The method of quantum clustering

David Horn, Assaf Gottlieb

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 scalespace probability function. The novelty of our approach is the study of an operator in Hilbert space, represented by the Sch R&D ie;odinger equation of which the probability function is a solution. This Sch R&D ie;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 Sch R&D ie;odinger potential to the locations of data points, we can apply this method to problems in high dimensions.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 14 - Proceedings of the 2001 Conference, NIPS 2001
PublisherNeural information processing systems foundation
ISBN (Print)0262042088, 9780262042086
StatePublished - 2002
Event15th Annual Neural Information Processing Systems Conference, NIPS 2001 - Vancouver, BC, Canada
Duration: 3 Dec 20018 Dec 2001

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258


Conference15th Annual Neural Information Processing Systems Conference, NIPS 2001
CityVancouver, BC


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