Kernel mean shift clustering

Kernel mean shift clustering for 2- to 6-dimensional data.

Usage

kms(x, y, H, max.iter=400, tol.iter, tol.clust, min.clust.size, merge=TRUE,
    keep.path=FALSE, verbose=FALSE)

# S3 method for class 'kms'
plot(x, display="splom", col, col.fun, alpha=1, xlab, ylab, zlab, theta=-30, 
    phi=40, add=FALSE, ...)
# S3 method for class 'kms'
summary(object, ...)

Arguments

x: matrix of data values or object of class kms
y: matrix of candidate data values for which the mean shift will estimate their cluster labels. If missing, y=x.
H: bandwidth matrix/scalar bandwidth. If missing, Hpi(x,deriv.order=1,nstage=2-(d>2)) is called by default.
max.iter: maximum number of iterations. Default is 400.
tol.iter: distance under which two successive iterations are considered convergent. Default is 0.001*min marginal IQR of x.
tol.clust: distance under which two cluster modes are considered to form one cluster. Default is 0.01*max marginal IQR of x.
min.clust.size: minimum cluster size (cardinality). Default is 0.01*nrow(y).
merge: flag to merge clusters which are smaller than min.clust.size. Default is TRUE.
keep.path: flag to store the density gradient ascent paths. Default is FALSE.
verbose: flag to print out progress information. Default is FALSE.
object: object of class kms
display: type of display, "splom" (>=2-d) or "plot3D" (3-d)
col,col.fun: vector or colours (one for each group) or colour function
alpha: colour transparency. Default is 1.
xlab,ylab,zlab: axes labels
theta,phi: graphics parameters for perspective plots (3-d)
add: flag to add to current plot. Default is FALSE.
...: other (graphics) parameters

Value

A kernel mean shift clusters set is an object of class kms which is a list with fields:

x,y: data points - same as input
end.points: matrix of final iterates starting from y
H: bandwidth matrix
label: vector of cluster labels
nclust: number of clusters
nclust.table: frequency table of cluster labels
mode: matrix of cluster modes
names: variable names
tol.iter,tol.clust,min.clust.size: tuning parameter values - same as input
path: list of density gradient ascent paths where path[[i]] is the path of y[i,] (if keep.path=TRUE)

Details

Mean shift clustering belongs to the class of modal or density-based clustering methods. The mean shift recurrence of the candidate point \({\bold x}\) is \({\bold x}_{j+1} = {\bold x}_j + \bold{{\rm H}} {\sf D} \hat{f}({\bold x}_j)/\hat{f}({\bold x}_j)\) where \(j\geq 0\) and \({\bold x}_0 = {\bold x}\). The sequence \(\{{\bold x}_0, {\bold x}_1, \dots \}\) follows the density gradient ascent paths to converge to a local mode of the density estimate \(\hat{f}\). Hence \({\bold x}\) is iterated until it converges to its local mode, and this determines its cluster label.

The mean shift recurrence is terminated if successive iterations are less than tol.iter or the maximum number of iterations max.iter is reached. Final iterates which are less than tol.clust distance apart are considered to form a single cluster. If merge=TRUE then the clusters whose cardinality is less than min.clust.size are iteratively merged with their nearest cluster.

If the bandwidth H is missing, then the default bandwidth is the plug-in selector for the density gradient Hpi(x,deriv.order=1). Any bandwidth that is suitable for the density gradient is also suitable for the mean shift.

References

Chacon, J.E. & Duong, T. (2013) Data-driven density estimation, with applications to nonparametric clustering and bump hunting. Electronic Journal of Statistics 7, 499–532.

Comaniciu, D. & Meer, P. (2002) Mean shift: a robust approach toward feature space analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence 24, 603–619.

Examples

data(crabs, package="MASS")
kms.crabs <- kms(x=crabs[,c("FL","CW")])
plot(kms.crabs, pch=16)

summary(kms.crabs)
#> Number of clusters = 4 
#> Cluster label table = 49 51 57 43 
#> Cluster modes =
#>         FL       CW
#> 1 13.02325 32.01357
#> 2 14.90668 36.59668
#> 3 20.97492 53.83624
#> 4 14.66395 32.84520

kms.crabs <- kms(x=crabs[,c("FL","CW","RW")])
plot(kms.crabs, pch=16)

plot(kms.crabs, display="plot3D", pch=16)