The Method of Quantum Clustering

We propose a novel clustering method that is an extension of ideas inher- ent to scale-space clustering and support-vector clustering. Like the lat- ter, 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 Schr odinger equation of which the probability function is a solution. This Schr odinger equation contains a potential function that can be derived analytically from the probability function. The method has one variable parameter, the scale of its Gaussian kernel.