The Method of Quantum Clustering

Part of Advances in Neural Information Processing Systems 14 (NIPS 2001)

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David Horn, Assaf Gottlieb


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. 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 Schr¨odinger potential to the locations of data points, we can apply this method to problems in high dimensions.