MoE_entropy: Entropy of a fitted MoEClust model

In MoEClust: Gaussian Parsimonious Clustering Models with Covariates and a Noise Component

Entropy of a fitted MoEClust model

Description

Calculates the normalised entropy of a fitted MoEClust model.

Usage

MoE_entropy(x)

Arguments

x	An object of class "MoEClust" generated by MoE_clust, or an object of class "MoECompare" generated by MoE_compare. Models with gating and/or expert covariates and/or a noise component are facilitated here too.

Details

This function calculates the normalised entropy via

H=-\frac{1}{n\log(G)}∑_{i=1}^n∑_{g=1}^G\hat{z}_{ig}\log(\hat{z}_{ig}),

where n and G are the sample size and number of components, respectively, and \hat{z}_{ig} is the estimated posterior probability at convergence that observation i belongs to component g. Note that G=x$G for models without a noise component and G=x$G + 1 for models with a noise component.

Value

A single number, given by 1-H, in the range [0,1], such that larger values indicate clearer separation of the clusters.

Note

This function will always return a normalised entropy of 1 for models fitted using the "CEM" algorithm (see MoE_control), or models with only one component.

Author(s)

Keefe Murphy - <[e-mail]>

References

Murphy, K. and Murphy, T. B. (2020). Gaussian parsimonious clustering models with covariates and a noise component. Advances in Data Analysis and Classification, 14(2): 293-325. <doi: 10.1007/s11634-019-00373-8>.

See Also

MoE_clust, MoE_control, MoE_AvePP

Examples

data(ais)
res <- MoE_clust(ais[,3:7], G=3, gating= ~ BMI + sex, 
                 modelNames="EEE", network.data=ais)

# Calculate the normalised entropy
MoE_entropy(res)

MoEClust documentation built on Dec. 28, 2022, 2:24 a.m.