# Matrix Cluster Scatter Measures Functions compute two base matrix cluster scatter measures. ```r wcls.matrix(data,clust,cluster.center) bcls.matrix(cluster.center,cluster.size,mean) ``` ## Arguments - `data`: `numeric matrix` or `data.frame` where columns correspond to variables and rows to observations - `clust`: integer `vector` with information about cluster id the object is assigned to. If vector is not integer type, it will be coerced with warning. - `cluster.center`: `matrix` or `data.frame` where columns correspond to variables and rows to cluster centers defined by `data` and `clust` parameters. - `cluster.size`: integer `vector` with information about size of each cluster computed using `clust` vector. - `mean`: **mean** of all data objects. ## Details There are two base matrix scatter measures. 1. **within-cluster scatter measure** defined as: W = sum(forall k in 1:cluster.num) W(k) where W(k) = sum(forall x) (x - m(k))*(x - m(k))' ||| |:--|:--| |x|- object belongs to cluster k,| |m(k)|- center of cluster k.| 2. **between-cluster scatter measure** defined as: B = sum(forall k in 1:cluster.num) |C(k)|*( m(k) - m )*( m(k) - m )' ||| |:--|:--| |\|C(k)\||- size of cluster k,| |m(k)|- center of cluster k,| |m|- center of all data objects.| ## Returns ||| |:--|:--| |`wcls.matrix`|returns W matrix ( **within-cluster scatter measure** ),| |`bcls.matrix`|returns B matrix ( **between-cluster scatter measure** ).| ## References T. Hastie, R. Tibshirani, G. Walther **Estimating the number of data clusters via the Gap statistic**, [http://citeseer.ist.psu.edu/tibshirani00estimating.html](http://citeseer.ist.psu.edu/tibshirani00estimating.html) ## Examples ```r # load and prepare data library(clv) data(iris) iris.data <- iris[,1:4] # cluster data pam.mod <- pam(iris.data,5) # create five clusters v.pred <- as.integer(pam.mod$clustering) # get cluster ids associated to given data objects # compute cluster sizes, center of each cluster # and mean from data objects cls.attr <- cls.attrib(iris.data, v.pred) center <- cls.attr$cluster.center size <- cls.attr$cluster.size iris.mean <- cls.attr$mean # compute matrix scatter measures W.matrix <- wcls.matrix(iris.data, v.pred, center) B.matrix <- bcls.matrix(center, size, iris.mean) T.matrix <- W.matrix + B.matrix # example of indices based on W, B i T matrices mx.scatt.crit1 = sum(diag(W.matrix)) mx.scatt.crit2 = sum(diag(B.matrix))/sum(diag(W.matrix)) mx.scatt.crit3 = det(W.matrix)/det(T.matrix) ``` ## Author(s) Lukasz Nieweglowski

wcls_bcls_matrices function