rrcov: PcaLocantore – R documentation

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PcaLocantore

Spherical Principal Components

Description

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.

Usage

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, ...)

Arguments

`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=ncol(x)`.
`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.
`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 `scale=FALSE` (default) or `scale=NULL` no scaling is performed (a vector of 1s is returned in the scale slot). If `scale=TRUE` the data are scaled by `mad`. Alternatively it can be a function like `sd` or `Qn` or a vector of length equal the number of columns of `x`. The value is passed to the underlying function and the result returned is stored in the scale slot. Default is `scale=FALSE`.
`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 `signflip = FALSE`
`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 `trace = FALSE`

Details

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.

Value

An S4 object of class PcaLocantore-class which is a subclass of the virtual class PcaRobust-class.

Author(s)

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/

References

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. URL http://www.jstatsoft.org/v32/i03/.

Examples

## 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)

rrcov

Scalable Robust Estimators with High Breakdown Point

v1.5-5

GPL (>= 2)

Authors

Valentin Todorov [aut, cre] (<https://orcid.org/0000-0003-4215-0245>)

Initial release

2020-07-31