msClustering: Function to perform clustering using the mean shift...
In MeanShift: Clustering via the Mean Shift Algorithm
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
This function implements the mean shift algorithm. The algorithm locates the modes of a kernel density estimator and associates each data point to exactly one of the modes, thus effectively clustering the data.
Usage
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msClustering(X, h = NULL, kernel = "epanechnikovKernel",
tol.stop = 1e-06, tol.epsilon = 0.001, multi.core = FALSE)
Arguments
X
a p \times n matrix containing n ≥ 1 p-dimensional numeric vectors stored as columns. Each column of X represents a sample point.
h
a strictly positive bandwidth parameter.
kernel
a kernel function (as a character string). The following kernels are supported:
Epanechnikov: K(x) = \frac{3}{2}(1-x^2)I_{[0,1]}(x) ; kernel="epanechnikovKernel"
cubic: K(x) = 4(1-x)^3I_{[0,1]}(x) ; kernel="cubicKernel"
Gaussian: K(x) = √{\frac{2}{π}}e^{-\frac{x^2}{2}}I_{[0,∞)}(x) ; kernel="gaussianKernel"
exponential K(x) = e^{-x}I_{[0,∞)}(x) ; kernel="exponentialKernel".
tol.stop
a strictly positive tolerance parameter. The algorithm stops when all of the updates generate steps of length smaller than tol.stop. tol.stop should be considerably smaller than tol.epsilon.
tol.epsilon
a strictly positive tolerance parameter. Points that are less than tol.epsilon- separated are grouped in the same cluster once the algorithm stops.
multi.core
logical. If TRUE, the mean shift algorithm is parallelized.
Details
It is generally recommended to standardize X so that each variable has
unit variance prior to running the algorithm on the data.
Roughly speaking, larger values of h produce a coarser clustering (i.e. few and large clusters). For sufficiently large values of h, the algorithm produces a unique cluster containing all the data points. Smaller values of h produce a finer clustering (i.e. many small clusters). For sufficiently small values of h, each cluster that is identified by the algorithm will contain exactly one data point.
If h is not specified in the function call, then h is by default set to the 30th percentile of the empirical distribution of distances between the columns of X, i.e. h=quantile( dist( t( X ) ), 0.3 ).
In their implementation, gaussianKernel and exponentialKernel are rescaled to assign probability of at least 0.99 to the unit interval [0,1]. This ensures that all the kernels are roughly on the same scale.
To specify the number of cores when multi.core=TRUE, the option
mc.cores needs to be set with options( mc.cores=n.cores ), where
n.cores is the number of cores that the mean shift algorithm is allowed to use for parallel computation.
Value
The function invisibly returns a list with names
components
a matrix containing the modes/cluster representatives by column.
labels
an integer vector of cluster labels.
Author(s)
Mattia Ciollaro and Daren Wang
References
Carreira-Perpinan, M. A. (2015) A review of mean-shift algorithms for clustering.
arXiv http://arxiv.org/abs/1503.00687
See Also
Examples
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## an example using the iris dataset
## help( iris )
## prepare data matrix (a subset of the iris dataset)
set.seed( 2 )
indices <- sample( 1:nrow( iris ), 80 )
iris.data <- t( iris[indices,c( "Sepal.Length", "Sepal.Width" )] )
## run mean shift algorithm
clustering <- msClustering( iris.data, h=0.8 )
print( clustering )
## plot the clusters
## Not run:
plot( iris.data[1,], iris.data[2,], col=clustering$labels+2, cex=0.8,
pch=16, xlab="Sepal.Length", ylab="Sepal.Width" )
points( clustering$components[1,], clustering$components[2,],
col=2+( 1:ncol( clustering$components ) ), cex=1.8, pch=16 )
## End(Not run)
## using multiple cores (2)
## Not run:
options( mc.cores=2 )
clustering.mc <- msClustering( iris.data, multi.core=TRUE )
## End(Not run)
Example output
Loading required package: parallel
Loading required package: wavethresh
Loading required package: MASS
WaveThresh: R wavelet software, release 4.6.8, installed
Copyright Guy Nason and others 1993-2016
Note: nlevels has been renamed to nlevelsWT
Running mean-shift algorithm...
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Mean-shift algorithm ran successfully.
Finding clusters...
The algorithm found 2 clusters.
$components
mode1 mode2
Sepal.Length 5.003879 6.327882
Sepal.Width 3.376633 2.999923
$labels
[1] 1 2 2 1 2 2 1 2 2 2 2 1 2 2 2 2 2 1 2 1 2 1 2 1 1 2 2 2 2 1 1 2 2 2 2 2 2 1
[39] 2 2 2 2 1 1 2 2 2 1 2 2 1 2 2 2 1 2 2 2 2 2 2 2 2 1 2 1 2 1 1 1 2 2 1 1 1 2
[77] 1 2 1 1
Running mean-shift algorithm...
