Functions for mean shift, iterative mean shift, and mean shift clustering.
The main function is ms which, for a given bandwidth, detects the local modes
(`local principal points') and performs the clustering.
meanshift(X, x, h)
ms.rep(X, x, h, thresh= 0.0001, iter=200)
ms(X, h, subset, thr=0.01, scaled= 1, iter=200, plot=TRUE, ...)The main function ms produces an object of class ms,
with components:
a matrix which gives the coordinates of the estimated density modes (i.e., of the mean-shift based cluster centers).
assigns each data point to the cluster center to which its mean shift trajectory has converged.
assigns each data point to the closest cluster center in terms of Euclidean distance.
the data frame (scaled if scaled=TRUE).
the user-supplied value, could be boolean or numerical.
the data were scaled by dividing each variable through the values provided in this vector.
For all other functions, use names().
data matrix or vector.
scalar or vector-valued bandwidth (by default, 5 percent of
the data range, or 20 percent of the standard deviation, respectively, in each direction). If set manually and scaled>0, this
bandwidth needs to be set on the scaled scale; for instance setting
scaled=1 and h=0.10 will use a bandwidth of \(10\) percent of the data range in either direction.
point from which we wish to shift to the local mean.
vector specifying a subset of 1:n, where n is the sample size. This allows to run the iterative mean shift procedure only from a subset of points (if unspecified, 1:n is used here, i.e. each data point serves as a starting point).
if equal to 1 (default), each variable is divided by its range, and if equal to 2 (or any other positive value other than 1), each variable is divided by its standard deviation. If equal to 0, then no scaling is applied.
mean shift iterations are stopped when the
mean shift length (relative to the distance of of x to the overall mean; see Note section) falls below
thresh, or after iter iterations (whatever event
happens first).
adjacent mean shift clusters are merged if their relative distance falls below this threshold (see Note section).
if equal to 0, then no plotted output. For bivariate
data, plot=1 gives by default a dynamically created color plot showing the mean
shift trajectories and the resulting clustering.
further graphical parameters.
J. Einbeck. See LPCM-package for further
acknowledgements.
The methods implemented here can be used for density mode estimation, clustering, and the selection of starting points for the LPC algorithm.
Chen (1995) showed that, if the mean shift is computed iteratively, the resulting sequence of local means converges to a mode of the estimated density function. By assigning each data point to the mode to which it has converged, this turns into a clustering technique.
The concepts of coverage and self-coverage, which were originally introduced in the principal curve context, adapt straightforwardly to this setting (Einbeck, 2011).
The goodness-of-fit measure Rc can also be applied in this context. For
instance, a value of \(R_C=0.8\) means that,
after the clustering, the mean absolute residual length has been
reduced by \(80\%\) (compared to the distances to the overall mean).
Chen, Y. (1995). Mean Shift, Mode Seeking, and Clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17, 790-799.
Einbeck, J. (2011). Bandwidth selection for mean-shift based unsupervised learning techniques: a unified approach via self-coverage. Journal of Pattern Recognition Research 6, 175-192.
Rc, plot.ms
data(faithful)
# Mean shift clustering with default bandwidth (5 percent of data range)
ms(faithful)
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