find_outmost_convexhull_points {archetypal}

Function which finds the outermost convex hull points in order to be used as initial solution in archetypal analysis

Description

Function which finds the outermost convex hull points in order to be used as initial solution in archetypal analysis

Usage

find_outmost_convexhull_points(df, kappas)

Arguments

df

The data frame with dimensions n x d

kappas

The number of archetypes

Details

This function uses the chull when d=2 (see [1], [2]) and the convhulln for d>2 (see [3]) cases.

Value

A list with members:

1. outmost, the first kappas most frequent outermost points as rows of data frame

2. outmostall, all the outermost points that have been found as rows of data frame

3. outmostfrequency, a matrix with frequency and cumulative frequency for outermost rows

References

[1] Eddy, W. F. (1977). A new convex hull algorithm for planar sets. ACM Transactions on Mathematical Software, 3, 398-403. doi: 10.1145/355759.355766.

[2] Eddy, W. F. (1977). Algorithm 523: CONVEX, A new convex hull algorithm for planar sets [Z]. ACM Transactions on Mathematical Software, 3, 411-412. doi: 10.1145/355759.355768.

[3] Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull algorithm for convex hulls" ACM Trans. on Mathematical Software, 22(4):469-483, Dec 1996, http://www.qhull.org

See Also

find_furthestsum_points, find_outmost_projected_convexhull_points,

find_outmost_partitioned_convexhull_points & find_outmost_points

Examples

data("wd2") #2D demo 
df = wd2
yy = find_outmost_convexhull_points(df, kappas = 3)
yy$outmost #the rows of 3 outermost points
df[yy$outmost,] #the 3 outermost points
yy$outmostall #all outermost cH rows
yy$outmostfrequency #their frequency
#
###
#
data("wd3") #3D demo 
df = wd3
yy = find_outmost_convexhull_points(df, kappas = 4)
yy$outmost #the rows of 4 outermost points
df[yy$outmost,] #the 4 outermost points
yy$outmostall #all outermost cH rows
yy$outmostfrequency #their frequency