# Cut a Minimax Linkage Tree To Get a Clustering Cuts a minimax linkage tree to get one of n - 1 clusterings. Works like `cutree` except also returns the prototypes of the resulting clustering. ```r protocut(hc, k = NULL, h = NULL) ``` ## Arguments - `hc`: an object returned by `protoclust` - `k`: the number of clusters desired - `h`: the height at which to cut the tree ## Returns A list corresponding to the clustering from cutting tree: - **cl**: vector of cluster memberships - **protos**: vector of prototype indices corresponding to the k clusters created. `protos[i]` gives the index of the prototype for all elements with `cl==i` - **imerge**: vector describing the nodes where prototypes occur. We use the naming convention of the `merge` matrix in `hclust`: if `imerge[i]` is positive, it is the interior node (counting from the bottom) of the cluster with elements `which(cl==i)`; if `imerge[i]` is negative, then this is a singleton cluster with a leaf as prototype. ## Details Given a minimax linkage hierarchical clustering, this function cuts the tree at a given height or so that a specified number of clusters is created. It returns both the indices of the prototypes and their locations. This latter information is useful for plotting a dendrogram with prototypes (see `plotwithprototypes`). As with `cutree`, if both k and h are given, h is ignored. Unlike `cutree`, in current version k and h cannot be vectors. ## Examples ```r # generate some data: set.seed(1) n <- 100 p <- 2 x <- matrix(rnorm(n * p), n, p) rownames(x) <- paste("A", 1:n, sep="") d <- dist(x) # perform minimax linkage clustering: hc <- protoclust(d) # cut the tree to yield a 10-cluster clustering: k <- 10 # number of clusters cut <- protocut(hc, k=k) h <- hc$height[n - k] # plot dendrogram (and show cut): plotwithprototypes(hc, imerge=cut$imerge, col=2) abline(h=h, lty=2) # get the prototype assigned to each point: pr <- cut$protos[cut$cl] # find point farthest from its prototype: dmat <- as.matrix(d) ifar <- which.max(dmat[cbind(1:n, pr[1:n])]) # note that this distance is exactly h: stopifnot(dmat[ifar, pr[ifar]] == h) # since this is a 2d example, make 2d display: plot(x, type="n") points(x, pch=20, col="lightblue") lines(rbind(x[ifar, ], x[pr[ifar], ]), col=3) points(x[cut$protos, ], pch=20, col="red") text(x[cut$protos, ], labels=hc$labels[cut$protos], pch=19) tt <- seq(0, 2 * pi, length=100) for (i in cut$protos) { lines(x[i, 1] + h * cos(tt), x[i, 2] + h * sin(tt)) } ``` ## References Bien, J., and Tibshirani, R. (2011), "Hierarchical Clustering with Prototypes via Minimax Linkage," **The Journal of the American Statistical Association**, 106(495), 1075-1084. ## See Also `protoclust`, `cutree`, `plotwithprototypes` ## Author(s) Jacob Bien and Rob Tibshirani

protocut function