = c("Regularized","EM"), 
       scale = TRUE, method.cv = c("gcv","loo","Kfold"), nbsim = 100, 
	   pNA = 0.05, threshold=1e-4)

Arguments

a data.frame with continuous variables; with missing entries or not

ncp.min

integer corresponding to the minimum number of components to test

ncp.max

integer corresponding to the maximum number of components to test

method

"Regularized" by default or "EM"

scale

boolean. TRUE implies a same weight for each variable

method.cv

string with the values "gcv" for generalised cross-validation, "loo" for leave-one-out or "Kfold" cross-validation

nbsim

number of simulations, useful only if method.cv="Kfold"

pNA

percentage of missing values added in the data set, useful only if method.cv="Kfold"

threshold

the threshold for assessing convergence

Value

ncpthe number of components retained for the PCA
criterionthe criterion (the MSEP) calculated for each number of components

Details

For leave-one-out (loo) cross-validation, each cell of the data matrix is alternatively removed and predicted with a PCA model using ncp.min to ncp.max dimensions. The number of components which leads to the smallest mean square error of prediction (MSEP) is retained. For the Kfold cross-validation, pNA percentage of missing values is inserted and predicted with a PCA model using ncp.min to ncp.max dimensions. This process is repeated nbsim times. The number of components which leads to the smallest MSEP is retained. For both cross-validation methods, missing entries are predicted using the imputePCA function, it means using the regularized iterative PCA algorithm (method="Regularized") or the iterative PCA algorithm (method="EM"). The regularized version is more appropriate when there are already many missing values in the dataset to avoid overfitting issues. Cross-validation (especially method.cv="loo") is time-consuming. The generalised cross-validation criterion (method.cv="gcv") can be seen as an approximation of the loo cross-validation criterion which provides a straightforward way to estimate the number of dimensions without resorting to a computationally intensive method. This argument scale has to be chosen in agreement with the PCA that will be performed. If one wants to perform a normed PCA (where the variables are centered and scaled, i.e. divided by their standard deviation), then the argument scale has to be set to the value TRUE.

References

Bro, R., Kjeldahl, K. Smilde, A. K. and Kiers, H. A. L. (2008) Cross-validation of component models: A critical look at current methods. Analytical and Bioanalytical Chemistry, 5, 1241-1251. Josse, J. & Husson, F. (2011). Selecting the number of components in PCA using cross-validation approximations. Computational Statististics and Data Analysis. 56 (6), pp. 1869-1879.

Examples

Run this code

data(orange)
nb <- estim_ncpPCA(orange,ncp.min=0,ncp.max=4)

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