kkmeans {kernlab} | R Documentation

## Kernel k-means

### Description

A weigthed kernel version of the famous k-means algorithm.

### Usage

    ## S4 method for signature 'formula':
    kkmeans(x, data = NULL, na.action = na.omit, ...)

    ## S4 method for signature 'matrix':
    kkmeans(x, centers, kernel = "rbfdot", kpar = list(sigma = 0.1),alg="kkmeans", p=1, na.action = na.omit, ...)

    ## S4 method for signature 'kernelMatrix':
    kkmeans(x, centers, ...)

    ## S4 method for signature 'list':
    kkmeans(x, centers, kernel = "stringdot", kpar = list(length=4, lambda=0.5), alg ="kkmeans", p = 1, na.action = na.omit, ...)

### Arguments

`x` | the matrix of data to be clustered, or a symbolic description of the model to be fit, or a kernel Matrix of class `kernelMatrix`, or a list of character vectors.
`data` | an optional data frame containing the variables in the model. By default the variables are taken from the environment which `kkmeans' is called from.
`centers` | Either the number of clusters or a set of initial cluster centers. If the first, a random set of rows in the eigenvectors matrix are chosen as the initial centers.
`kernel` | the kernel function used in training and predicting. This parameter can be set to any function, of class kernel, which computes a inner product in feature space between two vector arguments (see `link{kernels}`). `kernlab` provides the most popular kernel functions which can be used by setting the kernel parameter to the following strings: `rbfdot` Radial Basis kernel "Gaussian" `polydot` Polynomial kernel `vanilladot` Linear kernel `tanhdot` Hyperbolic tangent kernel `laplacedot` Laplacian kernel `besseldot` Bessel kernel `anovadot` ANOVA RBF kernel `splinedot` Spline kernel `stringdot` String kernel Setting the kernel parameter to "matrix" treats `x` as a kernel matrix calling the `kernelMatrix` interface. The kernel parameter can also be set to a user defined function of class kernel by passing the function name as an argument.
`kpar` | a character string or the list of hyper-parameters (kernel parameters). The default character string `"automatic"` uses a heuristic the determine a suitable value for the width parameter of the RBF kernel. A list can also be used containing the parameters to be used with the kernel function. Valid parameters for existing kernels are : `sigma` inverse kernel width for the Radial Basis kernel function "rbfdot" and the Laplacian kernel "laplacedot". `degree, scale, offset` for the Polynomial kernel "polydot" `scale, offset` for the Hyperbolic tangent kernel function "tanhdot" `sigma, order, degree` for the Bessel kernel "besseldot". `sigma, degree` for the ANOVA kernel "anovadot". `length, lambda, normalized` for the "stringdot" kernel where length is the length of the strings considered, lambda the decay factor and normalized a logical parameter determining if the kernel evaluations should be normalized. Hyper-parameters for user defined kernels can be passed through the kpar parameter as well.
`alg` | the algorithm to use. Options currently include `kkmeans` and `kerninghan`.
`p` | a parameter used to keep the affinity matrix positive semidefinite
`na.action` | The action to perform on NA
`...` | additional parameters

### Details

The algorithm is implemented using the triangle inequality to avoid unnecessary and computational expensive distance calculations. This leads to significant speedup particularly on large data sets with a high number of clusters.
With a particular choice of weights this algorithm becomes equivalent to Kernighan-Lin, and the norm-cut graph partitioning algorithms.
The function also support input in the form of a kernel matrix or a list of characters for text clustering.
The data can be passed to the `kkmeans` function in a `matrix` or a `data.frame`, in addition `kkmeans` also supports input in the form of a kernel matrix of class `kernelMatrix` or as a list of character vectors where a string kernel has to be used.

### Value

An S4 object of class `specc` wich extends the class `vector` containing integers indicating the cluster to which each point is allocated. The following slots contain useful information

`centers` | A matrix of cluster centers.
`size` | The number of point in each cluster
`withinss` | The within-cluster sum of squares for each cluster
`kernelf` | The kernel function used

### Author(s)

Alexandros Karatzoglou
alexandros.karatzoglou@ci.tuwien.ac.at

### References

Inderjit Dhillon, Yuqiang Guan, Brian Kulis
A Unified view of Kernel k-means, Spectral Clustering and Graph Partitioning
UTCS Technical Report
http://www.cs.utexas.edu/users/kulis/pubs/spectral_techreport.pdf

### See Also

`specc`, `kpca`, `kcca`

### Examples

    ## Cluster the iris data set.
    data(iris)

    sc <- kkmeans(as.matrix(iris[,-5]), centers=3)

    sc
    centers(sc)
    size(sc)
    withinss(sc)

[Package kernlab version 0.8-1 Index]