archetypoids_norm_frob: Archetypoid algorithm with the Frobenius norm

Description

This function is the same as archetypoids but the 2-norm is replaced by the Frobenius norm. Thus, the comparison with the robust archetypoids can be directly made.

Usage

archetypoids_norm_frob(numArchoid, data, huge = 200, ArchObj)

Arguments

numArchoid

Number of archetypoids.

data

Data matrix. Each row corresponds to an observation and each column corresponds to a variable. All variables are numeric.

huge

Penalization added to solve the convex least squares problems.

ArchObj

The list object returned by the stepArchetypesRawData_norm_frob function.

Value

A list with the following elements:

cases: Final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
archet_ini: Vector of initial archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
resid: Matrix with the residuals.

References

Eugster, M.J.A. and Leisch, F., From Spider-Man to Hero - Archetypal Analysis in R, 2009. Journal of Statistical Software 30(8), 1-23, https://doi.org/10.18637/jss.v030.i08

Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036

Vinue, G., Epifanio, I., and Alemany, S., Archetypoids: a new approach to define representative archetypal data, 2015. Computational Statistics and Data Analysis 87, 102-115, https://doi.org/10.1016/j.csda.2015.01.018

Vinue, G., Anthropometry: An R Package for Analysis of Anthropometric Data, 2017. Journal of Statistical Software 77(6), 1-39, https://doi.org/10.18637/jss.v077.i06

Examples

Run this code

# NOT RUN {
data(mtcars)
data <- mtcars

k <- 3
numRep <- 2
huge <- 200

lass <- stepArchetypesRawData_norm_frob(data = data, numArch = k, 
                                        numRep = numRep, verbose = FALSE)

res <- archetypoids_norm_frob(k, data, huge, ArchObj = lass)
str(res)  
res$cases
res$rss                                                           

# }