find_optimal_kappas {archetypal}

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)

...

Other arguments to be passed to function archetypal

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.

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. 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

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

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
#

}