# wrap.multinomial: Prepare Data on Multinomial Manifold In Riemann: Learning with Data on Riemannian Manifolds

## 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

 1 wrap.multinomial(input) 

## Arguments

 input data vectors to be wrapped as riemdata class. Following inputs are considered, matrixan (n \times p) matrix of row observations. lista 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

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 #------------------------------------------------------------------- # 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 June 20, 2021, 5:07 p.m.