Negative Eigenfraction — nef • maotai

Negative Eigenfraction (NEF) is a measure of distortion for the data whether they are lying in Euclidean manner or not. When the value is exactly 0, it means the data is Euclidean. On the other hand, when NEF is far away from 0, it means not Euclidean. The concept of NEF is closely related to the definiteness of a Gram matrix.

nef(data)

Arguments

data: an \((n\times p)\) matrix whose rows are observations.

Value

a nonnegative NEF value.

References

Pękalska E, Harol A, Duin RPW, Spillmann B, Bunke H (2006). “Non-Euclidean or Non-Metric Measures Can Be Informative.” In Yeung D, Kwok JT, Fred A, Roli F, de Ridder D (eds.), Structural, Syntactic, and Statistical Pattern Recognition, 871--880. ISBN 978-3-540-37241-7.

Examples

## use simple example of iris dataset 
data(iris) 
mydat = as.matrix(iris[,1:4])

## calculate NEF
nef(mydat)
#> [1] 4.968432e-16