grid_archetypal {GeomArchetypal}

Performs the Archetypal Analysis of a Data Frame by using as Archetypes the Archetypal Grid

Description

The archetypal grid is the expand grid of all intervals (X.imin,X.imax), i=1,...,d for a d-dimensional data frame.
That grid is used as archetypes and then only the A-update part of PCHA algorithm is used for computing the compositions of all data points.
The number of archetypes is always kappas = 2^d.

Usage

grid_archetypal(dg,  
                diag_less = 1e-2,
                niter = 30, 
                use_seed = NULL, 
                verbose = TRUE)

Arguments

dg

The data frame with dimensions n x d

diag_less

The expected mean distance from 1 for the diagonal elements of submatrix A[1:kappas,:]

niter

The number of times that the A-update process should be done

use_seed

If it is not NULL, then is used at the set.seed() for reproducibility reasons

verbose

If it is set to TRUE, then both initialization and iteration details are printed out

Details

The archetypal grid defines a hyper-volume which contains the 100 % of all data points, if we take those grid points as the Convex Hull of all points. Although the archetypal grid points do not necessarily lie inside the data frame, here we do not care about that property: we only seek for the matrix of convex combinations (or composition matrix) A.

Value

An object of class grid_archetypal which is a list with members:

1. grid, the archetypal grid

2. aa, an object of class 'archetypal' which includes the archetypal grid as the first 2^d rows

3. A, the A-matrix with dimensions n x d that defines the compositions of all data points

4. Y, the matrix of initial data points

See Also

closer_grid_archetypal

Examples

  
# Load package  
library(GeomArchetypal)
# Create random data:
set.seed(20140519)
df=matrix(runif(90) , nrow = 30, ncol=3) 
colnames(df)=c("x","y","z")
# Grid Archetypal:
gaa=grid_archetypal(df, diag_less = 1e-6, 
                    niter = 70, verbose = FALSE)
# Print class "grid_archetypal":
gaa
# Summary class "grid_archetypal":
summary(gaa)
# Plot class "grid_archetypal":
plot(gaa)
# Observe the Grid Archetypes at the 8 corners of the cube ..