PcaLocantore {rrcov} | R Documentation |
The Spherical Principal Components procedure was proposed by Locantore et al., (1999) as a functional data analysis method. The idea is to perform classical PCA on the data, projected onto a unit sphere. The estimates of the eigenvectors are consistent and the procedure is extremely fast. The simulations of Maronna (2005) show that this method has very good performance.
PcaLocantore(x, ...) ## Default S3 method: PcaLocantore(x, k = 0, kmax = ncol(x), corr=FALSE, delta = 0.001, na.action = na.fail, trace=FALSE, ...) ## S3 method for class 'formula': PcaLocantore(formula, data = NULL, subset, na.action, ...)
formula |
a formula with no response variable, referring only to numeric variables. |
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 NA s. The default is set by
the na.action setting of options , and is
na.fail if that is unset. The default is na.omit . |
... |
arguments passed to or from other methods. |
x |
a numeric matrix (or data frame) which provides the data for the principal components analysis. |
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. |
corr |
a logical value indicating whether the calculation should use
the correlation matrix or the covariance matrix (the correlation matrix
can only be used if there are no constant variables). Default is corr=FALSE . |
delta |
an accuracy parameter |
trace |
whether to print intermediate results. Default is trace = FALSE |
PcaLocantore
, serving as a constructor for objects of class PcaLocantore-class
is a generic function with "formula" and "default" methods. For details see the relevant references.
An S4 object of class PcaLocantore-class
which is a subclass of the
virtual class PcaRobust-class
.
Valentin Todorov valentin.todorov@chello.at The SPC algorithm is implemented on the bases of the available from the web site of the book Maronna et al. (2006) code http://www.wiley.com/legacy/wileychi/robust_statistics/
N. Locantore, J. Marron, D. Simpson, N. Tripoli, J. Zhang and K. Cohen K. (1999), Robust principal components for functional data. Test, 8, 1-28.
R. Maronna, D. Martin and V. Yohai (2006), Robust Statistics: Theory and Methods. Wiley, New York.
R. Maronna (2005). Principal components and orthogonal regression based on robust scales. Technometrics, 47, 264-273.
## PCA of the Hawkins Bradu Kass's Artificial Data ## using all 4 variables data(hbk) pca <- PcaLocantore(hbk) pca ## Compare with the classical PCA prcomp(hbk) ## or PcaClassic(hbk) ## If you want to print the scores too, use print(pca, print.x=TRUE) ## Using the formula interface PcaLocantore(~., data=hbk) ## To plot the results: plot(pca) # distance plot pca2 <- PcaLocantore(hbk, k=2) plot(pca2) # PCA diagnostic plot (or outlier map) ## Use the standard plots available for for prcomp and princomp screeplot(pca) biplot(pca)