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

Research output: Chapter in book / Conference proceeding › Conference article published in proceeding or book › Academic research › peer-review

7 Citations (Scopus)

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 - 10th IAPR-TC-15 InternationalWorkshop, GbRPR 2015, Proceedings
Editors	Bin Luo, Walter G. Kropatsch, Cheng-Lin Liu, Jian Cheng
Publisher	Springer Verlag
Pages	252-261
Number of pages	10
ISBN (Electronic)	9783319182230
DOIs	https://doi.org/10.1007/978-3-319-18224-7_25
Publication status	Published - May 2015
Externally published	Yes
Event	10th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition, GbRPR 2015 - Beijing, China Duration: 13 May 2015 → 15 May 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9069
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition, GbRPR 2015
Country/Territory	China
City	Beijing
Period	13/05/15 → 15/05/15

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

More information

10.1007/978-3-319-18224-7_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 B. Luo, W. G. Kropatsch, C.-L. Liu, & J. Cheng (Eds.), Graph-Based Representations in Pattern Recognition - 10th IAPR-TC-15 InternationalWorkshop, GbRPR 2015, Proceedings (pp. 252-261). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9069). Springer Verlag. 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 InternationalWorkshop, GbRPR 2015, Proceedings. editor / Bin Luo ; Walter G. Kropatsch ; Cheng-Lin Liu ; Jian Cheng. Springer Verlag, 2015. pp. 252-261 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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.}",

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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 B Luo, WG Kropatsch, C-L Liu & J Cheng (eds), Graph-Based Representations in Pattern Recognition - 10th IAPR-TC-15 InternationalWorkshop, GbRPR 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9069, Springer Verlag, pp. 252-261, 10th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition, 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 InternationalWorkshop, GbRPR 2015, Proceedings. ed. / Bin Luo; Walter G. Kropatsch; Cheng-Lin Liu; Jian Cheng. Springer Verlag, 2015. p. 252-261 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9069).

Research output: Chapter in book / Conference proceeding › Conference article published in proceeding or book › Academic research › peer-review

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AU - Rossi, Luca

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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 Luo B, Kropatsch WG, Liu CL, Cheng J, editors, Graph-Based Representations in Pattern Recognition - 10th IAPR-TC-15 InternationalWorkshop, GbRPR 2015, Proceedings. Springer Verlag. 2015. p. 252-261. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-18224-7_25

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

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