R: Tools for Exploring Multivariate Data via ICS/ICA

ICS-package {ICS}

R Documentation

Tools for Exploring Multivariate Data via ICS/ICA

Description

Implementation of Tyler, Critchley, Duembgen and Oja's (JRSS B, 2009, <doi:10.1111/j.1467-9868.2009.00706.x>) and Oja, Sirkia and Eriksson's (AJS, 2006, <https://www.ajs.or.at/index.php/ajs/article/view/vol35,%20no2%263%20-%207>) method of two different scatter matrices to obtain an invariant coordinate system or independent components, depending on the underlying assumptions.

Details

Package:	ICS
Type:	Package
Title:	Tools for Exploring Multivariate Data via ICS/ICA
Version:	1.4-1
Date:	2023-09-17
Authors@R:	c(person("Klaus", "Nordhausen", email = "klausnordhausenR@gmail.com", role = c("aut", "cre"), comment = c(ORCID = "0000-0002-3758-8501")), person("Andreas", "Alfons", email = "alfons@ese.eur.nl", role = "aut", comment = c(ORCID = "0000-0002-2513-3788")), person("Aurore", "Archimbaud", email = "aurore.archimbaud@live.fr", role = "aut", comment = c(ORCID = "0000-0002-6511-9091")), person("Hannu", "Oja", email = "", role = c("aut"), comment = c(ORCID = "0000-0002-4945-5976")), person("Anne", "Ruiz-Gazen", email = "anne.ruiz-gazen@tse-fr.eu", role = "aut", comment = c(ORCID = "0000-0001-8970-8061")), person("David E.", "Tyler", email = "", role = c("aut")))
Author:	Klaus Nordhausen [aut, cre] (<https://orcid.org/0000-0002-3758-8501>), Andreas Alfons [aut] (<https://orcid.org/0000-0002-2513-3788>), Aurore Archimbaud [aut] (<https://orcid.org/0000-0002-6511-9091>), Hannu Oja [aut] (<https://orcid.org/0000-0002-4945-5976>), Anne Ruiz-Gazen [aut] (<https://orcid.org/0000-0001-8970-8061>), David E. Tyler [aut]
Maintainer:	Klaus Nordhausen <klausnordhausenR@gmail.com>
Depends:	R (>= 2.5.0), methods, mvtnorm
Imports:	survey, graphics
Suggests:	pixmap, robustbase, MASS, ICSNP, testthat (>= 3.0.0), ICSOutlier
Description:	Implementation of Tyler, Critchley, Duembgen and Oja's (JRSS B, 2009, <doi:10.1111/j.1467-9868.2009.00706.x>) and Oja, Sirkia and Eriksson's (AJS, 2006, <https://www.ajs.or.at/index.php/ajs/article/view/vol35,%20no2%263%20-%207>) method of two different scatter matrices to obtain an invariant coordinate system or independent components, depending on the underlying assumptions.
License:	GPL (>= 2)
LazyLoad:	yes
Encoding:	UTF-8
NeedsCompilation:	no
Roxygen:	list(markdown = TRUE)
RoxygenNote:	7.2.3
Config/testthat/edition:	3

Some multivariate tests and estimates are not affine equivariant by nature. A possible remedy for the lack of that property is to transform the data points to an invariant coordinate system, construct tests and estimates from the transformed data, and if needed, retransform the estimates back. The use of two different scatter matrices to obtain invariant coordinates is implemeted in this package by the function ICS. For an invariant coordinate selection no assumptions are made about the data or the scatter matrices and it can be seen as a data transformation method. If the data come, however, from a so called independent component model the ICS function can recover the independent components and estimate the mixing matrix under general assumptions. Besides, the function ICS provides these package tools to work with objects of this class, and some scatter matrices which can be used in the ICS function. Furthermore, there are also two tests for multinormality. Note that starting with version 1.4-0 the functions ics and ics2 are not recommended anymore and everything can be done in a more efficient way using the function ICS which combines the functionality of the original two functions and also provides an improved algorithm for certain scatter combinations. Furthermore, does ICS return an S3 object and not anymore S4 objects as ics and ics2 did. In the long run functions ics and ics2 will be removed from the package.

