Euclidean space \(\mathbf{R}^p\) is the most common space for data analysis, which can be considered as a Riemannian manifold with flat metric. Since the space of matrices is isomorphic to Euclidean space after vectorization, we consider the inputs as \(p\)-dimensional vectors.
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 \(\mathbf{R}^p\).
- size
dimension of the ambient space.
- name
name of the manifold of interests, "euclidean"
Examples
#-------------------------------------------------------------------
# Checker for Two Types of Inputs
#
# Generate 5 observations in R^3 in Matrix and List.
#-------------------------------------------------------------------
## DATA GENERATION
d1 = array(0,c(5,3))
d2 = list()
for (i in 1:5){
single = stats::rnorm(3)
d1[i,] = single
d2[[i]] = single
}
## RUN
test1 = wrap.euclidean(d1)
test2 = wrap.euclidean(d2)