Cutler-Breiman archetypes (ESL eqs 14.75-14.77): X is approximated by
W H with H = B X, the rows of W and B on the unit simplex, minimising
||X - W B X||^2 by exact alternating convex steps (each row of W by
simplex-constrained least squares; each archetype in turn by block
coordinate descent), so the criterion never increases. Archetypes start
at a farthest-point traversal from the centroid.
Usage
morie_esl_archetypes(X, r, max_iter = 200, tol = 1e-10)
Arguments
- X
Numeric matrix, N by p.
- r
Number of archetypes.
- max_iter, tol
Stop when the criterion changes by less than tol relatively.
Value
Named list: archetypes, W, B, rss, rss_path, iterations, converged.
References
Cutler, A. & Breiman, L. (1994). Technometrics 36, 338-347.
Examples
X <- rbind(c(0, 0), c(4, 0), c(4, 3), c(0, 3), c(1, 1), c(2, 2), c(3, 1))
morie_esl_archetypes(X, 4)$archetypes
#> [,1] [,2]
#> [1,] 4 3
#> [2,] 0 0
#> [3,] 4 0
#> [4,] 0 3
