Dynamic Quantum Clustering: A Tool for Unsupervised Exploration of Structures in Data

PDF Version Also Available for Download.

Description

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 through ... continued below

Physical Description

26 pages

Creation Information

Weinstein, Marvin; /SLAC; Horn, David & U., /Tel Aviv October 30, 2008.

Context

This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

Who

People and organizations associated with either the creation of this article or its content.

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this article. Follow the links below to find similar items on the Digital Library.

Description

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 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.

Physical Description

26 pages

Source

  • Journal Name: Proceedings of the National Academy of Sciences

Language

Item Type

Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

  • Report No.: SLAC-PUB-13435
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 940290
  • Archival Resource Key: ark:/67531/metadc901726

Collections

This article is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

What responsibilities do I have when using this article?

When

Dates and time periods associated with this article.

Creation Date

  • October 30, 2008

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

Description Last Updated

  • Dec. 5, 2016, 2:30 p.m.

Usage Statistics

When was this article last used?

Yesterday: 0
Past 30 days: 4
Total Uses: 9

Interact With This Article

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

Citations, Rights, Re-Use

Weinstein, Marvin; /SLAC; Horn, David & U., /Tel Aviv. Dynamic Quantum Clustering: A Tool for Unsupervised Exploration of Structures in Data, article, October 30, 2008; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc901726/: accessed September 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.