find_optimal_kappas function

Function for finding the optimal number of archetypes

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

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)
• ...: Other arguments to be passed to function archetypal

Returns

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. d2uik, the UIK for the absolute values of the estimated best fit SSE second derivatives, after using second order forward divided differences approximation
7. optimal_kappas, the knee point from best fit SSE results

Details

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

Examples

{
# Run may take a while depending on your machine ...
# Load data frame "wd2"
data("wd2")
df = wd2
# Run:
t1 = Sys.time()
yy = find_optimal_kappas(df, maxkappas = 10)
t2 = Sys.time();print(t2-t1)
# Results:
names(yy)
# Best fit SSE:
yy$bestfit_sse 
# Optimal kappas from UIK method:
yy$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: http://dx.doi.org/10.2139/ssrn.3043076

See Also

archetypal