Kernel k-means
A weighted kernel version of the famous k-means algorithm.
## S4 method for signature 'formula'
kkmeans(x, data = NULL, na.action = na.omit, ...)
## S4 method for signature 'matrix'
kkmeans(x, centers, kernel = "rbfdot", kpar = "automatic",
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, ...)x |
the matrix of data to be clustered, or a symbolic
description of the model to be fit, or a kernel Matrix of class
|
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 matrix of initial cluster centers. If the first a random initial partitioning is used. |
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
Setting the kernel parameter to "matrix" treats 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 A list can also be used containing the parameters to be used with the kernel function. Valid parameters for existing kernels are :
Hyper-parameters for user defined kernels can be passed through the kpar parameter as well. |
alg |
the algorithm to use. Options currently include
|
p |
a parameter used to keep the affinity matrix positive semidefinite |
na.action |
The action to perform on NA |
... |
additional parameters |
kernel k-means uses the 'kernel trick' (i.e. implicitly projecting all data
into a non-linear feature space with the use of a kernel) in order to
deal with one of the major drawbacks of k-means that is that it cannot
capture clusters that are not linearly separable in input space.
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.
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 |
Alexandros Karatzoglou
alexandros.karatzoglou@ci.tuwien.ac.at
Inderjit Dhillon, Yuqiang Guan, Brian Kulis
A Unified view of Kernel k-means, Spectral Clustering and Graph
Partitioning
UTCS Technical Report
http://people.bu.edu/bkulis/pubs/spectral_techreport.pdf
## Cluster the iris data set. data(iris) sc <- kkmeans(as.matrix(iris[,-5]), centers=3) sc centers(sc) size(sc) withinss(sc)
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