Using 2 cores...
Mean-shift algorithm ran successfully.
Finding clusters...
The algorithm found 3 clusters.
MeanShift documentation built on May 29, 2017, 2:27 p.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
This function implements the mean shift algorithm. The algorithm locates the modes of a kernel density estimator and associates each data point to exactly one of the modes, thus effectively clustering the data.
Usage
1 2 | msClustering(X, h = NULL, kernel = "epanechnikovKernel",
tol.stop = 1e-06, tol.epsilon = 0.001, multi.core = FALSE)
|
Arguments
X |
a p \times n matrix containing n ≥ 1 p-dimensional numeric vectors stored as columns. Each column of |
h |
a strictly positive bandwidth parameter. |
kernel |
a kernel function (as a character string). The following kernels are supported:
|
tol.stop |
a strictly positive tolerance parameter. The algorithm stops when all of the updates generate steps of length smaller than |
tol.epsilon |
a strictly positive tolerance parameter. Points that are less than |
multi.core |
logical. If |
Details
It is generally recommended to standardize X so that each variable has
unit variance prior to running the algorithm on the data.
Roughly speaking, larger values of h produce a coarser clustering (i.e. few and large clusters). For sufficiently large values of h, the algorithm produces a unique cluster containing all the data points. Smaller values of h produce a finer clustering (i.e. many small clusters). For sufficiently small values of h, each cluster that is identified by the algorithm will contain exactly one data point.
If h is not specified in the function call, then h is by default set to the 30th percentile of the empirical distribution of distances between the columns of X, i.e. h=quantile( dist( t( X ) ), 0.3 ).
In their implementation, gaussianKernel and exponentialKernel are rescaled to assign probability of at least 0.99 to the unit interval [0,1]. This ensures that all the kernels are roughly on the same scale.
To specify the number of cores when multi.core=TRUE, the option
mc.cores needs to be set with options( mc.cores=n.cores ), where
n.cores is the number of cores that the mean shift algorithm is allowed to use for parallel computation.
Value
The function invisibly returns a list with names
components |
a matrix containing the modes/cluster representatives by column. |
labels |
an integer vector of cluster labels. |
Author(s)
Mattia Ciollaro and Daren Wang
References
Carreira-Perpinan, M. A. (2015) A review of mean-shift algorithms for clustering. arXiv http://arxiv.org/abs/1503.00687
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ## an example using the iris dataset
## help( iris )
## prepare data matrix (a subset of the iris dataset)
set.seed( 2 )
indices <- sample( 1:nrow( iris ), 80 )
iris.data <- t( iris[indices,c( "Sepal.Length", "Sepal.Width" )] )
## run mean shift algorithm
clustering <- msClustering( iris.data, h=0.8 )
print( clustering )
## plot the clusters
## Not run:
plot( iris.data[1,], iris.data[2,], col=clustering$labels+2, cex=0.8,
pch=16, xlab="Sepal.Length", ylab="Sepal.Width" )
points( clustering$components[1,], clustering$components[2,],
col=2+( 1:ncol( clustering$components ) ), cex=1.8, pch=16 )
## End(Not run)
## using multiple cores (2)
## Not run:
options( mc.cores=2 )
clustering.mc <- msClustering( iris.data, multi.core=TRUE )
## End(Not run)
|
Example output
Loading required package: parallel
Loading required package: wavethresh
Loading required package: MASS
WaveThresh: R wavelet software, release 4.6.8, installed
Copyright Guy Nason and others 1993-2016
Note: nlevels has been renamed to nlevelsWT
Running mean-shift algorithm...
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Mean-shift algorithm ran successfully.
Finding clusters...
The algorithm found 2 clusters.
$components
mode1 mode2
Sepal.Length 5.003879 6.327882
Sepal.Width 3.376633 2.999923
$labels
[1] 1 2 2 1 2 2 1 2 2 2 2 1 2 2 2 2 2 1 2 1 2 1 2 1 1 2 2 2 2 1 1 2 2 2 2 2 2 1
[39] 2 2 2 2 1 1 2 2 2 1 2 2 1 2 2 2 1 2 2 2 2 2 2 2 2 1 2 1 2 1 1 1 2 2 1 1 1 2
[77] 1 2 1 1
Running mean-shift algorithm...
Using 2 cores...
Mean-shift algorithm ran successfully.
Finding clusters...
The algorithm found 3 clusters.
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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