Description

The class Pca searves as a base class for deriving all other classes representing the results of the classical and robust Principal Component Analisys methods

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

call:

Object of class "language"

center:

Object of class "vector" the center of the data

scale:

Object of class "vector" the scaling applied to each variable of the data

loadings:

Object of class "matrix" the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors)

eigenvalues:

Object of class "vector" the eigenvalues

scores:

Object of class "matrix" the scores - the value of the projected on the space of the principal components data (the centred (and scaled if requested) data multiplied by the loadings matrix) is returned. Hence, cov(scores) is the diagonal matrix diag(eigenvalues)

k:

Object of class "numeric" number of (choosen) principal components

sd:

Object of class "Uvector" Score distances within the robust PCA subspace

od:

Object of class "Uvector" Orthogonal distances to the robust PCA subspace

cutoff.sd:

Object of class "numeric" Cutoff value for the score distances

cutoff.od:

Object of class "numeric" Cutoff values for the orthogonal distances

flag:

Object of class "Uvector" The observations whose score distance is larger than cutoff.sd or whose orthogonal distance is larger than cutoff.od can be considered as outliers and receive a flag equal to zero. The regular observations receive a flag 1

crit.pca.distances

criterion to use for computing the cutoff values for the orthogonal and score distances. Default is 0.975.

n.obs:

Object of class "numeric" the number of observations

Methods

getCenter

signature(obj = "Pca"): center of the data

getScale

signature(obj = "Pca"): return the scaling applied to each variable

getEigenvalues

signature(obj = "Pca"): the eigenvalues of the covariance/correlation matrix, though the calculation is actually done with the singular values of the data matrix)

getLoadings

signature(obj = "Pca"): returns the matrix loadings (i.e., a matrix whose columns contain the eigenvectors). The function prcomp returns this matrix in the element rotation.

getPrcomp

signature(obj = "Pca"): returns an S3 object prcomp for compatibility with the functions prcomp() and princomp(). Thus the standard plots screeplot() and biplot() can be used

getScores

signature(obj = "Pca"): returns the rotated data (the centred (and scaled if requested) data multiplied by the loadings matrix).

getSdev

signature(obj = "Pca"): returns the standard deviations of the principal components (i.e., the square roots of the eigenvalues of the covariance/correlation matrix, though the calculation is actually done with the singular values of the data matrix)

plot

signature(x = "Pca"): produces a distance plot (if k=rank) or distance-distance plot (ifk<rank)

print

signature(x = "Pca"): prints the results. The difference to the show() method is that additional parametesr are possible.

show

signature(object = "Pca"): prints the results

predict

signature(object = "Pca"): calculates prediction using the results in object. An optional data frame or matrix in which to look for variables with which to predict. If omitted, the scores are used. If the original fit used a formula or a data frame or a matrix with column names, newdata must contain columns with the same names. Otherwise it must contain the same number of columns, to be used in the same order. See also predict.prcomp and predict.princomp

screeplot

signature(x = "Pca"): plots the variances against the number of the principal component. See also plot.prcomp and plot.princomp

Author(s)

Valentin Todorov valentin.todorov@chello.at

References

Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1–47. URL http://www.jstatsoft.org/v32/i03/.

See Also

PcaClassic, PcaClassic-class, PcaRobust-class

Examples