Quantum clustering with k-Means: A hybrid approach
Quantum computing, based on quantum theory, holds great promise as an advanced computational paradigm for achieving fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including machine learning. In this p...
Saved in:
| Published in: | Theoretical computer science Vol. 992; p. 114466 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
21.04.2024
|
| Subjects: | |
| ISSN: | 0304-3975, 1879-2294 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Quantum computing, based on quantum theory, holds great promise as an advanced computational paradigm for achieving fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including machine learning. In this paper, we design, implement, and evaluate three hybrid quantum k-Means algorithms, exploiting different degrees of parallelism. Indeed, each algorithm incrementally leverages quantum parallelism to reduce the complexity of the cluster assignment step up to a constant cost. In particular, we exploit quantum phenomena to speed up the computation of distances. The core idea is that the computation of distances between records and centroids can be executed simultaneously, thus saving time, especially for big datasets. We show that our hybrid quantum k-Means algorithms are theoretically faster than the classical algorithm, while experiments suggest that it is possible to obtain comparable clustering results. |
|---|---|
| AbstractList | Quantum computing, based on quantum theory, holds great promise as an advanced computational paradigm for achieving fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including machine learning. In this paper, we design, implement, and evaluate three hybrid quantum k-Means algorithms, exploiting different degrees of parallelism. Indeed, each algorithm incrementally leverages quantum parallelism to reduce the complexity of the cluster assignment step up to a constant cost. In particular, we exploit quantum phenomena to speed up the computation of distances. The core idea is that the computation of distances between records and centroids can be executed simultaneously, thus saving time, especially for big datasets. We show that our hybrid quantum k-Means algorithms are theoretically faster than the classical algorithm, while experiments suggest that it is possible to obtain comparable clustering results. |
| ArticleNumber | 114466 |
| Author | Poggiali, Alessandro Guidotti, Riccardo Berti, Alessandro Del Corso, Gianna M. Bernasconi, Anna |
| Author_xml | – sequence: 1 givenname: Alessandro orcidid: 0000-0002-1591-7925 surname: Poggiali fullname: Poggiali, Alessandro email: alessandro.poggiali@phd.unipi.it organization: Department of Computer Science, University of Pisa, Largo B. Pontecorvo, Pisa, 56127, Italy – sequence: 2 givenname: Alessandro surname: Berti fullname: Berti, Alessandro organization: Department of Computer Science, University of Pisa, Largo B. Pontecorvo, Pisa, 56127, Italy – sequence: 3 givenname: Anna surname: Bernasconi fullname: Bernasconi, Anna organization: Department of Computer Science, University of Pisa, Largo B. Pontecorvo, Pisa, 56127, Italy – sequence: 4 givenname: Gianna M. surname: Del Corso fullname: Del Corso, Gianna M. organization: Department of Computer Science, University of Pisa, Largo B. Pontecorvo, Pisa, 56127, Italy – sequence: 5 givenname: Riccardo surname: Guidotti fullname: Guidotti, Riccardo organization: Department of Computer Science, University of Pisa, Largo B. Pontecorvo, Pisa, 56127, Italy |
