nhdist {Ball} | R Documentation |
This function computes and returns the numeric distance matrix computed by using the specified distance measure to compute the distances between the rows of a data matrix.
nhdist(x, method = "geodesic")
x |
a numeric matrix, data frame or numeric array of dimension k \times m \times n containing n samples in k \times m dimension. |
method |
the distance measure to be used. This must be one of |
Available distance measures are geodesic, compositional and riemann. Denoting any two sample in the dataset as x and y, we give the definition of distance measures as follows.
geodesic:
The shortest route between two points on the Earth's surface, namely, a segment of a great circle.
\arccos(x^{T}y), \|x\|_{2} = \|y\|_{2} = 1
compositional:
First, we apply scale transformation to it, i.e., (x_{i1}/t, ..., x_{ip}/t_{i}), t_{i} = ∑_{d=1}^{p}{x_{d}} . Then, apply the square root transformation to data and calculate the geodesic distance between samples.
riemann:
k \times m \times n array where k = number of landmarks, m = number of dimensions and n = sample size. Detail about riemannian shape distance was given in Kendall, D. G. (1984).
n \times n numeric distance matrix
Kendall, D. G. (1984). Shape manifolds, Procrustean metrics and complex projective spaces, Bulletin of the London Mathematical Society, 16, 81-121.
data('bdvmf') Dmat <- nhdist(bdvmf[['x']], method = "geodesic") data("ArcticLake") Dmat <- nhdist(ArcticLake[['x']], method = "compositional") data("macaques") Dmat <- nhdist(macaques[["x"]], method = "riemann") # unambiguous substring also available: Dmat <- nhdist(macaques[["x"]], method = "rie")