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.
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., \((x_{i1}/t, ..., x_{ip}/t_{i}), t_{i} = \sum_{d=1}^{p}{x_{d}}\) . 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).
References
Kendall, D. G. (1984). Shape manifolds, Procrustean metrics and complex projective spaces, Bulletin of the London Mathematical Society, 16, 81-121.