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.
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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
PcaLocantoreclass
is a generic function with "formula"
and "default" methods. For details see the relevant references.
An S4 object of class PcaLocantoreclass
which is a subclass of the
virtual class PcaRobustclass
.
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, 128.
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, 264273.
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/.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  ## 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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