Dynamic quantum clustering: a tool for visual exploration of structures in data

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A given set of data-points in some feature space may be associated with a Schroedinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schroedinger equation. Moreover, we approximate this Hamiltonian formalism by a truncated calculation within a set of Gaussian wave functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among ... continued below

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38 pages

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Weinstein, Marvin; /SLAC; Horn, David & U., /Tel Aviv October 17, 2009.

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A given set of data-points in some feature space may be associated with a Schroedinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schroedinger equation. Moreover, we approximate this Hamiltonian formalism by a truncated calculation within a set of Gaussian wave functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition or feature filtering.

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38 pages

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  • Journal Name: Submitted to Physical Review E

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  • Report No.: SLAC-PUB-13759
  • Grant Number: AC02-76SF00515
  • DOI: 10.1103/PhysRevE.80.066117 | External Link
  • Office of Scientific & Technical Information Report Number: 968525
  • Archival Resource Key: ark:/67531/metadc927264

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  • October 17, 2009

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 15, 2016, 3:23 p.m.

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Weinstein, Marvin; /SLAC; Horn, David & U., /Tel Aviv. Dynamic quantum clustering: a tool for visual exploration of structures in data, article, October 17, 2009; United States. (digital.library.unt.edu/ark:/67531/metadc927264/: accessed November 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.