find_outmost_convexhull_points function

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

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.

Returns

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

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

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