qp.analyse {qp}R Documentation

Performs some exploratory analyses on the q-partial graph

Description

Using the output of qp.search this function provides some exploratory analyses on the resulting q-partial graph.

Usage

qp.analyse(qp.output, threshold, largest.clique=TRUE,
           plot.image=TRUE, exact.calculation=FALSE,
           approximation.iterations=100)

Arguments

qp.output output of qp.search
threshold threshold on the minimum non-rejection rate required for edge removal
largest.clique when this flag is set to TRUE it calculates the size of the largest clique
plot.image when this flag is set it plots the incidence matrix resulting of thresholding the non-rejection rates
exact.calculation when this flag is set to TRUE, the exact maximum clique size is calculated and when set to FALSE a lower bound is calculated instead. It applies only when largest.clique=TRUE
approximation.iterations number of iterations performed to calculate the lower bound on the clique number of each graph. It applies only when largest.clique=TRUE and \ exact.calculation=FALSE

Details

Returns an object of the class matrix showing the number of selected edges, the number of edges of the complete graph and the percentage of selected edges. When largest.clique=TRUE it gives also the size of the largest clique and when plot.image=TRUE it plots the incidence matrix resulting of thresholding the non-rejection rates.

Beware that setting largest.clique=TRUE and exact.calculation=TRUE when giving breakpoints between 0.95 and 1.0 (which may result into very dense graphs) can lead to a very long time of computation due to the NP-completeness of the problem of calculating the size of the largest clique which is therefore bounded by an exponential growth of the running time as function of the graph density (cf.~Pardalos and Xue, 1994).

The lower bound on the maximum clique size is calculated by ranking the vertices by their connectivity degree, put the first vertex in a set and go through the rest of the ranking adding those vertices to the set that form a clique with the vertices currently within the set. Once the entire ranking has been examined a large clique should have been built and hopefully the largest one. This process is repeated a number of times (approximation.iterations) each of which the ranking is altered with increasing levels of randomness acyclically (altering 1 to $p$ vertices and again). Larger values of approximation.iterations should provide tighter lower bounds and eventually the exact maximum clique size (the clique number).

Author(s)

Robert Castelo and Alberto Roverato

References

Castelo, R. and Roverato, A. (2006). A robust procedure for Gaussian graphical model search from microarray data with p larger than n, J. Mach. Learn. Res., 7:2621-2650

Pardalos, P.M. and Xue, J. (1994). The maximum clique problem, J. Global Optim., 4:301-328

See Also

qp.search, qp.clique

Examples

data(jmlr06data)
qp.analyse(qp.out.bd5.N20.q10,threshold=0.9,largest.clique=TRUE)

[Package qp version 0.2-1 Index]