| 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) = \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