cclust: Convex Clustering In cclust: Convex Clustering Methods and Clustering Indexes

Description

The data given by `x` is clustered by an algorithm.

If `centers` is a matrix, its rows are taken as the initial cluster centers. If `centers` is an integer, `centers` rows of `x` are randomly chosen as initial values.

The algorithm stops, if no cluster center has changed during the last iteration or the maximum number of iterations (given by `iter.max`) is reached.

If `verbose` is `TRUE`, only for `"kmeans"` method, displays for each iteration the number of the iteration and the numbers of cluster indices which have changed since the last iteration is given.

If `dist` is `"euclidean"`, the distance between the cluster center and the data points is the Euclidian distance (ordinary kmeans algorithm). If `"manhattan"`, the distance between the cluster center and the data points is the sum of the absolute values of the distances of the coordinates.

If `method` is `"kmeans"`, then we have the kmeans clustering method, which works by repeatedly moving all cluster centers to the mean of their Voronoi sets. If `"hardcl"` we have the On-line Update (Hard Competitive learning) method, which works by performing an update directly after each input signal, and if `"neuralgas"` we have the Neural Gas (Soft Competitive learning) method, that sorts for each input signal the units of the network according to the distance of their reference vectors to input signal.

If `rate.method` is `"polynomial"`, the polynomial learning rate is used, that means 1/t, where t stands for the number of input data for which a particular cluster has been the winner so far. If `"exponentially decaying"`, the exponential decaying learning rate is used according to par1*{(par2/par1)}^{(iter/itermax)} where par1 and par2 are the initial and final values of the learning rate.

The parameters `rate.par` of the learning rate, where if `rate.method` is `"polynomial"` then by default `rate.par=1.0`, otherwise `rate.par=(0.5,1e-5)`.

Usage

 ```1 2``` ```cclust (x, centers, iter.max=100, verbose=FALSE, dist="euclidean", method= "kmeans", rate.method="polynomial", rate.par=NULL) ```

Arguments

 `x` Data matrix where columns correspond to variables and rows to observations `centers` Number of clusters or initial values for cluster centers `iter.max` Maximum number of iterations `verbose` If `TRUE`, make some output during learning `dist` If `"euclidean"`, then mean square error, if `"manhattan "`, the mean absolute error is used. `method` If `"kmeans"`, then we have the kmeans clustering method, if `"hardcl"` we have the On-line Update (Hard Competitive learning) method, and if `"neuralgas"`, we have the Neural Gas (Soft Competitive learning) method. Abbreviations of the method names are accepted. `rate.method` If `"kmeans"`, then k-means learning rate, otherwise exponential decaying learning rate. It is used only for the Hardcl method. `rate.par` The parameters of the learning rate.

Value

`cclust` returns an object of class `"cclust"`.

 `centers` The final cluster centers. `initcenters` The initial cluster centers. `ncenters` The number of the centers. `cluster` Vector containing the indices of the clusters where the data points are assigned to. `size` The number of data points in each cluster. `iter` The number of iterations performed. `changes` The number of changes performed in each iteration step with the Kmeans algorithm. `dist` The distance measure used. `method` The algorithm method being used. `rate.method` The learning rate being used by the Hardcl clustering method. `rate.par` The parameters of the learning rate. `call` Returns a call in which all of the arguments are specified by their names. `withinss` Returns the sum of square distances within the clusters.

Author(s)

`predict.cclust`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```## a 2-dimensional example x<-rbind(matrix(rnorm(100,sd=0.3),ncol=2), matrix(rnorm(100,mean=1,sd=0.3),ncol=2)) cl<-cclust(x,2,20,verbose=TRUE,method="kmeans") plot(x, col=cl\$cluster) ## a 3-dimensional example x<-rbind(matrix(rnorm(150,sd=0.3),ncol=3), matrix(rnorm(150,mean=1,sd=0.3),ncol=3), matrix(rnorm(150,mean=2,sd=0.3),ncol=3)) cl<-cclust(x,6,20,verbose=TRUE,method="kmeans") plot(x, col=cl\$cluster) ## assign classes to some new data y<-rbind(matrix(rnorm(33,sd=0.3),ncol=3), matrix(rnorm(33,mean=1,sd=0.3),ncol=3), matrix(rnorm(3,mean=2,sd=0.3),ncol=3)) ycl<-predict(cl, y) plot(y, col=ycl\$cluster) ```