VICatMix (version 1.0)

minVI: Minimize the posterior expected Variation of Information

Description

Finds a representative partition of the posterior by minimizing the lower bound to the posterior expected Variation of Information from Jensen's Inequality.

Usage

minVI(psm, cls.draw=NULL, method=c("avg","comp","draws","all"), 
      max.k=NULL)

Value

cl

clustering with minimal value of expected loss. If method="all" a matrix containing the clustering with the smallest value of the expected loss over all methods in the first row and the clusterings of the individual methods in the next rows.

value

value of posterior expected loss. A vector corresponding to the rows of cl if method="all".

method

the optimization method used.

Arguments

psm

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

cls.draw

a matrix of the samples of clusterings of the ncol(cls) data points that have been used to compute psm. Note: cls.draw has to be provided if method="draw" or "all".

method

the optimization method used. Should be one of "avg", "comp", "draws", or "all". Defaults to "avg".

max.k

integer, if method="avg" or "comp" the maximum number of clusters up to which the hierarchical clustering is cut. Defaults to ceiling(nrow(psm)/4).

Author

Sara Wade,

Details

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

We provide several optimization methods. For method="avg" and "comp", the search is restricted to the clusterings obtained from a hierarchical clustering with average/complete linkage and 1-psm as a distance matrix (the clusterings with number of clusters 1:max.k are considered).
Method "draws" restricts the search to the clusterings sampled. If method="all" all minimization methods are applied by default.

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

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)

labels_avg <- minVI(psm, method = 'avg',max.k = 10)$cl

print(labels_avg)