pcaPP (version 1.8-3)

PCAgrid: Robust Principal Components using the Grid search algorithm

Description

Computes a desired number of (robust) principal components using the grid search algorithm in the plane. The global optimum of the objective function is searched in planes, not in the p-dimensional space, using regular grids in these planes.

Usage

PCAgrid(x, k = 2, method = c("mad", "sd", "qn"), maxiter = 10, splitcircle = 10, 
scores = TRUE, anglehalving = TRUE, fact2dim = 10, scale = NULL, center = l1median, control)

Arguments

x

a numeric matrix or data frame which provides the data for the principal components analysis.

k

desired number of components to compute

method

scale estimator used to detect the direction with the largest variance. Possible values are "sd", "mad" and "qn", the latter can be called "Qn" too. "mad" is the default value.

maxiter

maximum number of iterations.

splitcircle

the number of directions in which the algorithm should search for the largest variance. The direction with the largest variance is searched for in the directions defined by a number of equally spaced points on the unit circle. This argument deter

scores

a logical value indicating whether the scores of the principal component should be calculated.

anglehalving

boolean stating whether angle halving is to be used or not. Angle halving will usually improve the solution quite a lot.

fact2dim

an integer that is multiplied to splitcircle if x is only two-dimensional. In higher dimensions, fewer search directions are needed to allow for faster computation. In two dimensions, more search directions are required to grant higher precisio

scale

this argument indicates how the data is to be rescaled. It can be a function like sd or mad or a vector of length ncol(x) containing the scale valu

center

this argument indicates how the data is to be centered. It can be a function like mean or median or a vector of length ncol(x) containing the

control

a list whose elements must be the same as (or a subset of) the parameters above. If the control object is supplied, the parameters from it will be used and any other given parameters are overridden.

Value

• The function returns an object of class "princomp", i.e. a list similar to the output of the function princomp.
• sdev
  the (robust) standard deviations of the principal components.
• loadings
  the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors). This is of class "loadings": see loadings for its print method.
• center
  the means that were subtracted.
• scale
  the scalings applied to each variable.
• n.obs
  the number of observations.
• scores
  if scores = TRUE, the scores of the supplied data on the principal components.
• call
  the matched call.

Details

Angle halving is an extension of the original algorithm. In the original algorithm, the search directions are determined by a number of points on the unit circle in the interval [-pi/2 ; pi/2). Angle halving means this angle is halved in each iteration, eg. for the first approximation, the above mentioned angle is used, for the second approximation, the angle is halved to [-pi/4 ; pi/4) and so on. This usually gives better results with less iterations needed. Similar to the function princomp, there is a print method for the these objects that prints the results in a nice format and the plot method produces a scree plot (screeplot). There is also a biplot method.

References

C. Croux, P. Filzmoser, M. Oliveira, (2007). Algorithms for Projection-Pursuit Robust Principal Component Analysis, Chemometrics and Intelligent Laboratory Systems, Vol. 87, pp. 218-225.

See Also

PCAproj, ScaleAdv, princomp

Examples

# multivariate data with outliers
  library(mvtnorm)
  x <- rbind(rmvnorm(200, rep(0, 6), diag(c(5, rep(1,5)))),
             rmvnorm( 15, c(0, rep(20, 5)), diag(rep(1, 6))))
  # Here we calculate the principal components with PCAgrid
  pc <- PCAgrid(x)
  # we could draw a biplot too:
  biplot(pc)
  # now we want to compare the results with the non-robust principal components
  pc <- princomp(x)
  # again, a biplot for comparison:
  biplot(pc)