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.