Bclust function

Bootstrapped hclust

Bootstraps (or jacknifes) hierarchical clustering

Bclust(data, method.d="euclidean", method.c="ward.D", FUN=function(.x)
 hclust(dist(.x, method=method.d), method=method.c),iter=1000,
 mc.cores=1, monitor=TRUE, bootstrap=TRUE, relative=FALSE, hclist=NULL)

## S3 method for class 'Bclust'
plot(x, main="", xlab=NULL, ...)

Arguments

• data: Data suitable for the chosen distance method
• method.d: Method for dist()
• method.c: Method for hclust()
• FUN: Function to make 'hclust' objects
• iter: Number of replicates
• mc.cores: integer, number of processes to run in parallel
• monitor: If TRUE (default), prints a dot for each replicate
• bootstrap: If FALSE (not default), performs jacknife (and makes 'iter=ncol(data)')
• relative: If TRUE (not default), use the relative matching of branches (see in Details)
• hclist: Allows to supply the list of 'hclust' objects
• x: Object of the class 'Bclust'
• main: Plot title
• xlab: Horizontal axis label
• ...: Additional arguments to the plot.hclust()

Returns

Returns object of class 'Bclust' which is a list with components: 'values' for bootstrapped frequencies of each node, 'hcl' for original 'hclust' object, 'consensus' which is a sum of all Hcl2mat() matrices, 'meth' (bootstrap or jacknife), and 'iter', for number of iterations.

Details

This function provides bootstrapping for hierarchical clustering (hclust objects). Internally, it uses Hcl2mat() which converts 'hclust' objects into binary matrix of cluster memberships.

The default clustering method is the variance-minimizing "ward.D" (which works better with Euclidean distances); to make it coherent with hclust() default, specify 'method.c="complete"'. Also, it sometimes makes sense to transform non-Euclidean distances into Euclidean with 'dist(non_euclidean_dist)'.

Bclust() and companion functions were based on functions from the 'bootstrap' package of Sebastian Gibb.

Option 'hclist' presents the special case when list of 'hclust' objects is pre-build. In that case, other arguments (except 'mc.cores' and 'monitor') will be ignored, and the first component of 'hclist', that is 'hclist[[1]]', will be used as "original" clustering to compare with all other objects in the 'hclist'. Number of replicates is the length of 'hclist' minus one.

Option 'relative' changes the mechanism of how branches of reference clustering ("original") and bootstrapped clustering ("current") compared. If 'relative=FALSE' (default), only absolute matches (present or absent) are count, and vector of matches is binary (either 0 or 1). If 'relative=TRUE', branches of "original" which have no matches in "current", are checked additionally for the similarity with all branches of "current", and the minimal (asymmetric) binary dissimilarity value is used as a match. Therefore, the matching vector in this case is numeric instead of binary. This will typically result in the reliable raising of bootstrap values. The underlying methodology is similar to what is defined in Lemoine et al. (2018) as a "transfer bootstrap". As the asymmetric binary is the proportion of items in which only one is "1" amongst those which have one or two "1", it is possible to rephrase Lemoine et al. (2018), and say that this distance is equal to the proportion of items that must be removed to make both branches identical. Please note that with 'relative=TRUE', the whole algorithm is several times slower then default.

Please note that Bclust() frequently underestimates the cluster stability when number of characters is relatively small. One of possible remedies is to use hyper-binding (like "cbind(data, data, data)") to reach the reliable number of characters.

plot.Bclust() designed for quick plotting and plots labels (bootstrap support values) with the following defaults: 'percent=TRUE, pos=3, offset=0.1'. To change how labels are plotted, use separate Bclabels() command.

References

Felsenstein J. 1985. Confidence limits on phylogenies: an approach using the bootstrap. Evolution. 39 (4): 783--791.

Efron B., Halloran E., Holmes S. 1996. Bootstrap confidence levels for phylogenetic trees. Proceedings of the National Academy of Sciences. 93 (23): 13429--13429.

Lemoine F. et al. 2018. Renewing Felsenstein's phylogenetic bootstrap in the era of big data. Nature, 556(7702): 452--456

See Also

Jclust, BootA, Hcl2mat, Bclabels, Hcoords

Examples

data <- t(atmospheres)

## standard use
(bb <- Bclust(data)) # specify 'mc.cores=4' or similar to speed up the process
plot(bb)

## more advanced plotting with Bclabels()
plot(bb$hclust)
Bclabels(bb$hclust, bb$values, threshold=0.5, col="grey", pos=1)

## how to use the consensus data
plot(hclust(dist(bb$consensus)), main="Net consensus tree") # net consensus
## majority rule is 'consensus >= 0.5', strict is like 'round(consensus) == 1'

## how to make user-defined function
bb1 <- Bclust(t(atmospheres), FUN=function(.x) hclust(Gower.dist(.x)))
plot(bb1)

## how to jacknife
bb2 <- Bclust(data, bootstrap=FALSE, monitor=FALSE)
plot(bb2)

## how to make (and use) the pre-build list of clusterings
hclist <- vector("list", length=0)
hclist[[1]] <- hclust(dist(data)) # "orig" is the first
for (n in 2:101) hclist[[n]] <- hclust(dist(data[, sample.int(ncol(data), replace=TRUE)]))
(bb3 <- Bclust(hclist=hclist))
plot(bb3)

## how to use the relative matching
bb4 <- Bclust(data, relative=TRUE)
plot(bb4)

## how to hyper-bind
bb5 <- Bclust(cbind(data, data, data)) # now data has 24 characters
plot(bb5)

## how to use hclust() defaults
bb6 <- Bclust(data, method.c="complete")
plot(bb6)