nhdist {Ball} R Documentation

## Distance Matrix Computation for Non-Hilbert Data

### Description

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.

### Usage

nhdist(x, method = "geodesic")


### Arguments

 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 "geodesic", "compositional", or "riemann". Any unambiguous substring can be given.

### Details

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).

### Value

n \times n numeric distance matrix

### References

Kendall, D. G. (1984). Shape manifolds, Procrustean metrics and complex projective spaces, Bulletin of the London Mathematical Society, 16, 81-121.

### Examples

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")



[Package Ball version 1.3.12 Index]