specc {kernlab} | R Documentation

## Spectral Clustering

### Description

A spectral clustering algorithm. Clustering is performed by embedding the data into the subspace of the eigenvectors of an affinity matrix.

### Usage

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

    ## S4 method for signature 'matrix'
    specc(x, centers,
          kernel = "rbfdot", kpar = "automatic",
          nystrom.red = FALSE, nystrom.sample = dim(x)[1]/6,
          iterations = 200, mod.sample = 0.75, na.action = na.omit, ...)

    ## S4 method for signature 'kernelMatrix'
    specc(x, centers, nystrom.red = FALSE, iterations = 200, ...)

    ## S4 method for signature 'list'
    specc(x, centers,
          kernel = "stringdot", kpar = list(length=4, lambda=0.5),
          nystrom.red = FALSE, nystrom.sample = length(x)/6,
          iterations = 200, mod.sample = 0.75, 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 ‘specc’ 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 computing the affinity matrix. This parameter can be set to any function, of class kernel, which computes a dot product between two vector arguments. kernlab provides the most popular kernel functions which can be used by setting the kernel parameter to the following strings:

- `rbfdot` Radial Basis kernel function "Gaussian"

- `polydot` Polynomial kernel function

- `vanilladot` Linear kernel function

- `tanhdot` Hyperbolic tangent kernel function

- `laplacedot` Laplacian kernel function

- `besseldot` Bessel kernel function

- `anovadot` ANOVA RBF kernel function

- `splinedot` Spline kernel

- `stringdot` String kernel

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 to determine a suitable value for the width parameter of the RBF kernel. The second option `"local"` (local scaling) uses a more advanced heuristic and sets a width parameter for every point in the data set. This is particularly useful when the data incorporates multiple scales. 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.

`nystrom.red` | use nystrom method to calculate eigenvectors. When `TRUE` a sample of the dataset is used to calculate the eigenvalues, thus only a n x m matrix where n the sample size is stored in memory (default: `FALSE`
`nystrom.sample` | number of data points to use for estimating the eigenvalues when using the nystrom method. (default : dim(x)[1]/6)
`mod.sample` | proportion of data to use when estimating sigma (default: 0.75)
`iterations` | the maximum number of iterations allowed.
`na.action` | the action to perform on NA
`...` | additional parameters

### Details

Spectral clustering works by embedding the data points of the partitioning problem into the subspace of the k largest eigenvectors of a normalized affinity/kernel matrix. Using a simple clustering method like `kmeans` on the embedded points usually leads to good performance. It can be shown that spectral clustering methods boil down to graph partitioning.
The data can be passed to the `specc` function in a `matrix` or a `data.frame`, in addition `specc` 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` which 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

Andrew Y. Ng, Michael I. Jordan, Yair Weiss
On Spectral Clustering: Analysis and an Algorithm
Neural Information Processing Symposium 2001
http://papers.nips.cc/paper/2092-on-spectral-clustering-analysis-and-an-algorithm.pdf

### See Also

`kkmeans`, `kpca`, `kcca`

### Examples

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

    sc <- specc(spirals, centers=2)

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

    plot(spirals, col=sc)

[Package kernlab version 0.9-27 Index]