| BookMark | eNp9z81KAzEUhuEgFWyrF-BubmDGJJOfia5K8Q8qIug6ZE4yNrXNlCRVevdOqSsXPZuzej94JmgU-uAQuia4IpiIm1WVIVUUU1YRwpgQZ2hMGqlKShUboTGuMStrJfkFmqS0wsNxKcaIvu1MyLtNAetdyi768Fn8-LwsvsoXZ0K6LWbFct9Gbwuz3cbewPISnXdmndzV35-ij4f79_lTuXh9fJ7PFiXUDOeygRpo03HTOtkKJRpQYKjgYDHlpLYGBAbGlLQdUZYT2UnRgqKOcyuM5fUUkeMuxD6l6Dq9jX5j4l4TrA9ovdIDWh_Q-ogeGvmvAZ9N9n3I0fj1yfLuWLqB9O1d1Am8C-Csjw6ytr0_Uf8CHKFzBQ |
| CitedBy_id | crossref_primary_10_24201_es_2024v42_e2664 crossref_primary_10_1007_s10586_024_04664_4 crossref_primary_10_1007_s42484_025_00266_4 crossref_primary_10_1016_j_patcog_2025_111342 crossref_primary_10_1109_ACCESS_2025_3585799 crossref_primary_10_1177_14727978251355787 crossref_primary_10_1016_j_tcs_2024_114716 crossref_primary_10_1038_s41598_025_99990_x crossref_primary_10_1007_s13369_024_09468_7 crossref_primary_10_1007_s42484_025_00293_1 crossref_primary_10_1007_s42484_024_00210_y crossref_primary_10_1007_s42484_024_00213_9 crossref_primary_10_1016_j_sysarc_2025_103431 crossref_primary_10_1016_j_engappai_2024_109258 |
| Cites_doi | 10.1007/s11222-007-9033-z 10.1007/s11128-021-03384-7 10.1007/s10489-021-02513-0 10.1016/0377-0427(87)90125-7 10.1103/PhysRevLett.88.018702 10.1007/s11128-021-03071-7 10.1109/TC.2020.3037932 10.1103/PhysRevA.103.042415 10.19026/rjaset.6.3638 10.1016/j.eswa.2009.12.017 10.1038/nature23474 10.1080/00107514.2014.964942 10.22331/q-2018-08-06-79 10.1007/s42484-020-00035-5 10.1209/0295-5075/119/60002 |
| ContentType | Journal Article |
| Copyright | 2024 The Author(s) |
| Copyright_xml | – notice: 2024 The Author(s) |
| DBID | 6I. AAFTH AAYXX CITATION |
| DOI | 10.1016/j.tcs.2024.114466 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics Computer Science |
| EISSN | 1879-2294 |
| ExternalDocumentID | 10_1016_j_tcs_2024_114466 S0304397524000811 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 123 1B1 1RT 1~. 1~5 4.4 457 4G. 5VS 6I. 7-5 71M 8P~ 9JN AABNK AACTN AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAXUO AAYFN ABAOU ABBOA ABJNI ABMAC ABMYL ABYKQ ACAZW ACDAQ ACGFS ACRLP ACZNC ADBBV ADEZE AEBSH AEKER AENEX AFKWA AFTJW AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AJOXV AKRWK ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ARUGR AXJTR BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HVGLF IHE IXB J1W KOM LG9 M26 M41 MHUIS MO0 N9A O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 RIG ROL RPZ SCC SDF SDG SES SEW SPC SPCBC SSV SSW T5K TN5 WH7 YNT ZMT ~G- 29Q 9DU AAEDT AAQXK AATTM AAXKI AAYWO AAYXX ABDPE ABEFU ABFNM ABWVN ABXDB ACLOT ACNNM ACRPL ACVFH ADCNI ADMUD ADNMO ADVLN AEIPS AEUPX AEXQZ AFJKZ AFPUW AGHFR AGQPQ AIGII AIIUN AKBMS AKYEP ANKPU APXCP ASPBG AVWKF AZFZN CITATION EFKBS EJD FGOYB G-2 HZ~ R2- SSZ TAE WUQ ZY4 ~HD |
| ID | FETCH-LOGICAL-c340t-8c3c28f5abe7b6968c9ca265cd02513dac60c4497df19d517f76bc92e55d6ad53 |
| ISICitedReferencesCount | 19 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001196600600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0304-3975 |
| IngestDate | Tue Nov 18 21:31:42 EST 2025 Sat Nov 29 07:24:10 EST 2025 Sat Mar 16 16:14:26 EDT 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Clustering Data mining Quantum machine learning |
| Language | English |
| License | This is an open access article under the CC BY-NC-ND license. |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c340t-8c3c28f5abe7b6968c9ca265cd02513dac60c4497df19d517f76bc92e55d6ad53 |
