Robust Principal Components using the algorithm of Croux and Ruiz-Gazen (2005)
Computes a desired number of (robust) principal components using the algorithm of Croux and Ruiz-Gazen (JMVA, 2005).
PCAproj(x, k = 2, method = c("mad", "sd", "qn"), CalcMethod = c("eachobs",
"lincomb", "sphere"), nmax = 1000, update = TRUE, scores = TRUE, maxit = 5,
maxhalf = 5, scale = NULL, center = l1median_NLM, zero.tol = 1e-16, control)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 |
CalcMethod |
the variant of the algorithm to be used. Possible values are
|
nmax |
maximum number of directions to search in each step (only when
using |
update |
a logical value indicating whether an update algorithm should be used. |
scores |
a logical value indicating whether the scores of the principal component should be calculated. |
maxit |
maximim number of iterations. |
maxhalf |
maximum number of steps for angle halving. |
scale |
this argument indicates how the data is to be rescaled. It
can be a function like |
center |
this argument indicates how the data is to be centered. It
can be a function like |
zero.tol |
the zero tolerance used internally for checking convergence, etc. |
control |
a list which 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. |
Basically, this algrithm considers the directions of each observation
through the origin of the centered data as possible projection directions.
As this algorithm has some drawbacks, especially if ncol(x) > nrow(x)
in the data matrix, there are several improvements that can be used with this
algorithm.
updateAn updating step basing on the algorithm for finding the
eigenvectors is added to the algorithm. This can be used with any
CalcMethod
sphereAdditional search directions are added using random directions. The random directions are determined using random data points generated from a p-dimensional multivariate standard normal distribution. These new data points are projected to the unit sphere, giving the new search directions.
lincombAdditional search directions are added using linear
combinations of the observations. It is similar to the
"sphere"-algorithm, but the new data points are generated using linear
combinations of the original data b_1*x_1 + ... + b_n*x_n where the
coefficients b_i come from a uniform distribution in the interval
[0, 1].
The function returns a list 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 |
center |
the means that were subtracted. |
scale |
the scalings applied to each variable. |
n.obs |
the number of observations. |
scores |
if |
call |
the matched call. |
Heinrich Fritz, Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
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.
# 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 <- PCAproj(x, 6)
# we could draw a biplot too:
biplot(pc)
# we could use another calculation method and another objective function, and
# maybe only calculate the first three principal components:
pc <- PCAproj(x, 3, "qn", "sphere")
biplot(pc)
# now we want to compare the results with the non-robust principal components
pc <- princomp(x)
# again, a biplot for comparision:
biplot(pc)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.