Prepare Data on Multinomial Manifold — wrap.multinomial • Riemann

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 $$\Delta^{p-1} = \lbrace x \in \mathbf{R}^p~\vert~ \sum_{i=1}^p x_i = 1, x_i > 0 \rbrace$$ 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 $\Delta^{p-1}$.
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)