| ORCID | 0000-0002-1591-7925 |
| OpenAccessLink | https://dx.doi.org/10.1016/j.tcs.2024.114466 |
| ParticipantIDs | crossref_primary_10_1016_j_tcs_2024_114466 crossref_citationtrail_10_1016_j_tcs_2024_114466 elsevier_sciencedirect_doi_10_1016_j_tcs_2024_114466 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-04-21 |
| PublicationDateYYYYMMDD | 2024-04-21 |
| PublicationDate_xml | – month: 04 year: 2024 text: 2024-04-21 day: 21 |
| PublicationDecade | 2020 |
| PublicationTitle | Theoretical computer science |
| PublicationYear | 2024 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Benlamine, Bennani, Zaiou, Hibti, Matei, Grozavu (br0160) 2019 Zaiou, Bennani, Matei, Hibti (br0210) 2021 Tan (br0240) 2005 Benlamine, Bennani, Grozavu, Matei (br0190) 2020 Nielsen, Chuang (br0130) 2010 Golub, Van Loan (br0360) 1996 Lloyd, Mohseni, Rebentrost (br0090) 2013 Preskill (br0260) 2018; 2 Von Luxburg (br0230) 2007; 17 Otterbach, Manenti, Alidoust, Bestwick, Block, Bloom, Caldwell, Didier, Fried, Hong (br0080) 2017 Khan, Awan, Vall-Llosera (br0320) 2019 Farhi, Goldstone, Gutmann, Sipser (br0100) 2000 Poggiali, Berti, Bernasconi, Del Corso, Giudotti (br0060) 2022 Horn, Gottlieb (br0070) 2001; 88 de Veras, De Araujo, Park, da Silva (br0340) 2020; 70 Wu, Song, Zhang (br0170) 2022; 21 Schuld, Sinayskiy, Petruccione (br0020) 2015; 56 MacQueen (br0030) 1967 Schuld, Fingerhuth, Petruccione (br0040) 2017; 119 Xiao, Yan, Zhang, Tang (br0110) 2010; 37 Aïmeur, Brassard, Gambs (br0120) 2006 Kerenidis, Landman, Luongo, Prakash (br0050) 2019; 32 Aïmeur, Brassard, Gambs (br0140) 2007 Eybpoosh, Rezghi, Heydari (br0300) 2022; 52 Thakare, Bagal (br0180) 2015; 110 Schuld (br0280) 2018 Mengoni, Incudini, Di Pierro (br0290) 2021; 3 Biamonte, Wittek, Pancotti, Rebentrost, Wiebe, Lloyd (br0010) 2017; 549 Gong, Dong, Gani, Qi (br0200) 2021; 20 Kerenidis, Landman (br0220) 2021; 103 Mohamad, Usman (br0350) 2013; 6 Park, Petruccione, Rhee (br0310) 2019; 9 Berti (br0330) 2023 Rousseeuw (br0370) 1987; 20 Grover (br0150) 1996 Vassilvitskii, Arthur k-means (br0250) 2006 Rosenberg, Hirschberg (br0380) 2007 Berti, Bernasconi, Del Corso, Guidotti (br0270) 2022 Preskill (10.1016/j.tcs.2024.114466_br0260) 2018; 2 Vassilvitskii (10.1016/j.tcs.2024.114466_br0250) 2006 Berti (10.1016/j.tcs.2024.114466_br0270) 2022 Rousseeuw (10.1016/j.tcs.2024.114466_br0370) 1987; 20 Rosenberg (10.1016/j.tcs.2024.114466_br0380) 2007 Von Luxburg (10.1016/j.tcs.2024.114466_br0230) 2007; 17 Otterbach (10.1016/j.tcs.2024.114466_br0080) Zaiou (10.1016/j.tcs.2024.114466_br0210) 2021 Berti (10.1016/j.tcs.2024.114466_br0330) 2023 Park (10.1016/j.tcs.2024.114466_br0310) 2019; 9 Wu (10.1016/j.tcs.2024.114466_br0170) 2022; 21 de Veras (10.1016/j.tcs.2024.114466_br0340) 2020; 70 Kerenidis (10.1016/j.tcs.2024.114466_br0050) 2019; 32 Kerenidis (10.1016/j.tcs.2024.114466_br0220) 2021; 103 Mengoni (10.1016/j.tcs.2024.114466_br0290) 2021; 3 Tan (10.1016/j.tcs.2024.114466_br0240) 2005 Farhi (10.1016/j.tcs.2024.114466_br0100) Biamonte (10.1016/j.tcs.2024.114466_br0010) 2017; 549 Horn (10.1016/j.tcs.2024.114466_br0070) 2001; 88 Khan (10.1016/j.tcs.2024.114466_br0320) Benlamine (10.1016/j.tcs.2024.114466_br0190) 2020 Eybpoosh (10.1016/j.tcs.2024.114466_br0300) 2022; 52 Lloyd (10.1016/j.tcs.2024.114466_br0090) Thakare (10.1016/j.tcs.2024.114466_br0180) 2015; 110 Aïmeur (10.1016/j.tcs.2024.114466_br0120) 2006 Gong (10.1016/j.tcs.2024.114466_br0200) 