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.
Arguments
- input
data vectors to be wrapped as
riemdataclass. 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)