A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

Lu Bai; Luca Rossi; Peng Ren; Zhihong Zhang; Edwin R. Hancock

doi:10.1007/978-3-319-18224-7_25

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

Lu Bai, Luca Rossi, Peng Ren, Zhihong Zhang, Edwin R. Hancock

College of Engineering and Physical Sciences

Research output: Chapter in Book/Published conference output › Conference publication

Abstract

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Original language	English
Title of host publication	Graph-based representations in pattern recognition
Subtitle of host publication	10th IAPR-TC-15 international workshop, GbRPR 2015, Beijing, China, May 13-15, 2015. Proceedings
Editors	Cheng-Lin Liu, Bin Luo, Walter G. Kropatsch, Jian Cheng
Place of Publication	Chem (CH)
Publisher	Springer
Pages	252-261
Number of pages	10
ISBN (Electronic)	978-3-319-18224-7
ISBN (Print)	978-3-319-18223-0
DOIs	https://doi.org/10.1007/978-3-319-18224-7_25
Publication status	Published - 2015
Event	10th IAPR-TC-15 international workshop, GbRPR 2015 - Beijing, China Duration: 13 May 2015 → 15 May 2015

Publication series

Name	Lecture notes in computer science
Publisher	Springer
Volume	9069
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Workshop

Workshop	10th IAPR-TC-15 international workshop, GbRPR 2015
Country/Territory	China
City	Beijing
Period	13/05/15 → 15/05/15

Bibliographical note

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-18224-7_25

Funding: UK Royal Society

Access to Document

10.1007/978-3-319-18224-7_25

Quantum Jensen-Shannon graph kernel using discrete-time quantum walks
The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-18224-7_25
Accepted author manuscript, 108 KB

http://link.springer.com/chapter/10.1007%2F978-3-319-18224-7_25

Cite this

Bai, L., Rossi, L., Ren, P., Zhang, Z., & Hancock, E. R. (2015). A quantum Jensen-Shannon graph kernel using discrete-time quantum walks. In C-L. Liu, B. Luo, W. G. Kropatsch, & J. Cheng (Eds.), Graph-based representations in pattern recognition: 10th IAPR-TC-15 international workshop, GbRPR 2015, Beijing, China, May 13-15, 2015. Proceedings (pp. 252-261). (Lecture notes in computer science ; Vol. 9069). Springer. https://doi.org/10.1007/978-3-319-18224-7_25

Bai, Lu ; Rossi, Luca ; Ren, Peng et al. / A quantum Jensen-Shannon graph kernel using discrete-time quantum walks. Graph-based representations in pattern recognition: 10th IAPR-TC-15 international workshop, GbRPR 2015, Beijing, China, May 13-15, 2015. Proceedings. editor / Cheng-Lin Liu ; Bin Luo ; Walter G. Kropatsch ; Jian Cheng. Chem (CH) : Springer, 2015. pp. 252-261 (Lecture notes in computer science ).

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title = "A quantum Jensen-Shannon graph kernel using discrete-time quantum walks",

abstract = "In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.",

author = "Lu Bai and Luca Rossi and Peng Ren and Zhihong Zhang and Hancock, {Edwin R.}",

note = "The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-18224-7_25 Funding: UK Royal Society; 10th IAPR-TC-15 international workshop, GbRPR 2015 ; Conference date: 13-05-2015 Through 15-05-2015",

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isbn = "978-3-319-18223-0",

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Bai, L, Rossi, L, Ren, P, Zhang, Z & Hancock, ER 2015, A quantum Jensen-Shannon graph kernel using discrete-time quantum walks. in C-L Liu, B Luo, WG Kropatsch & J Cheng (eds), Graph-based representations in pattern recognition: 10th IAPR-TC-15 international workshop, GbRPR 2015, Beijing, China, May 13-15, 2015. Proceedings. Lecture notes in computer science , vol. 9069, Springer, Chem (CH), pp. 252-261, 10th IAPR-TC-15 international workshop, GbRPR 2015, Beijing, China, 13/05/15. https://doi.org/10.1007/978-3-319-18224-7_25

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks. / Bai, Lu; Rossi, Luca; Ren, Peng et al.
Graph-based representations in pattern recognition: 10th IAPR-TC-15 international workshop, GbRPR 2015, Beijing, China, May 13-15, 2015. Proceedings. ed. / Cheng-Lin Liu; Bin Luo; Walter G. Kropatsch; Jian Cheng. Chem (CH): Springer, 2015. p. 252-261 (Lecture notes in computer science ; Vol. 9069).

Research output: Chapter in Book/Published conference output › Conference publication

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T1 - A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

AU - Bai, Lu

AU - Rossi, Luca

AU - Ren, Peng

AU - Zhang, Zhihong

AU - Hancock, Edwin R.

N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-18224-7_25 Funding: UK Royal Society

PY - 2015

Y1 - 2015

N2 - In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

AB - In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

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Bai L, Rossi L, Ren P, Zhang Z, Hancock ER. A quantum Jensen-Shannon graph kernel using discrete-time quantum walks. In Liu C-L, Luo B, Kropatsch WG, Cheng J, editors, Graph-based representations in pattern recognition: 10th IAPR-TC-15 international workshop, GbRPR 2015, Beijing, China, May 13-15, 2015. Proceedings. Chem (CH): Springer. 2015. p. 252-261. (Lecture notes in computer science ). doi: 10.1007/978-3-319-18224-7_25