PcaLocantore | 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 = ncol(x), kmax = ncol(x), delta = 0.001,
na.action = na.fail, scale = FALSE, signflip = TRUE,
crit.pca.distances = 0.975, 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
|
subset |
an optional vector used to select rows (observations) of the
data matrix |
na.action |
a function which indicates what should happen
when the data contain |
... |
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 |
kmax |
maximal number of principal components to compute.
Default is |
delta |
an accuracy parameter |
scale |
a value indicating whether and how the variables should be scaled
to have unit variance (only possible if there are no constant
variables). If |
signflip |
a logical value indicating wheather to try to solve
the sign indeterminancy of the loadings - ad hoc approach setting
the maximum element in a singular vector to be positive. Default is
|
crit.pca.distances |
criterion to use for computing the cutoff values for the orthogonal and score distances. Default is 0.975. |
trace |
whether to print intermediate results. Default is |
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 https://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.
Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1–47. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v032.i03")}.
## 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)
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