R_NX: The R_{NX}(K) criterion

In gdkrmr/coRanking: Co-Ranking Matrix

The R_{NX}(K) criterion

Description

A curve indicating the improvement of the embedding over a random embedding for the neighborhood size K. Values range from 0, for a random embedding, to 1 for a perfect embedding.

Usage

R_NX(Q)

Arguments

Q	a co-ranking matrix

Details

R_{NX}(K) is calculated as follows:

Q_{NX}(K) = \sum_{1\leq k\leq K}\sum_{1\leq l\leq K} \frac{q_{kl}}{KN}

Counts the upper left K-by-K block of Q, i.e. it considers the preserved ranks on the diagonal and the permutations within a neighborhood.

R_{NX}(K) = \frac{(N-1)Q_{NX}(K)-K}{N-1-K}

A resulting vale of 0 corresponds to a random embedding, a value of 1 to a perfect embedding of the K-ary neighborhood.

Value

A vector with the values for R_NX(K)

Author(s)

Guido Kraemer

References

Lee, J.A., Lee, J.A., Verleysen, M., 2009. Quality assessment of dimensionality reduction: Rank-based criteria. Neurocomputing 72.

Lee, J. A., Peluffo-Ordóñez, D. H., & Verleysen, M., 2015. Multi-scale similarities in stochastic neighbour embedding: Reducing dimensionality while preserving both local and global structure. Neurocomputing, 169, 246–261. https://doi.org/10.1016/j.neucom.2014.12.095

gdkrmr/coRanking documentation built on March 23, 2023, 5:43 a.m.