The stochastic nature of the alpha coefficients implies that they exist on a standard (K1)simplex with the K archetypes Z as the corners, and the coefficients as the coordinate with respect to these corners. A standard simplex can be projected to two dimensions via a skew orthogonal projection, where all the vertices of the simplex are shown on a circle connected by edges. The individual alpha coefficients can be then projected into this circle.
1 2 3 4 5 6  simplexplot(object, radius = 10, order = NULL, labels_cex = 1,
labels = NULL, show_labels = TRUE, points_col = "#00000044",
points_pch = 19, points_cex = 1, projection = simplex_projection,
show_points = TRUE, show_circle = TRUE, circle_col = "lightgray",
show_edges = TRUE, edges_col = "lightgray", show_direction = FALSE,
direction_length = 1, directions_col = points_col, ...)

object 
An 
radius 
Radius of the projection 
order 
Order of the archetypes 
labels_cex 
Label expansion 
labels 
Labels 
show_labels 
Show labels 
points_col 
Color of the points 
points_pch 
Plot character of the points 
points_cex 
Character expansion of the points 
projection 
Projection function; see

show_points 
Show the points 
show_circle 
Show the circle 
circle_col 
Color of the circle 
show_edges 
Show the edges 
edges_col 
Color of the edges 
direction_length 
Expansion of the direction pointers 
directions_col 
Color of the direction pointers 
show_direction 
Show direction pointers 
... 
Additional arguments; currently ignored 
Invisible list of all computed components needed for the simplex visualization.
See Section 6 in "Probabilistic Archetypal Analysis" by Seth and Eugster (2014), http://arxiv.org/abs/1312.7604.
1 2 3 4 5 6 7 8 9 10 11 12 13 14  ### This example reproduces parts of the Figure 7 shown in
### "Probabilistic Archetypal Analysis" by Seth and Eugster (2014)
data("toy", package = "archetypes")
set.seed(1234); a3 < archetypes(toy, k = 3)
set.seed(1237); a4 < archetypes(toy, k = 4)
set.seed(1238); a5 < archetypes(toy, k = 5)
simplexplot(a3)
simplexplot(a3, show_direction = TRUE, show_points = FALSE)
simplexplot(a4, projection = tspsimplex_projection)
simplexplot(a5, show_direction = TRUE, show_points = FALSE,
direction_length = 2, directions_col = "black")

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