2021; 20 Mohamad (10.1016/j.tcs.2024.114466_br0350) 2013; 6 Schuld (10.1016/j.tcs.2024.114466_br0020) 2015; 56 Xiao (10.1016/j.tcs.2024.114466_br0110) 2010; 37 MacQueen (10.1016/j.tcs.2024.114466_br0030) 1967 Grover (10.1016/j.tcs.2024.114466_br0150) 1996 Benlamine (10.1016/j.tcs.2024.114466_br0160) 2019 Schuld (10.1016/j.tcs.2024.114466_br0040) 2017; 119 Aïmeur (10.1016/j.tcs.2024.114466_br0140) 2007 Nielsen (10.1016/j.tcs.2024.114466_br0130) 2010 Schuld (10.1016/j.tcs.2024.114466_br0280) 2018 Poggiali (10.1016/j.tcs.2024.114466_br0060) 2022 Golub (10.1016/j.tcs.2024.114466_br0360) 1996 |
| References_xml | – start-page: 1 year: 2020 end-page: 7 ident: br0190 article-title: Quantum collaborative k-means publication-title: 2020 International Joint Conference on Neural Networks (IJCNN) – volume: 549 start-page: 195 year: 2017 end-page: 202 ident: br0010 article-title: Quantum machine learning publication-title: Nature – volume: 103 year: 2021 ident: br0220 article-title: Quantum spectral clustering publication-title: Phys. Rev. A – start-page: 281 year: 1967 end-page: 297 ident: br0030 article-title: Some methods for classification and analysis of multivariate observations publication-title: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1 – start-page: 251 year: 2023 end-page: 256 ident: br0330 publication-title: Logarithmic Quantum Forking – year: 2000 ident: br0100 article-title: Quantum computation by adiabatic evolution – volume: 2 start-page: 79 year: 2018 ident: br0260 article-title: Quantum computing in the NISQ era and beyond publication-title: Quantum – volume: 3 start-page: 1 year: 2021 end-page: 11 ident: br0290 article-title: Facial expression recognition on a quantum computer publication-title: Quantum Mach. Intell. – year: 2013 ident: br0090 article-title: Quantum algorithms for supervised and unsupervised machine learning – year: 2005 ident: br0240 article-title: Introduction to Data Mining – volume: 20 start-page: 53 year: 1987 end-page: 65 ident: br0370 article-title: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis publication-title: J. Comput. Appl. Math. – year: 2010 ident: br0130 article-title: Quantum Computation and Quantum Information – start-page: 410 year: 2007 end-page: 420 ident: br0380 article-title: V-measure: a conditional entropy-based external cluster evaluation measure publication-title: Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning (EMNLP-CoNLL) – year: 2022 ident: br0060 article-title: Clustering classical data with quantum k-means publication-title: Proceedings of the 23rd Italian Conference on Theoretical Computer Science – start-page: 1 year: 2021 end-page: 7 ident: br0210 article-title: Balanced k-means using quantum annealing publication-title: 2021 IEEE Symposium Series on Computational Intelligence (SSCI) – volume: 37 start-page: 4966 year: 2010 end-page: 4973 ident: br0110 article-title: A quantum-inspired genetic algorithm for k-means clustering publication-title: Expert Syst. Appl. – year: 1996 ident: br0360 article-title: Matrix Computations – volume: 21 start-page: 1 year: 2022 end-page: 10 ident: br0170 article-title: Quantum k-means algorithm based on Manhattan distance publication-title: Quantum Inf. Process. – volume: 17 start-page: 395 year: 2007 end-page: 416 ident: br0230 article-title: A tutorial on spectral clustering publication-title: Stat. Comput. – volume: 9 start-page: 1 year: 2019 end-page: 8 ident: br0310 