Index of help topics:

ICS-S3                  Two Scatter Matrices ICS Transformation
ICS-package             Tools for Exploring Multivariate Data via
                        ICS/ICA
ICS_scatter             Location and Scatter Estimates for ICS
Mean3Cov4               Location Vector Based on 3rd Moments and
                        Scatter Matrix Based on 4th Moments
MeanCov                 Mean Vector and Covariance Matrix
coef.ICS-S3             To extract the Coefficient Matrix of the ICS
                        Transformation
coef.ics                To extract the Unmixing Matrix
components              To extract the Component Scores of the ICS
                        Transformation
cov4                    Scatter Matrix based on Fourth Moments
cov4.wt                 Weighted Scatter Matrix based on Fourth Moments
covAxis                 One step Tyler Shape Matrix
covOrigin               Covariance Matrix with Respect to the Origin
covW                    One-step M-estimator
fitted.ICS-S3           Fitted Values of the ICS Transformation
fitted.ics              Fitted Values of an ICS Object
gen_kurtosis            To extract the Generalized Kurtosis Values of
                        the ICS Transformation
ics                     Two Scatter Matrices ICS Transformation
ics-class               Class ICS
ics.components          Extracting ICS Components
ics2                    Two Scatter Matrices ICS Transformation
                        Augmented by Two Location Estimates
ics2-class              Class ICS2
mean3                   Location Estimate based on Third Moments
mvnorm.kur.test         Test of Multivariate Normality Based on
                        Kurtosis
mvnorm.skew.test        Test of Multivariate Normality Based on
                        Skewness
plot.ICS-S3             Scatterplot Matrix of Component Scores from the
                        ICS Transformation
plot.ics                Scatterplot for a ICS Object
print.ICS-S3            Basic information of ICS Object
print.ics               Basic information of ICS Object
print.ics2              Basic information of ICS2 Object
scovq                   Supervised scatter matrix based on quantiles
screeplot.ICS-S3        Screeplot for an 'ICS' Object
screeplot.ics           Screeplot for an ICS Object
summary.ICS-S3          To summarize an 'ICS' object
summary.ics             To summarize an ICS object
summary.ics2            To summarize an ICS2 object
tM                      Joint M-estimation of Location and Scatter for
                        a Multivariate t-distribution

Author(s)

Klaus Nordhausen [aut, cre] (<https://orcid.org/0000-0002-3758-8501>), Andreas Alfons [aut] (<https://orcid.org/0000-0002-2513-3788>), Aurore Archimbaud [aut] (<https://orcid.org/0000-0002-6511-9091>), Hannu Oja [aut] (<https://orcid.org/0000-0002-4945-5976>), Anne Ruiz-Gazen [aut] (<https://orcid.org/0000-0001-8970-8061>), David E. Tyler [aut]

Maintainer: Klaus Nordhausen <klausnordhausenR@gmail.com>

References

Tyler, D.E., Critchley, F., Dümbgen, L. and Oja, H. (2009), Invariant co-ordinate selecetion, Journal of the Royal Statistical Society,Series B, 71, 549–592. <doi:10.1111/j.1467-9868.2009.00706.x>.

Oja, H., Sirkiä, S. and Eriksson, J. (2006), Scatter matrices and independent component analysis, Austrian Journal of Statistics, 35, 175–189.

Nordhausen, K., Oja, H. and Tyler, D.E. (2008), Tools for exploring multivariate data: The package ICS, Journal of Statistical Software, 28, 1–31. <doi:10.18637/jss.v028.i06>.

Archimbaud, A., Drmac, Z., Nordhausen, K., Radojicic, U. and Ruiz-Gazen, A. (2023), Numerical considerations and a new implementation for ICS, SIAM Journal on Mathematics of Data Science, 5, 97–121. <doi:10.1137/22M1498759>.

[Package ICS version 1.4-1 Index]