| kappa_tools {archetypal} | R Documentation |
Compute kappa tools for data dimensionality analysis
Description
For a given data set and a given Archetypal Analysis (AA) solution, it finds a set of useful proxies for the dimensionality.
Usage
kappa_tools(aa, df = NULL, numBins = 100, chvertices = NULL, verbose = FALSE, ...)
Arguments
aa |
An object of the class 'archetypal' |
df |
The data frame that was used for AA |
numBins |
The number of bins to be used for computing entropy |
chvertices |
The Convex Hull vertices, if they are given |
verbose |
Logical, set to TRUE if details must be printed |
... |
Other areguments, not used. |
Details
The ECDF for the Squared Errors (SE) is computed and then the relevant curve is classified as 'convex' or 'concave' and its UIK & inflcetion point is found. Then the number of used rows for cfreating archetypes is found. A procedure for creating BIC and andjusted BIC is used. Finally the pecentage of used points that lie on the exact Convex Hull is given.
Value
A list with next arguments:
ecdf |
The ECDF of SE |
Convexity |
The convex or concave classification for ECDF curve |
UIK |
The UIK points of ECDF curve by using [1] |
INFLECTION |
The inflection points of ECDF curve by using [2] |
NumberRowsUsed |
The number of rows used for creating archetypes |
RowsUsed |
The exact rows used for creating archetypes |
SSE |
The Sum of SE |
BIC |
The computed BIC by using [3], [4] |
adjBIC |
The computed adjusted BIC by using [3], [4] |
CXHE |
The percentage of used points that lie on the exact Convex Hull |
Author(s)
Demetris T. Christopoulos, David F. Midgley (creator of BIC and adjBIC procedures)
References
[1] Demetris T. Christopoulos, Introducing Unit Invariant Knee (UIK) As an Objective Choice for Elbow Point in Multivariate Data Analysis Techniques (March 1, 2016). Available at SSRN: https://ssrn.com/abstract=3043076 or http://dx.doi.org/10.2139/ssrn.3043076
[2] Demetris T. Christopoulos, On the efficient identification of an inflection point,International Journal of Mathematics and Scientific Computing,(ISSN: 2231-5330), vol. 6(1), 2016.
[3] Felix Abramovich, Yoav Benjamini, David L. Donoho, Iain M. Johnstone. "Adapting to unknown sparsity by controlling the false discovery rate." The Annals of Statistics, 34(2) 584-653 April 2006. https://doi.org/10.1214/009053606000000074
[4] Murari, Andrea, Emmanuele Peluso, Francesco Cianfrani, Pasquale Gaudio, and Michele Lungaroni. 2019. "On the Use of Entropy to Improve Model Selection Criteria" Entropy 21, no. 4: 394. https://doi.org/10.3390/e21040394
Examples
{
## Use the sample data "wd2"
data(wd2)
ch=convhulln(as.matrix(wd2),'Fx')
chlist=as.list(ch)
chvertices = unique(do.call(c,chlist))
aa=archetypal(wd2, 3)
out=kappa_tools(aa , wd2, chvertices, verbose = T )
out
}