qkspecc {qkerntool}

qkernel spectral Clustering

Description

A qkernel spectral clustering algorithm. Clustering is performed by embedding the data into the subspace of the eigenvectors of a graph Laplacian matrix.

Usage

## S4 method for signature 'matrix'
qkspecc(x,kernel = "rbfbase", qpar = list(sigma = 2, q = 0.9),
          Nocent=NA, normalize="symmetric", maxk=20, iterations=200,
          na.action = na.omit, ...)

## S4 method for signature 'cndkernmatrix'
qkspecc(x, Nocent=NA, normalize="symmetric",
          maxk=20,iterations=200, ...)

## S4 method for signature 'qkernmatrix'
qkspecc(x, Nocent=NA, normalize="symmetric",
          maxk=20,iterations=200, ...)

Arguments

x

the matrix of data to be clustered or a kernel Matrix of class qkernmatrix or cndkernmatrix.

kernel

the kernel function used in computing the affinity matrix. This parameter can be set to any function, of class kernel, which computes a kernel function value between two vector arguments. kernlab provides the most popular kernel functions which can be used by setting the kernel parameter to the following strings:

• rbfbase Radial Basis qkernel function "Gaussian"

• nonlbase Non Linear qkernel function

• laplbase Laplbase qkernel function

• ratibase Rational Quadratic qkernel function

• multbase Multiquadric qkernel function

• invbase Inverse Multiquadric qkernel function

• wavbase Wave qkernel function

• powbase d qkernel function

• logbase Log qkernel function

• caubase Cauchy qkernel function

• chibase Chi-Square qkernel function

• studbase Generalized T-Student qkernel function

• nonlcnd Non Linear cndkernel function

• polycnd Polynomial cndkernel function

• rbfcnd Radial Basis cndkernel function "Gaussian"

• laplcnd Laplacian cndkernel function

• anocnd ANOVA cndkernel function

• raticnd Rational Quadratic cndkernel function

• multcnd Multiquadric cndkernel function

• invcnd Inverse Multiquadric cndkernel function

• wavcnd Wave cndkernel function

• powcnd d cndkernel function

• logcnd Log cndkernel function

• caucnd Cauchy cndkernel function

• chicnd Chi-Square cndkernel function

• studcnd Generalized T-Student cndkernel function

The kernel parameter can also be set to a user defined function of class kernel by passing the function name as an argument.

qpar

a character string or the list of hyper-parameters (kernel parameters). The default character string list(sigma = 2, q = 0.9) 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, q for the Radial Basis qkernel function "rbfbase" , the Laplacian qkernel function "laplbase" and the Cauchy qkernel function "caubase".

• alpha, q for the Non Linear qkernel function "nonlbase".

• c, q for the Rational Quadratic qkernel function "ratibase" , the Multiquadric qkernel function "multbase" and the Inverse Multiquadric qkernel function "invbase".

• theta, q for the Wave qkernel function "wavbase".

• d, q for the d qkernel function "powbase" , the Log qkernel function "logbase" and the Generalized T-Student qkernel function "studbase".

• alpha for the Non Linear cndkernel function "nonlcnd".

• d, alpha, c for the Polynomial cndkernel function "polycnd".

• gamma for the Radial Basis cndkernel function "rbfcnd" and the Laplacian cndkernel function "laplcnd" and the Cauchy cndkernel function "caucnd".

• d, sigma for the ANOVA cndkernel function "anocnd".

• c for the Rational Quadratic cndkernel function "raticnd" , the Multiquadric cndkernel function "multcnd" and the Inverse Multiquadric cndkernel function "invcnd".

• theta for the Wave cndkernel function "wavcnd".

• d for the d cndkernel function "powcnd" , the Log cndkernel function "logcnd" and the Generalized T-Student cndkernel function "studcnd". 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 qpar parameter as well.

Nocent

the number of clusters.

normalize

Normalisation of the Laplacian ("none", "symmetric" or "random-walk").

maxk

If k is NA, an upper bound for the automatic estimation. Defaults to 20.

iterations

the maximum number of iterations allowed.

na.action

the action to perform on NA.

...

additional parameters.

Details

The qkernel spectral clustering works by embedding the data points of the partitioning problem into the subspace of the eigenvectors corresponding to the k smallest eigenvalues of the graph Laplacian matrix. Using a simple clustering method like kmeans on the embedded points usually leads to good performance. It can be shown that qkernel spectral clustering methods boil down to graph partitioning.
The data can be passed to the qkspecc function in a matrix, in addition qkspecc also supports input in the form of a kernel matrix of class qkernmatrix or cndkernmatrix.

Value

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

clust

The cluster assignments

eVec

The corresponding eigenvector

eVal

The corresponding eigenvalues

ymatrix

The eigenvectors corresponding to the k smallest eigenvalues of the graph Laplacian matrix.

Author(s)

Yusen Zhang
[e-mail]

References

Andrew Y. Ng, Michael I. Jordan, Yair Weiss
On Spectral Clustering: Analysis and an Algorithm
Neural Information Processing Symposium 2001

See Also

qkernmatrix, cndkernmatrix, qkpca

Examples

data("iris")
x=as.matrix(iris[,-5])

qspe <- qkspecc(x,kernel = "rbfbase", qpar = list(sigma = 10, q = 0.9),
                Nocent=3, normalize="symmetric", maxk=15, iterations=1200)
plot(x, col = clust(qspe))

qkfunc <- nonlbase(alpha=1/15,q=0.8)
Ktrain <- qkernmatrix(qkfunc, x)
qspe <- qkspecc(Ktrain, Nocent=3, normalize="symmetric", maxk=20)
plot(x, col = clust(qspe))