VICatMix (version 1.0)

VI.lb: Compute the modified Variation of Information from swapping log and expectation.

Description

Based on samples of partitions (eg. from MCMC or different clustering initialisations), computes the modified Variation of Information which switches the log and expectation in the usual Variation of Information.

Usage

VI.lb(cls, psm)

Value

vector of length nrow(cls) of the posterior expected (modified) VoI.

Arguments

cls

a matrix of partitions where the posterior expected (modified) Variation of Information is to be evaluated. Each row corresponds to a clustering of ncol(cls) data points.

psm

a posterior similarity matrix, which can be obtained from clusterings through a call to comp.psm.

Author

Sara Wade,

Details

The Variation of Information (VoI) between two clusterings is defined as the sum of the entropies minus two times the mutual information. Computation of the posterior expected VoI can be expensive, as it requires a Monte Carlo estimate. The modified posterior expected VoI, obtained by swapping the log and expectation, is much more computationally efficient as it only depends on the posterior through the posterior similarity matrix. From Jensen's inequality, the problem of finding the optimal partition which minimizing the posterior expected modified VoI can be viewed as minimizing a lower bound to the posterior expected VoI.

References

Meila, M. (2007) Bayesian model based clustering procedures, Journal of Multivariate Analysis 98, 873--895.

Wade, S. and Ghahramani, Z. (2015) Bayesian cluster analysis: Point estimation and credible balls. Submitted. arXiv:1505.03339.

See Also

minVI which locates the partition that minimizes the posterior expected modified VoI.

Examples

set.seed(15)
generatedData <- generateSampleDataBin(100, 4, c(0.1, 0.2, 0.3, 0.4), 25, 0)
resultforpsm <- list()
for (i in 1:5){ #use 5 initialisations
  mix <- runVICatMix(generatedData$data, 10, 0.01, tol = 0.005)
  resultforpsm[[i]] <- mix$model$labels
}
p1 <- t(matrix(unlist(resultforpsm), 100, 5))
psm <- mcclust::comp.psm(p1)

# Compute modified Variation of Information for each partition from VICatMix runs
VI.lb(p1, psm)