clustComp (version 1.0.0)

flatVShier: Comparison of a hierarchical and a flat clusterings

Description

flatVShier carries out the comparison and visualisation of the relationships between a hierarchical and a flat clusterings. The hierarchical one is shown either as a complete or pruned tree, whose collapsed branches are nodes on the left hand side layer of a bi-graph. The flat clusters are represented on the right hand side. Branches and flat clusters are connected with edges, whose thickness represents the number of elements common to both sets. The number of edge crossings is minimised using the barycentre algorithm on the right hand side; also, the children corresponding to the last split in the dendrogram when exploring it by depth-first search are swapped if this decreases the number of crossings.

Usage

flatVShier(tree, flat.clustering, flat.order = NULL, max.branches = 100,  look.ahead = 2, pausing = TRUE, verbose = TRUE, h.min = 0.04, line.wd = 3,  greedy = TRUE, greedy.colours = NULL, score.function = "crossing",  expanded = FALSE, labels = NULL, cex.labels = 1, main = NULL)

Arguments

tree

an hclust object, or structure that can be converted to hclust object, corresponding to a data set of size N.

flat.clustering

a vector of length N containing the labels for each of the N objects clustered.

flat.order

an optional vector containing the initial ordering for the flat clusters (from bottom upward).

max.branches

an integer stating the maximum number of branches allowed in the dendogram.

look.ahead

the number of steps allowed to look further after finding a parent-node whose score is better that that of its children.

pausing

a Boolean argument; if TRUE, each step in the comparison is plotted and followed by a pause.

verbose

a Boolean argument; if TRUE, the situation in each iteration is described.

h.min

minimum separation between nodes in the flat layer; if the barycentre algorithm sets two nodes to be less than this distance apart, then the second node and the following ones are shifted (upwards).

line.wd

a numerical parameter that fixes the width of the thickest edge(s); the rest are drawn proportionally to their weights; 3 by default.

greedy

a Boolean argument; if TRUE, the branches produced by the optimal cutoffs are used to construct superclusters that will be mapped to superclusters on the flat side with the greedy algorithm in SCmapping.

greedy.colours

an optional vector containing the colours for each of the superclusters if the greedy algorithm is used; if the length of this vector is smaller than that of the number of resulting superclusters p, then it is recycled.

score.function

a string specifying whether the decision to split a given branch is based on the aesthetics ('crossing') or on the information theory ('it').

expanded

a Boolean parameter to state whether the hierarchical tree is displayed complete or pruned.

labels

an optional vector containing labels for the leaves of the tree.

cex.labels

a number indicating the magnification for the labels of the flat clusters and the branches in the hierarchical tree.

main

an optional character string for the title of the plot.

Value

a list of components including:

tree.partition

a vector of length N stating the branch each element belongs to.

tree.s.clustering

a vector of length N stating the supercluster on the tree side each element belongs to. If greedy=FALSE this component is not returned.

flat.s.clustering

a vector of length N stating the supercluster on the flat side each element belongs to. If greedy=FALSE this component is not returned.

tree.merging

a list of p components; the j-th element contains the labels of the tree that have been merged to produce the j-th supercluster. If greedy=FALSE this component is not returned.

flat.merging

a list of p components; the j-th element contains the labels of the flat clusters that have been merged to produce the j-th supercluster. If greedy=FALSE this component is not returned.

dendrogram

an hclust object with the appropriate ordering of the branches to minimise the number of crossings.

Details

The method cuts different branches of the tree at 'optimal' levels, which may be different at different branches, to find the best matches with the flat clustering. The method explores the tree depth-first, starting from the root. In each iteration the goal is to decide whether the branch under consideration (the parent node) is to be split. To that end, the user selects a scoring function based on the bi-graph aesthetics ('crossing') or an alternative based on mutual information between the flat and hierarchical clusterings ('it'). The selected score is first computed for the parent-node. Next it is replaced by its children; the barycentre algorithm, with the swapping strategy, is used on the flat side of the bi- graph. Later, the children in the tree are swapped and the positions on the flat side are likewise updated. The best score obtained by any of these layouts in the children tree is compared to the score of the parent-tree, sp. If it is better, then the splitting is allowed and the tree is subsequently explored. Otherwise, the splitting is discarded, unless it is allowed to look ahead. In that case, the score for the tree with one of the children of the parent-node replaced by its own children is compared to sp; this is repeated until we get a better score for the children or until the maximum number of looking-ahead steps is reached. After the optimal cut-offs are found, it is possible to run a greedy algorithm to determine sets of clusters from each side which have a large overlap. These sets, referred to as superclusters, determine the mapping between the two clusterings.

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

flatVSflat, barycentre, score.crossing, score.it, SCmapping

Examples

    # simulated data
    set.seed(0)
    dataset <- rbind(matrix(rnorm(20), 5, 4), sweep(matrix(rnorm(24), 6, 4),
        2, 1:4, "+"))
    tree <- hclust(dist(dataset))
    # two clusters
    flat <- kmeans(dataset,2)$cluster
    collapsed1 <- flatVShier(tree, flat, pausing = FALSE)
    # four clusters
    flat<-kmeans(dataset, 4)$cluster
    collapsed2 <- flatVShier(tree, flat)

    ## expanded tree
    expanded1 <- flatVShier(tree, flat, pausing = FALSE, score.function = "it",
        expanded = TRUE)