clustComp (version 1.0.0)

score.crossing: Computation of the aesthetics-based score of the parent and the children trees

Description

score.crossing computes the value of the scoring function based on the aesthetics of the bi-graph formed when comparing a dendrogram and a flat clustering, for both the parent-tree and the children-tree; the children-tree consists of the same branches as the parent-tree, except for the parent node, that has been split and replaced by some of its descendants.

Usage

score.crossing(weight.1, weight.2, N.cross)

Arguments

weight.1

a matrix of dimension (m-1)xn containing the intersection sizes (edge weights) between branches in the parent-tree and clusters from the flat partitioning. The ordering of the rows and columns is irrelevant for the computation of the score.

weight.2

a matrix of dimension (m+k)xn containing the intersection sizes (edge weights) between branches in the children-tree and clusters from the flat partitioning. k takes on values in 0,1,...,L, where L is the maximum number of steps that the comparison algorithm is allowed to look ahead. The ordering of the rows corresponding to branches that are not descendants of the parent node must coincide with that of the matrix weight.1 after discarding the parent node. The ordering of the columns is irrelevant for the computation of the score.

N.cross

the number of edge crossings induced in the subtree formed by the descendants of the parent-node.

Value

a list containing the following components:

sc1

the value of the scoring function for the parent-tree.

sc2

the value of the scoring function for the children-tree.

Details

The decision to split a given parent-node is based on achieving a better score for the children-tree than for the parent-tree. In the case of score.crossing, a better score is reflected by a larger value of the scoring function, which rewards few thicker edges, penalises many smaller edges, and accounts for the number of edge crossings in the resulting bigraph. The descendants of the parent-node considered in the children-tree are its two children if no look-ahead is carried out; otherwise, the descendants will reach subsequent generations and their number will increase by one at each look-ahead step.

References

Torrente, A. et al. (2005). A new algorithm for comparing and visualizing relationships between hierarchical and flat gene expression data clusterings. Bioinformatics, 21 (21), 3993-3999.

See Also

score.it, dyn.cross, flatVShier

Examples

    ### simulated data
    parent.clustering <- c(rep("B1", 5), rep("B2", 10), rep("B3", 10))
    # replace the branch 'B2' by its children 'B4' and 'B5'
    children.clustering <- c(rep("B1", 5), rep("B4", 3), rep("B5", 7),
        rep("B3", 10))
    flat.clustering <- c(rep(1, 6), rep(2, 6), rep(3, 4), rep(4, 9))
    # the ordering of flat clusters is '1','2','3' and '4'.
    parent.weights <- table(parent.clustering, flat.clustering)
    children.weights <- table(children.clustering, flat.clustering)
    descendant.cross <- dyn.cross(children.weights[c('B4', 'B5'), ])
    score.crossing(parent.weights, children.weights, descendant.cross) 
    ## better score for the parent.tree