# Systems and methods for determining optimal parameters for dynamic quantum clustering analyses

## Abstract

In the present work, quantum clustering is extended to provide a dynamical approach for data clustering using a time-dependent Schrodinger equation. 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. Additionally, the parameters of the analysis can be modified in order to improve the efficiency of the dynamic quantum clustering processes.

- Inventors:

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1493569

- Patent Number(s):
- 10,169,445

- Application Number:
- 14/492,677

- Assignee:
- The Board of Trustees of the Leland Stanford Junior University (Stanford, CA) (United States) SLAC

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Patent

- Resource Relation:
- Patent File Date: 2014 Sep 22

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Weinstein, Marvin, and Horn, David.
```*Systems and methods for determining optimal parameters for dynamic quantum clustering analyses*. United States: N. p., 2019.
Web.

```
Weinstein, Marvin, & Horn, David.
```*Systems and methods for determining optimal parameters for dynamic quantum clustering analyses*. United States.

```
Weinstein, Marvin, and Horn, David. Tue .
"Systems and methods for determining optimal parameters for dynamic quantum clustering analyses". United States. https://www.osti.gov/servlets/purl/1493569.
```

```
@article{osti_1493569,
```

title = {Systems and methods for determining optimal parameters for dynamic quantum clustering analyses},

author = {Weinstein, Marvin and Horn, David},

abstractNote = {In the present work, quantum clustering is extended to provide a dynamical approach for data clustering using a time-dependent Schrodinger equation. 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. Additionally, the parameters of the analysis can be modified in order to improve the efficiency of the dynamic quantum clustering processes.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2019},

month = {1}

}

Works referenced in this record:

##
Method and apparatus for clustering data

patent, February 2000

- Domany, Eyran; Blatt, Marcelo; Wiseman, Shai
- US Patent Document 6,021,383

##
Image segmentation using statistical clustering with saddle point detection

patent, August 2007

- Camaniciu, Dorin; Ramesh, Visvanathan
- US Patent Document 7,260,259

##
Systems, methods, and devices having stretchable integrated circuitry for sensing and delivering therapy

patent, September 2013

- de Graff, Bassel; Ghaffari, Roozbeh; Arora, William J.
- US Patent Document 8,536,667

##
Quantum clustering algorithms

conference, June 2007

- A�meur, Esma; Brassard, Gilles; Gambs, S�bastien
- Proceedings of the 24th international conference on Machine learning

##
Singular value decomposition for genome-wide expression data processing and modeling

journal, August 2000

- Alter, O.; Brown, P. O.; Botstein, D.
- Proceedings of the National Academy of Sciences, Vol. 97, Issue 18, p. 10101-10106

##
Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale methods

journal, May 2005

- Coifman, R. R.; Lafon, S.; Lee, A. B.
- Proceedings of the National Academy of Sciences, Vol. 102, Issue 21, p. 7432-7437

##
Molecular Classification of Cancer: Class Discovery and Class Prediction by Gene Expression Monitoring

journal, October 1999

- Golub, T. R.
- Science, Vol. 286, Issue 5439, p. 531-537

##
Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization

journal, September 2006

- Lafon, S.; Lee, A. B.
- IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 28, Issue 9, p. 1393-1403

##
Diffusion maps, spectral clustering and reaction coordinates of dynamical systems

journal, July 2006

- Nadler, Boaz; Lafon, St�phane; Coifman, Ronald R.
- Applied and Computational Harmonic Analysis, Vol. 21, Issue 1, p. 113-127

##
Self-Organizing Data Clustering Based on Quantum Entanglement Model

conference, June 2006

- Shuai, Dianxun; Liu, Yuzhe; Shuai, Qing
- Computer and Computational Sciences, 2006. IMSCCS '06. First International Multi-Symposiums on

##
Novel Unsupervised Feature Filtering of Biological Data

journal, July 2006

- Varshavsky, R.; Gottlieb, A.; Linial, M.
- Bioinformatics, Vol. 22, Issue 14, p. e507-e513

##
Learning from text: Matching readers and texts by latent semantic analysis

journal, January 1998

- Wolfe, Michael B.W.; Schreiner, M.E.; Rehder, Bob
- Discourse Processes, Vol. 25, Issue 2-3, p. 309-336

##
Parametric and non-parametric unsupervised cluster analysis

journal, February 1997

- Roberts, Stephen J.
- Pattern Recognition, Vol. 30, Issue 2, p. 261-272

##
Entanglement Partitioning of Quantum Particles for Data Clustering

conference, September 2006

- Shuai, Dianxun; Lu, Cunpai; Zhang, Bin
- Computer Software and Applications Conference, 2006. COMPSAC '06. 30th Annual International