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Title: Method for discovering relationships in data by dynamic quantum clustering

Abstract

Data clustering is provided according to a dynamical framework based on quantum mechanical time evolution of states corresponding to data points. To expedite computations, we can approximate the time-dependent 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 and/or feature filtering.

Inventors:
;
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1356210
Patent Number(s):
9,646,074
Application Number:
14/482,961
Assignee:
The Board of Trustees of the Leland Stanford Junior University SLAC
DOE Contract Number:
AC02-76SF00515
Resource Type:
Patent
Resource Relation:
Patent File Date: 2014 Sep 10
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Weinstein, Marvin, and Horn, David. Method for discovering relationships in data by dynamic quantum clustering. United States: N. p., 2017. Web.
Weinstein, Marvin, & Horn, David. Method for discovering relationships in data by dynamic quantum clustering. United States.
Weinstein, Marvin, and Horn, David. 2017. "Method for discovering relationships in data by dynamic quantum clustering". United States. doi:. https://www.osti.gov/servlets/purl/1356210.
@article{osti_1356210,
title = {Method for discovering relationships in data by dynamic quantum clustering},
author = {Weinstein, Marvin and Horn, David},
abstractNote = {Data clustering is provided according to a dynamical framework based on quantum mechanical time evolution of states corresponding to data points. To expedite computations, we can approximate the time-dependent 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 and/or feature filtering.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2017,
month = 5
}

Patent:

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  • Data clustering is provided according to a dynamical framework based on quantum mechanical time evolution of states corresponding to data points. To expedite computations, we can approximate the time-dependent 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 decompositionmore » and/or feature filtering.« less
  • No abstract prepared.
  • 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 with a small diffusion component. 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 throughmore » 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.« less
  • 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 amongmore » 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.« less
  • This invention relates to a method for exploring and discovering a uranium ore deposit located within a petrofluid system, comprising assaying the fluids and solids at a multiplicity of sites throughout the system with respect to at least four uranium daughter products, polonium-210, lead-210, bismuth-214, and radon-222 and thereby determining distances from the ore deposit to the assay point.