edmcr (version 0.2.0)

getConfig: Create a Point Configuration from a Distance Matrix

Description

getConfig - given an nxn Euclidean distance matrix, produces a d-dimensional point configuration of size n via eigendecomposition

Usage

getConfig(D, d)

Arguments

D

an nxn Euclidean distance matrix

d

the dimension for the configuration

Value

Y

an nxd matrix containing the d-dimensional point configuration

Accuracy

the ratio of the sum of retained eigenvalues to the sum of all n eigenvalues obtained during decomposition

Details

Given a distance matrix D, transform to a semi-definite matrix S using the linear transformation \(\tau(D)\). Using S, compute the eigen-decomposition \(S = ULV'\), where L is a diagonal matrix containing the singular-values of S, and the columns of U contain the eigen-vectors. A point configuration X is then computed as:

$$X = US^{.5}$$

To compute a configuration in d dimensions, the first d eigenvalues of S are used.

Examples

# NOT RUN {
set.seed(1337)
D <- matrix(c(0,3,4,3,4,3,
             3,0,1,NA,5,NA,
             4,1,0,5,NA,5,
             3,NA,5,0,1,NA,
             4,5,NA,1,0,5,
             3,NA,5,NA,5,0),byrow=TRUE, nrow=6)
d <- 3
DStar <- dpf(D,d)$D

getConfig(DStar,3)

# }