View source: R/kappa_tools.R View source: R/kappa_tools.R

kappa_tools | R Documentation |

For a given data set and a given Archetypal Analysis (AA) solution, it finds a set of useful proxies for the dimensionality.

```
kappa_tools(aa, df = NULL, numBins = 100, chvertices = NULL, verbose = FALSE, ...)
```

`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. |

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.

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 |

Demetris T. Christopoulos, David F. Midgley (creator of BIC and adjBIC procedures)

[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

```
{
## Use the sample data "wd2"
data(wd2)
require("geometry")
ch=convhulln(as.matrix(wd2),'Fx')
chlist=as.list(ch)
chvertices = unique(do.call(c,chlist))
aa=archetypal(wd2, 3)
out=kappa_tools(aa , df = wd2, numBins = 100, chvertices, verbose = T )
out
}
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.