wrap.multinomial: Prepare Data on Multinomial Manifold

In Riemann: Learning with Data on Riemannian Manifolds

Prepare Data on Multinomial Manifold

Description

Multinomial manifold is referred to the data that is nonnegative and sums to 1. Also known as probability simplex or positive orthant, we denote (p-1) simplex in \mathbf{R}^p by

Δ^{p-1} = \lbrace x \in \mathbf{R}^p~\vert~ ∑_{i=1}^p x_i = 1, x_i > 0 \rbrace

in that data are positive L_1 unit-norm vectors. In wrap.multinomial, normalization is applied when each data point is not on the simplex, but if vectors contain values not in (0,1), it returns errors.

Usage

wrap.multinomial(input)

Arguments

input

data vectors to be wrapped as riemdata class. Following inputs are considered, matrix an (n \times p) matrix of row observations. list a length-n list whose elements are length-p vectors.

Value

a named riemdata S3 object containing

data

a list of (p\times 1) matrices in Δ^{p-1}.

size

dimension of the ambient space.

name

name of the manifold of interests, "multinomial"

Examples

#-------------------------------------------------------------------
#                 Checker for Two Types of Inputs
#-------------------------------------------------------------------
## DATA GENERATION
d1 = array(0,c(5,3))
d2 = list()
for (i in 1:5){
  single  = abs(stats::rnorm(3))
  d1[i,]  = single
  d2[[i]] = single
}

## RUN
test1 = wrap.multinomial(d1)
test2 = wrap.multinomial(d2)

Riemann documentation built on March 18, 2022, 7:55 p.m.