A spectral clustering algorithm. Clustering is performed by embedding the data into the subspace of the eigenvectors of an affinity matrix.
# S4 method for formula
specc(x, data = NULL, na.action = na.omit, ...)# S4 method for 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 kernelMatrix
specc(x, centers, nystrom.red = FALSE, iterations = 200, ...)
# S4 method for 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, ...)
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.
an optional data frame containing the variables in the model. By default the variables are taken from the environment which `specc' is called from.
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.
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.
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.
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
number of data points to use for estimating the eigenvalues when using the nystrom method. (default : dim(x)[1]/6)
proportion of data to use when estimating sigma (default: 0.75)
the maximum number of iterations allowed.
the action to perform on NA
additional parameters
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
A matrix of cluster centers.
The number of point in each cluster
The within-cluster sum of squares for each cluster
The kernel function used
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.
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
# NOT RUN {
## Cluster the spirals data set.
data(spirals)
sc <- specc(spirals, centers=2)
sc
centers(sc)
size(sc)
withinss(sc)
plot(spirals, col=sc)
# }
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