GEnIs: Global measures of global index based on entropy
In ujaen-statistics/ThemAAs:

Description Usage Arguments Details Value References Examples

View source: R/GEnIs.R

General function that groups global measures of global index based on entropy. This function is made up of: Normalized mutual information using the arithmetic mean of the entropies on map and on ground truthing. Normalized mutual information using the geometric mean of the entropies on map and on ground truthing. Mutual information, which is a symmetric measure to quantify the statistical information shared between two distributions (Cover and Thomas, 1991), provides a sound indication of the shared information between a pair of clusterings. Normalized mutual information using the arithmetic mean of the maximum entropies on map and on ground truthing. Normalized mutual information using the entropy on ground truthing. Normalized mutual information using the entropy on map.

1	GEnIs(object)

object

a coMa object (confusion matrix object)

In the normalized mutual information using the arithmetic mean of the entropies on map and on ground truthing, Arithmetic mean is used because of the analogy with a normalized inner product in Hilbert space. In the normalized mutual information using the arithmetic mean of the maximum entropies on map and on ground truthing ,geometric mean is used because of the analogy with a normalized inner product in Hilbert space.

GEnIs returns a list with the following elements:

Strehl, A., & Ghosh, J. (2002). Cluster ensembles: A knowledge reuse framework for combining multiple partitions. Journal of Machine Learning Research, 3, 583-617.

Ghosh, J., Strehl, A., & Merugu, S. (2002). A consensus framework for integrating distributed clusterings under limited knowledge sharing. Proc. NSF Workshop on Next Generation Data Mining, 99-108.

Finn, J. T. (1993). Use of the average mutual information index in evaluating classification error and consistency. International Journal of Geographical Information Systems, 7, 349-366.

#Let evaluate measures of global index based on entropy
## Confusion matrix included in Congalton and Green (2009), pg. 108.
x <- coMa(cbind(c(65,6,0,4),c(4,81,11,7),c(22,5,85,3),c(24,8,19,90)))
## Measures of global index based on entropy
Entropy <- GEnIs(x)