find_pcha_optimal_parameters function

Finds the optimal updating parameters to be used for the PCHA algorithm

After creating a grid on the space of (mu_up, mu_down) it runs archetypal by using a given method & other running options passed by ellipsis (...) and finally finds those values which minimize the SSE at the end of testing_iters iterations (default=10).

find_pcha_optimal_parameters(df, kappas, method = "projected_convexhull", 
testing_iters = 10, nworkers = NULL, nprojected = 2, npartition = 10,
nfurthest = 100, sortrows = FALSE,
mup1 = 1.1, mup2 = 2.50, mdown1 = 0.1, mdown2 = 0.5, nmup = 10, nmdown = 10,
rseed = NULL, plot = FALSE, ...)

Arguments

• df: The data frame with dimensions n x d

• kappas: The number of archetypes

• method: The method that will be used for computing initial approximation:

  1. projected_convexhull, see find_outmost_projected_convexhull_points
  2. convexhull, see find_outmost_convexhull_points
  3. partitioned_convexhull, see find_outmost_partitioned_convexhull_points
  4. furthestsum, see find_furthestsum_points
  5. outmost, see find_outmost_points
  6. random, a random set of kappas points will be used

• testing_iters: The maximum number of iterations to run for every pair (mu_up, mu_down) of parameters

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

• nprojected: The dimension of the projected subspace for find_outmost_projected_convexhull_points

• npartition: The number of partitions for find_outmost_partitioned_convexhull_points

• nfurthest: The number of times that FurthestSum algorithm will be applied

• sortrows: If it is TRUE, then rows will be sorted in find_furthestsum_points

• mup1: The minimum value of mu_up, default is 1.1

• mup2: The maximum value of mu_up, default is 2.5

• mdown1: The minimum value of mu_down, default is 0.1

• mdown2: The maximum value of mu_down, default is 0.5

• nmup: The number of points to be taken for [mup1,mup2], default is 10

• nmdown: The number of points to be taken for [mdown1,mdown2]

• rseed: The random seed that will be used for setting initial A matrix. Useful for reproducible results

• plot: If it is TRUE, then a 3D plot for (mu_up, mu_down, SSE) is created

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

Returns

A list with members:

1. mu_up_opt, the optimal found value for muAup and muBup
2. mu_down_opt, the optimal found value for muAdown and muBdown
3. min_sse, the minimum SSE which corresponds to (mu_up_opt,mu_down_opt)
4. seed_used, the used random seed, absolutely necessary for reproducing optimal results
5. method_used, the method that was used for creating the initial solution
6. sol_initial, the initial solution that was used for all grid computations
7. testing_iters, the maximum number of iterations done by every grid computation

Examples

{
data("wd25")
out = find_pcha_optimal_parameters(df = wd25, kappas = 5, rseed = 2020)
# Time difference of 30.91101 secs
# mu_up_opt mu_down_opt     min_sse 
# 2.188889    0.100000    4.490980  
# Run now given the above optimal found parameters:
aa = archetypal(df = wd25, kappas = 5,
                initialrows = out$sol_initial, rseed = out$seed_used,
                muAup = out$mu_up_opt, muAdown = out$mu_down_opt,
                muBup = out$mu_up_opt, muBdown = out$mu_down_opt)
aa[c("SSE", "varexpl", "iterations", "time" )]
# $SSE
# [1] 3.629542
# 
# $varexpl
# [1] 0.9998924
# 
# $iterations
# [1] 146
# 
# $time
# [1] 21.96
# Compare it with a simple solution (time may vary)
aa2 = archetypal(df = wd25, kappas = 5, rseed = 2020)
aa2[c("SSE", "varexpl", "iterations", "time" )]
# $SSE
# [1] 3.629503
# 
# $varexpl
# [1] 0.9998924
# 
# $iterations
# [1] 164
# 
# $time
# [1] 23.55
## Of course the above was a "toy example", if your data has thousands or million rows,
## then the time reduction is much more conspicuous.
# Close plot device:
dev.off()

}

See Also

find_closer_points