archetypal (version 1.0.0)

find_optimal_kappas: Function for finding the optimal number of archetypes

Description

Function for finding the optimal number of archetypes in order to apply Archetypal Analysis for a data frame.

Usage

find_optimal_kappas(df, maxkappas = 15,
  method = "projected_convexhull", ntrials = 10, nworkers = NULL)

Arguments

df

The data frame with dimensions \(n \times d\)

maxkappas

The maximum number of archetypes for which algorithm will be applied

method

The method that will be used for computing the initial solution

ntrials

The number of times that algorithm will be applied for each kappas

nworkers

The number of logical processors that will be used for parallel computing (usually it is the double of available physical cores)

Value

A list with members:

1. all_sse, all available SSE for all kappas and all trials per kappas

2. all_sse1, all available SSE(k)/SSE(1) for all kappas and all trials per kappas

3. bestfit_sse, only the best fit SSE trial for each kappas

4. bestfit_sse1, only the best fit SSE(k)/SSE(1) trial for each kappas

5. all_kappas, the knee point of scree plot for all 4 SSE results

6. optimal_kappas, the knee point from best fit SSE results

Details

After having found the SSE for each kappas, method UIK (see [1]) is used for estimating the knee point as the optimal kappas.

References

[1] Christopoulos, Demetris T., Introducing Unit Invariant Knee (UIK) As an Objective Choice for Elbow Point in Multivariate Data Analysis Techniques (March 1, 2016). Available at SSRN: https://ssrn.com/abstract=3043076 or http://dx.doi.org/10.2139/ssrn.3043076

See Also

archetypal

Examples

# NOT RUN {
{
# }
# NOT RUN {
# Run may take a while...
# Create data frame:
t1=Sys.time()
p1=c(1,2);p2=c(3,5);p3=c(7,3) 
dp=rbind(p1,p2,p3);dp
set.seed(916070)
pts=t(sapply(1:20, function(i,dp){
  cc=runif(3)
  cc=cc/sum(cc)
  colSums(dp*cc)
},dp))
df=data.frame(pts)
colnames(df)=c("x","y")
# Run:
yy=find_optimal_kappas(df,maxkappas = 10)
# Results:
names(yy)
# Best fit SSE:
yy$bestfit_sse 
# Optimal kappas from UIK method:
yy$optimal_kappas
#
# }
# NOT RUN {
}
# }