archetypoids: Finding archetypoids

Description

Archetypoid algorithm. It is based on the PAM clustering algorithm. It is made up of two phases (a BUILD phase and a SWAP phase). In the BUILD phase, an initial set of archetypoids is determined. Unlike PAM, this collection is not derived in a stepwise format. Instead, it is suggested you choose the set made up of the nearest individuals returned by the archetypes function of the archetypes R package (Eugster et al. (2009)). This set can be defined in three different ways, see next section arguments. The goal of the SWAP step is the same as that of the SWAP step of PAM, but changing the objective function. The initial vector of archetypoids is attempted to be improved. This is done by exchanging selected individuals for unselected individuals and by checking whether these replacements reduce the objective function of the archetypoid analysis problem.

All details are given in Vinue et al. (2015).

Usage

archetypoids(numArchoid,data,huge=200,step,init,ArchObj,nearest="cand_ns",sequ,aux)

Value

A list with the following elements:

cases: Anthropometric cases (final vector of numArchoid archetypoids).

rss: Residual sum of squares corresponding to the final vector of numArchoid archetypoids.

archet_ini: Vector of initial archetypoids (cand_ns, cand_alpha or cand_beta).

alphas: Alpha coefficients for the optimal vector of archetypoids.

Arguments

numArchoid: Number of archetypoids (archetypal observations).
data: Data matrix. Each row corresponds to an observation and each column corresponds to an anthropometric variable. All variables are numeric.
huge: This is a penalization added to solve the convex least squares problems regarding the minimization problem to estimate archetypoids, see Eugster et al. (2009). Default value is 200.
step: Logical value. If TRUE, the archetypoid algorithm is executed repeatedly within stepArchetypoids. Therefore, this function requires the next argument init (but neither the ArchObj nor the nearest arguments) that specifies the initial vector of archetypoids, which has already been computed within stepArchetypoids. If FALSE, the archetypoid algorithm is executed once. In this case, the ArchObj and nearest arguments are required to compute the initial vector of archetypoids.
init: Initial vector of archetypoids for the BUILD phase of the archetypoid algorithm. It is computed within stepArchetypoids. See nearest argument below for an explanation of how this vector is calculated.
ArchObj: The list object returned by the stepArchetypesRawData function. This function is a slight modification of the original stepArchetypes function of archetypes to apply the archetype algorithm to raw data. The stepArchetypes function standardizes the data by default and this option is not always desired. This list is needed to compute the nearest individuals to archetypes. Required when step=FALSE.
nearest: Initial vector of archetypoids for the BUILD phase of the archetypoid algorithm. Required when step=FALSE. This initial vector contain the nearest individuals to the archetypes returned by the archetypes function of archetypes (In Vinue et al. (2015), archetypes are computed after running the archetype algorithm twenty times). This argument is a string vector with three different possibilities. The first and default option is "cand_ns" and allows us to calculate the nearest individuals by computing the Euclidean distance between the archetypes and the individuals and choosing the nearest. It is used in Epifanio et al. (2013). The second option is "cand_alpha" and allows us to calculate the nearest individuals by consecutively identifying the individual with the maximum value of alpha for each archetype, until the defined number of archetypes is reached. It is used in Eugster (2012). The third and final option is "cand_beta" and allows us to calculate the nearest individuals by identifying the individuals with the maximum beta value for each archetype, i.e. the major contributors in the generation of the archetypes.
sequ: Logical value. It indicates whether a sequence of archetypoids (TRUE) or only a single number of them (FALSE) is computed. It is determined by the number of archetypes computed by means of stepArchetypesRawData.
aux: If sequ=FALSE, this value is equal to numArchoid-1 since for a single number of archetypoids, the list associated with the archetype object only has one element.

Author

Irene Epifanio and Guillermo Vinue

Details

As mentioned, this algorithm is based on PAM. These types of algorithms aim to find good solutions in a short period of time, although not necessarily the best solution. Otherwise, the global minimum solution may always be obtained using as much time as it would be necessary, but this would be very inefficient computationally.

References

Vinue, G., Epifanio, I., and Alemany, S., (2015). Archetypoids: a new approach to define representative archetypal data, Computational Statistics and Data Analysis 87, 102--115.

Cutler, A., and Breiman, L., (1994). Archetypal Analysis, Technometrics 36, 338--347.

Epifanio, I., Vinue, G., and Alemany, S., (2013). Archetypal analysis: contributions for estimating boundary cases in multivariate accommodation problem, Computers & Industrial Engineering 64, 757--765.

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

Eugster, M. J. A., (2012). Performance profiles based on archetypal athletes, International Journal of Performance Analysis in Sport 12, 166--187.

Examples

Run this code

#Note: For a sportive example, see www.uv.es/vivigui/softw/more_examples.R 

#COCKPIT DESIGN PROBLEM:
#As a toy example, only the first 25 individuals are used.
USAFSurvey_First25 <- USAFSurvey[1:25, ]
#Variable selection:
variabl_sel <- c(48, 40, 39, 33, 34, 36)
#Changing to inches: 
USAFSurvey_First25_inch <- USAFSurvey_First25[,variabl_sel] / (10 * 2.54)

#Data preprocessing:
USAFSurvey_preproc <- preprocessing(USAFSurvey_First25_inch, TRUE, 0.95, TRUE)

#For reproducing results, seed for randomness:
#suppressWarnings(RNGversion("3.5.0"))
#set.seed(2010) 
#Run archetype algorithm repeatedly from 1 to numArch archetypes:
#This is a toy example. In other situation, choose numArch=10 and numRep=20.
numArch <- 5 ; numRep <- 2
lass <- stepArchetypesRawData(data = USAFSurvey_preproc$data, numArch = 1:numArch,
                              numRep = numRep, verbose = FALSE)  
#To understand the warning messages, see the vignette of the
#archetypes package.                              

#screeplot(lass)

numArchoid <- 3 #number of archetypoids.
res_ns <- archetypoids(numArchoid, USAFSurvey_preproc$data, huge = 200, step = FALSE,
                       ArchObj = lass, nearest = "cand_ns",sequ = TRUE)

Run the code above in your browser using DataLab