R: The R_{NX}(K) criterion

R_NX {coRanking} | R Documentation

## 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) = ∑_{1≤q k≤q K}∑_{1≤q l≤q 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

[Package coRanking version 0.2.2 Index]