article-title: Circuit-based quantum random access memory for classical data publication-title: Sci. Rep. – volume: 70 start-page: 2125 year: 2020 end-page: 2135 ident: br0340 article-title: Circuit-based quantum random access memory for classical data with continuous amplitudes publication-title: IEEE Trans. Comput. – year: 2022 ident: br0270 article-title: Effect of different encodings and distance functions on quantum instance-based classifiers publication-title: Proceedings 26th Pacific-Asia Conference on Knowledge Discovery and Data Mining PAKDD – volume: 56 start-page: 172 year: 2015 end-page: 185 ident: br0020 article-title: An introduction to quantum machine learning publication-title: Contemp. Phys. – volume: 119 year: 2017 ident: br0040 article-title: Implementing a distance-based classifier with a quantum interference circuit publication-title: Europhys. Lett. – volume: 32 year: 2019 ident: br0050 article-title: q-means: a quantum algorithm for unsupervised machine learning publication-title: Adv. Neural Inf. Process. Syst. – start-page: 431 year: 2006 end-page: 442 ident: br0120 article-title: Machine learning in a quantum world publication-title: Conference of the Canadian Society for Computational Studies of Intelligence – start-page: 1027 year: 2006 end-page: 1035 ident: br0250 article-title: The advantages of careful seeding publication-title: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms – volume: 88 year: 2001 ident: br0070 article-title: Algorithm for data clustering in pattern recognition problems based on quantum mechanics publication-title: Phys. Rev. Lett. – start-page: 212 year: 1996 end-page: 219 ident: br0150 article-title: A fast quantum mechanical algorithm for database search publication-title: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing – start-page: 1 year: 2007 end-page: 8 ident: br0140 article-title: Quantum clustering algorithms publication-title: Proceedings of the 24th International Conference on Machine Learning – start-page: 561 year: 2019 end-page: 572 ident: br0160 article-title: Distance estimation for quantum prototypes based clustering publication-title: Neural Information Processing: 26th International Conference – volume: 110 start-page: 12 year: 2015 end-page: 16 ident: br0180 article-title: Performance evaluation of k-means clustering algorithm with various distance metrics publication-title: Int. J. Comput. Appl. – volume: 20 start-page: 1 year: 2021 end-page: 22 ident: br0200 article-title: Quantum k-means algorithm based on trusted server in quantum cloud computing publication-title: Quantum Inf. Process. – year: 2018 ident: br0280 article-title: Supervised Learning with Quantum Computers – volume: 6 start-page: 3299 year: 2013 end-page: 3303 ident: br0350 article-title: Standardization and its effects on k-means clustering algorithm publication-title: Res. J. Appl. Sci. Eng. Technol. – year: 2017 ident: br0080 article-title: Unsupervised machine learning on a hybrid quantum computer – year: 2019 ident: br0320 article-title: K-means clustering on noisy intermediate scale quantum computers – volume: 52 start-page: 4443 year: 2022 end-page: 4457 ident: br0300 article-title: Applying inverse stereographic projection to manifold learning and clustering publication-title: Appl. Intell. – volume: 17 start-page: 395 issue: 4 year: 2007 ident: 10.1016/j.tcs.2024.114466_br0230 article-title: A tutorial on spectral clustering