TY - GEN

T1 - The method of quantum clustering

AU - Horn, David

AU - Gottlieb, Assaf

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84899018126&partnerID=8YFLogxK

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AN - SCOPUS:84899018126

SN - 0262042088

SN - 9780262042086

T3 - Advances in Neural Information Processing Systems

BT - Advances in Neural Information Processing Systems 14 - Proceedings of the 2001 Conference, NIPS 2001

PB - Neural information processing systems foundation

T2 - 15th Annual Neural Information Processing Systems Conference, NIPS 2001

Y2 - 3 December 2001 through 8 December 2001

ER -