Description Usage Arguments Details Value Author(s) References See Also Examples

Finds a representative partition of the posterior by minimizing the posterior expected loss with possible loss function of Binder's loss, the Variation of Information, and the modified Variation of Information through a greedy search algorithm.

1 2 |

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

`cls.draw` |
a matrix of the MCMC samples of clusterings of the |

`loss` |
the loss function used. Should be one of |

`start.cl` |
clustering used as starting point. If |

`maxiter` |
integer, maximum number of iterations. Defaults to |

`L` |
integer, specifies the number of local partitions considered at each iteration. Defaults to |

`suppress.comment` |
logical, for |

This function is called by `minVI`

and `minbinder.ext`

to optimize the posterior expected loss via a greedy search algorithm. Possible loss functions include Binder's loss (`"Binder"`

) and the Variation of Information (`"VI"`

). As computation of the posterior expected Variation of Information is expensive, a third option (`"VI.lb"`

) is to minimize a modified Variation of Information by swapping the log and expectation. From Jensen's inequality, this can be viewed as minimizing a lower bound to the posterior expected Variation of Information.

At each iteration of the algorithm, we consider the `L`

closest ancestors or descendants and move in the direction of minimum posterior expected; the distance is measured by Binder's loss or the Variation of Information, depending on the choice of `loss`

. We recommend trying different starting locations `cl.start`

and values of `l`

that control the amount of local exploration. A description of the algorithm at every iteration is printed if `suppress.comment=FALSE`

.

`cl` |
clustering with minimal value of expected loss. |

`value` |
value of posterior expected loss. |

`iter.greedy` |
the number of iterations the method needed to converge. |

Sara Wade, sara.wade@eng.cam.ac.uk

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

`minVI`

or `minbinder.ext`

which call `greedy`

to find the point estimate that minimizes the posterior expected loss.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
data(ex1.data)
x=ex1.data[,c(1,2)]
cls.true=ex1.data$cls.true
plot(x[,1],x[,2],xlab="x1",ylab="x2")
k=max(cls.true)
for(l in 2:k){
points(x[cls.true==l,1],x[cls.true==l,2],col=l)}
# Find representative partition of posterior
data(ex1.draw)
psm=comp.psm(ex1.draw)
ex1.VI=minVI(psm,method=("greedy"),suppress.comment=FALSE)
summary(ex1.VI)
# Different initlization
ex1.VI.v2=minVI(psm,method=("greedy"),suppress.comment=FALSE,start.cl=ex1.draw[nrow(ex1.draw),])
summary(ex1.VI.v2)
``` |

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