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Abstract:
We propose a novel clustering method that is an extension of
ideas inherent to scale-space clustering and support-vector
clustering. Like the latter, it associates every data point with
a vector in Hilbert space, and like the former it puts emphasis
on their total sum, that is equal to the scale-space probability
function. The novelty of our approach is the study of an operator
in Hilbert space, represented by the Schrödinger equation of
which the probability function is a solution. This
Schrödinger equation contains a potential function that can
be derived analytically from the probability function. We
associate minima of the potential with cluster centers. The
method has one variable parameter, the scale of its Gaussian
kernel. We demonstrate its applicability on known data sets. By
limiting the evaluation of the Schrödinger potential to the
locations of data points, we can apply this method to problems in
high dimensions.
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