| Title: | Co-Ranking Matrix |
| Version: | 0.2.5 |
| Description: | Calculates the co-ranking matrix to assess the quality of a dimensionality reduction. |
| URL: | https://coranking.guido-kraemer.com/ |
| BugReports: | https://github.com/gdkrmr/coRanking/issues |
| License: | GPL-3 | file LICENSE |
| Encoding: | UTF-8 |
| Imports: | methods, graphics, stats |
| RoxygenNote: | 7.3.2 |
| Collate: | 'coranking-package.R' 'coranking.R' 'coranking_internals.R' 'lcmc.R' 'criteria.R' 'image.R' 'rankmatrix.R' 'submatrix.R' 'r_nx.R' |
| Suggests: | testthat, knitr, rmarkdown, Rtsne, scatterplot3d |
| VignetteBuilder: | knitr |
| NeedsCompilation: | yes |
| Packaged: | 2024-09-30 09:10:26 UTC; gkraemer |
| Author: | Guido Kraemer 
[aut, cre] |
| Maintainer: | Guido Kraemer <guido.kraemer@uni-leipzig.de> |
| Repository: | CRAN |
| Date/Publication: | 2024-09-30 09:30:02 UTC |
Methods for the co-ranking matrix
Description
coRanking provides methods for the calculation of the co-ranking matrix and derived measures to assess the quality of a dimensionality reduction
Details
This package provides functions for calculating the co-ranking matrix, plotitng functions and some derived measures for quality assessment of dimensionality reductions.
Funding provided by the Department for Biogeochemical Integration, Empirical Inference of the Earth System Group, at the Max Plack Institute for Biogeochemistry, Jena.
Author(s)
Maintainer: Guido Kraemer guido.kraemer@uni-leipzig.de (ORCID)
References
Chen, L., Buja, A., 2006. Local Multidimensional Scaling for Nonlinear Dimension Reduction, Graph Layout and Proximity Analysis.
Lee, J.A., Lee, J.A., Verleysen, M., 2009. Quality assessment of dimensionality reduction: Rank-based criteria. Neurocomputing 72.
Lueks, W., Mokbel, B., Biehl, M., & Hammer, B. (2011). How to Evaluate Dimensionality Reduction? - Improving the Co-ranking Matrix. ArXiv:1110.3917 [Cs]. http://arxiv.org/abs/1110.3917
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
See Also
Useful links:
Area under the RN_X curve
Description
Area under the R_{NX}(K) curve when K is put on a logarithmic scale.
Usage
AUC_ln_K(R_NX)
Arguments
R_NX |
The R_NX curve, a vector of values |
Details
It is calculated as:
AUC_{\ln K}(R_{NX}(K)) = \left(\sum_{K=1}^{N-2}R_{NX}(K)/K\right)/\left(\sum_{K=1}^{N-2}1/K\right)
Value
A value, the area under the curve.
Author(s)
Guido Kraemer
References
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
The local continuity meta-criterion
Description
Calculate the local continuity meta-criterion from a co-ranking matrix.
Usage
LCMC(Q, K = 1:nrow(Q))
Arguments
Q |
a co-ranking matrix |
K |
vector of integers describing neighborhood size |
Details
The local continuity meta-criterion (Chen and Buja, 2006) is defined as
LCMC = \frac{K}{1-N} +
\frac{1}{NK} \sum_{(k,l)\in U L_K} q_{kl}
Higher values mean a better performance of the dimensionality reduction.
Value
A number, the local continuity meta-criterion
Author(s)
Guido Kraemer
The Q_{NX}(K) criterion
Description
A curve indicating the percentage of points that are mild in- and extrusions or keep their rank.
Usage
Q_NX(Q)
Arguments
Q |
a co-ranking matrix |
Details
Q_{NX}(K) = \frac{1}{KN} \sum_{k=1}^{K}\sum_{l=1}^{K}Q_{kl}
Value
A vector with the values for Q_NX(K)
Author(s)
Guido Kraemer
References
Lueks, W., Mokbel, B., Biehl, M., & Hammer, B. (2011). How to Evaluate Dimensionality Reduction? - Improving the Co-ranking Matrix. ArXiv:1110.3917 [Cs]. http://arxiv.org/abs/1110.3917
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
Co-Ranking Matrix
Description
Calculate the co-ranking matrix to assess the quality of a diminsionality reduction.
Usage
coranking(
Xi,
X,
input_Xi = c("data", "dist", "rank"),
input_X = input_Xi,
use = "C"
)
Arguments
Xi |
high dimensional data |
X |
low dimensional data |
input_Xi |
type of input of Xi (see. details) |
input_X |
type of input of X (see. details) |
use |
|
Details
Calculate the coranking matrix, to assess the quality of a dimensionality
reduction. Xi is input in high dimensions, X is input in low
dimensions the type of input is given in input_Xi and input_X,
they can be one of c('data', 'dist', 'rank').
Value
a matrix of class 'coranking'
Author(s)
Guido Kraemer
See Also
Image function for the co-ranking matrix
Description
Plots the co-ranking matrix nicely
Usage
imageplot(
Q,
lwd = 2,
bty = "n",
main = "co-ranking matrix",
xlab = expression(R),
ylab = expression(Ro),
col = colorRampPalette(colors = c("gray85", "red", "yellow", "green", "blue"))(100),
axes = FALSE,
legend = TRUE,
...
)
Arguments
Q |
of class |
lwd |
linewidth in legend |
bty |
boxtype of legend |
main |
title of plot |
xlab |
label of the x axis |
ylab |
label of the y axis |
col |
a palette for coloring |
axes |
ligical draw axes |
legend |
if |
... |
parameters for the |
Details
Plots the co-ranking matrix nicely for visual inspection. uses the
image function internaly, ... is passed down to the image
function. The values in the co-ranking matrix are logscaled for
better contrast.
Author(s)
Guido Kramer
Plot the R_{NX}(K) curve
Description
Produces a plot with the R_{NX}(K) curves from the arguments
Usage
plot_R_NX(R_NXs, pal = grDevices::palette(), ylim = c(0, 0.9), ...)
Arguments
R_NXs |
A list of R_NX curves, names from the list will appear in the legend |
pal |
a vector of colors |
ylim |
set the y-axis limits of the plot |
... |
options for the plotting function |
Value
Nothing, produces a plot.
Author(s)
Guido Kraemer
References
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
Rank matrix
Description
Replaces the elements of X with their rank in the column vector of
the distance matrix
Usage
rankmatrix(X, input = c("data", "dist"), use = "C")
Arguments
X |
data, dist object, or distance matrix |
input |
type of input |
use |
if 'C' uses the compiled library, else uses the native R code |
Details
Each column vector in the distance matrix (or the distance matrix computed from the input) is replaced by a vector indicating the rank of the distance inside that vector.
This is a computation step necessary for the co-ranking matrix and provided mainly so that the user has the possibility to save computation time.
Value
returns a matrix of class 'rankmatrix'
Author(s)
Guido Kraemer