Embedding quality, alienation coefficient and dissimilarity checks

EmbeddingQuality: trustworthiness and continuity (Venna and Kaski 2001), \(Q_{NX}\) (Lee and Verleysen 2009) and LCMC (Chen and Buja 2009) at neighbourhood size k. AlienationCoefficient: Guttman's \(K = \sqrt{1 - \mu^2}\) with \(\mu\) the congruence of distances and disparities (Borg and Groenen 2005). DissimilarityCheck: symmetry, triangle inequality violations and Euclidean embeddability (Gower 1966).

Usage

EmbeddingQuality(D_high, D_low, k)

AlienationCoefficient(dhat, d)

DissimilarityCheck(delta, tol = 1e-12)

Arguments

D_high, D_low

Distance matrices.

k

Neighbourhood size.

dhat, d

Disparities and distances.

delta

Dissimilarity matrix.

tol

Tolerance.

Value

List or number.

References

Venna, J. and Kaski, S. (2001). Neighborhood preservation in nonlinear projection methods: an experimental study. ICANN 2001, LNCS 2130, 485-491.

Borg, I. and Groenen, P. J. F. (2005). Modern Multidimensional Scaling, 2nd edn. Springer.

Examples

D <- as.matrix(dist(1:4))
EmbeddingQuality(D, D, 1)$trustworthiness
#> [1] 1
AlienationCoefficient(c(1, 2, 3), c(1.1, 1.9, 3.2))
#> [1] 0.05289925
DissimilarityCheck(rbind(c(0, 1, 5), c(1, 0, 1), c(5, 1, 0)))$triangle_violations
#> [1] 1