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Title: Nonnegative/Binary matrix factorization with a D-Wave quantum annealer

Abstract

D-Wave quantum annealers represent a novel computational architecture and have attracted significant interest. Much of this interest has focused on the quantum behavior of D-Wave machines, and there have been few practical algorithms that use the D-Wave. Machine learning has been identified as an area where quantum annealing may be useful. Here, we show that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method. This method takes a matrix as input and produces two low-rank matrices as output—one containing latent features in the data and another matrix describing how the features can be combined to approximately reproduce the input matrix. Despite the limited number of bits in the D-Wave hardware, this method is capable of handling a large input matrix. The D-Wave only limits the rank of the two output matrices. We apply this method to learn the features from a set of facial images and compare the performance of the D-Wave to two classical tools. This method is able to learn facial features and accurately reproduce the set of facial images. The performance of the D-Wave shows some promise, but has some limitations. It outperforms the two classical codes in a benchmark whenmore » only a short amount of computational time is allowed (200-20,000 microseconds), but these results suggest heuristics that would likely outperform the D-Wave in this benchmark.« less

Authors:
ORCiD logo; ; ; ;
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1485190
Alternate Identifier(s):
OSTI ID: 1489946
Report Number(s):
LA-UR-17-22557
Journal ID: ISSN 1932-6203; 10.1371/journal.pone.0206653
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Published Article
Journal Name:
PLoS ONE
Additional Journal Information:
Journal Name: PLoS ONE Journal Volume: 13 Journal Issue: 12; Journal ID: ISSN 1932-6203
Publisher:
Public Library of Science (PLoS)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Computer Science; Mathematics

Citation Formats

O’Malley, Daniel, Vesselinov, Velimir V., Alexandrov, Boian S., Alexandrov, Ludmil B., and Olier, ed., Ivan. Nonnegative/Binary matrix factorization with a D-Wave quantum annealer. United States: N. p., 2018. Web. https://doi.org/10.1371/journal.pone.0206653.
O’Malley, Daniel, Vesselinov, Velimir V., Alexandrov, Boian S., Alexandrov, Ludmil B., & Olier, ed., Ivan. Nonnegative/Binary matrix factorization with a D-Wave quantum annealer. United States. https://doi.org/10.1371/journal.pone.0206653
O’Malley, Daniel, Vesselinov, Velimir V., Alexandrov, Boian S., Alexandrov, Ludmil B., and Olier, ed., Ivan. Mon . "Nonnegative/Binary matrix factorization with a D-Wave quantum annealer". United States. https://doi.org/10.1371/journal.pone.0206653.
@article{osti_1485190,
title = {Nonnegative/Binary matrix factorization with a D-Wave quantum annealer},
author = {O’Malley, Daniel and Vesselinov, Velimir V. and Alexandrov, Boian S. and Alexandrov, Ludmil B. and Olier, ed., Ivan},
abstractNote = {D-Wave quantum annealers represent a novel computational architecture and have attracted significant interest. Much of this interest has focused on the quantum behavior of D-Wave machines, and there have been few practical algorithms that use the D-Wave. Machine learning has been identified as an area where quantum annealing may be useful. Here, we show that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method. This method takes a matrix as input and produces two low-rank matrices as output—one containing latent features in the data and another matrix describing how the features can be combined to approximately reproduce the input matrix. Despite the limited number of bits in the D-Wave hardware, this method is capable of handling a large input matrix. The D-Wave only limits the rank of the two output matrices. We apply this method to learn the features from a set of facial images and compare the performance of the D-Wave to two classical tools. This method is able to learn facial features and accurately reproduce the set of facial images. The performance of the D-Wave shows some promise, but has some limitations. It outperforms the two classical codes in a benchmark when only a short amount of computational time is allowed (200-20,000 microseconds), but these results suggest heuristics that would likely outperform the D-Wave in this benchmark.},
doi = {10.1371/journal.pone.0206653},
journal = {PLoS ONE},
number = 12,
volume = 13,
place = {United States},
year = {2018},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1371/journal.pone.0206653

Citation Metrics:
Cited by: 3 works
Citation information provided by
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Figures / Tables:

Fig. 1 Fig. 1: Face image reconstruction using features learned by NBMF. The five-by-seven matrix of images on the right shows the features that were learned. The two images on the left show the original image (top) and the reconstruction (bottom). The reconstruction is obtained by summing the features that are boxedmore » in green. Note that although some of the features appear to be all black, they actually contain facial features that are small in magnitude (black corresponds to 0, white corresponds to 1).« less

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