publication-title: Stat. Comput. doi: 10.1007/s11222-007-9033-z – volume: 21 start-page: 1 issue: 1 year: 2022 ident: 10.1016/j.tcs.2024.114466_br0170 article-title: Quantum k-means algorithm based on Manhattan distance publication-title: Quantum Inf. Process. doi: 10.1007/s11128-021-03384-7 – start-page: 1 year: 2020 ident: 10.1016/j.tcs.2024.114466_br0190 article-title: Quantum collaborative k-means – start-page: 281 year: 1967 ident: 10.1016/j.tcs.2024.114466_br0030 article-title: Some methods for classification and analysis of multivariate observations – year: 2018 ident: 10.1016/j.tcs.2024.114466_br0280 – volume: 52 start-page: 4443 issue: 4 year: 2022 ident: 10.1016/j.tcs.2024.114466_br0300 article-title: Applying inverse stereographic projection to manifold learning and clustering publication-title: Appl. Intell. doi: 10.1007/s10489-021-02513-0 – volume: 9 start-page: 1 issue: 1 year: 2019 ident: 10.1016/j.tcs.2024.114466_br0310 article-title: Circuit-based quantum random access memory for classical data publication-title: Sci. Rep. – ident: 10.1016/j.tcs.2024.114466_br0320 – volume: 20 start-page: 53 year: 1987 ident: 10.1016/j.tcs.2024.114466_br0370 article-title: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(87)90125-7 – start-page: 1 year: 2007 ident: 10.1016/j.tcs.2024.114466_br0140 article-title: Quantum clustering algorithms – volume: 88 issue: 1 year: 2001 ident: 10.1016/j.tcs.2024.114466_br0070 article-title: Algorithm for data clustering in pattern recognition problems based on quantum mechanics publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.88.018702 – volume: 20 start-page: 1 issue: 4 year: 2021 ident: 10.1016/j.tcs.2024.114466_br0200 article-title: Quantum k-means algorithm based on trusted server in quantum cloud computing publication-title: Quantum Inf. Process. doi: 10.1007/s11128-021-03071-7 – year: 2010 ident: 10.1016/j.tcs.2024.114466_br0130 – volume: 70 start-page: 2125 issue: 12 year: 2020 ident: 10.1016/j.tcs.2024.114466_br0340 article-title: Circuit-based quantum random access memory for classical data with continuous amplitudes publication-title: IEEE Trans. Comput. doi: 10.1109/TC.2020.3037932 – ident: 10.1016/j.tcs.2024.114466_br0080 – volume: 103 issue: 4 year: 2021 ident: 10.1016/j.tcs.2024.114466_br0220 article-title: Quantum spectral clustering publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.103.042415 – year: 1996 ident: 10.1016/j.tcs.2024.114466_br0360 – ident: 10.1016/j.tcs.2024.114466_br0090 – start-page: 1027 year: 2006 ident: 10.1016/j.tcs.2024.114466_br0250 article-title: The advantages of careful seeding – volume: 110 start-page: 12 issue: 11 year: 2015 ident: 10.1016/j.tcs.2024.114466_br0180 article-title: Performance evaluation of k-means clustering algorithm with various distance metrics publication-title: Int. J. Comput. Appl. – start-page: 1 year: 2021 ident: 10.1016/j.tcs.2024.114466_br0210 article-title: Balanced k-means using quantum annealing – volume: 6 start-page: 3299 issue: 17 year: 2013 ident: 10.1016/j.tcs.2024.114466_br0350 article-title: Standardization and its effects on k-means clustering algorithm publication-title: Res. J. Appl. Sci. Eng. Technol. doi: 10.19026/rjaset.6.3638 – volume: 37 start-page: 4966 issue: 7 year: 2010 ident: 10.1016/j.tcs.2024.114466_br0110 article-title: A quantum-inspired genetic algorithm for k-means clustering publication-title: Expert Syst. Appl. doi: 10.1016/j.eswa.2009.12.017 – volume: 549 start-page: 195 issue: 7671 year: 2017 ident: 10.1016/j.tcs.2024.114466_br0010 article-title: Quantum machine learning publication-title: Nature doi: 10.1038/nature23474 – start-page: 212 year: 1996 ident: 10.1016/j.tcs.2024.114466_br0150 article-title: A fast quantum mechanical algorithm for database search – start-page: 561 year: 2019 ident: 10.1016/j.tcs.2024.114466_br0160 article-title: Distance estimation for quantum prototypes based clustering – start-page: 431 year: 2006 ident: 10.1016/j.tcs.2024.114466_br0120 article-title: Machine learning in a quantum world – start-page: 251 year: 2023 ident: 10.1016/j.tcs.2024.114466_br0330 publication-title: Logarithmic Quantum Forking – volume: 32 year: 2019 ident: 10.1016/j.tcs.2024.114466_br0050 article-title: q-means: a quantum algorithm for unsupervised machine learning publication-title: Adv. Neural Inf. Process. Syst. – volume: 56 start-page: 172 issue: 2 year: 2015 ident: 10.1016/j.tcs.2024.114466_br0020 article-title: An introduction to quantum machine learning publication-title: Contemp. Phys. doi: 10.1080/00107514.2014.964942 – year: 2005 ident: 10.1016/j.tcs.2024.114466_br0240 – year: 2022 ident: 10.1016/j.tcs.2024.114466_br0270 article-title: Effect of different encodings and distance functions on quantum instance-based classifiers – start-page: 410 year: 2007 ident: 10.1016/j.tcs.2024.114466_br0380 article-title: V-measure: a conditional entropy-based external cluster evaluation measure – year: 2022 ident: 10.1016/j.tcs.2024.114466_br0060 article-title: Clustering classical data with quantum k-means – volume: 2 start-page: 79 year: 2018 ident: 10.1016/j.tcs.2024.114466_br0260 article-title: Quantum computing in the NISQ era and beyond publication-title: Quantum doi: 10.22331/q-2018-08-06-79 – volume: 3 start-page: 1 issue: 1 year: 2021 ident: 10.1016/j.tcs.2024.114466_br0290 article-title: Facial expression recognition on a quantum computer publication-title: Quantum Mach. Intell. doi: 10.1007/s42484-020-00035-5 – volume: 119 issue: 6 year: 2017 ident: 10.1016/j.tcs.2024.114466_br0040 article-title: Implementing a distance-based classifier with a quantum interference circuit publication-title: Europhys. Lett. doi: 10.1209/0295-5075/119/60002 – ident: 10.1016/j.tcs.2024.114466_br0100 |
| SSID | ssj0000576 |
| Score | 2.5646403 |
| Snippet | Quantum computing, based on quantum theory, holds great promise as an advanced computational paradigm for achieving fast computations. Quantum algorithms are... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 114466 |
| SubjectTerms | Clustering Data mining Quantum machine learning |
| Title | Quantum clustering with k-Means: A hybrid approach |
| URI | https://dx.doi.org/10.1016/j.tcs.2024.114466 |
| Volume | 992 |
| WOSCitedRecordID | wos001196600600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1879-2294 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000576 issn: 0304-3975 databaseCode: AIEXJ dateStart: 20211209 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3db9MwELeqjgd44GOANhjIDzytStU6dmzzVo0hQOs0REF9C47t7Kt409JO47_nHDtptQ3EkHiJqriuk7tfz3fn-0DoDWBkaMHsSowlRUK1LZMCFHH4uw-YFVkpijqa8Nse398X06k86HS-N7kwlzPunLi6kuf_ldVwD5jtU2fvwO72R-EGfAamwxXYDte_YvznBRBr8aOnZwtfBKF1tp4mY-u15joV_einz9RqK4qvqqiTldRGHXs-9OJG2QrSs8NDeJPjmCJTVcrXPWhNexuDBG4dcqoCGzyMO9fuCu-s92KA-l976gG0TvXG_VWnBKljWcjSKXEzWyZkaPlTGBk6pfRtELiCy4SQ0Oi4kcgytMe7Id2Do-GkP9e-0DqhvtAxza5V0q735i9-Lb-UD5EFrQfs4zXCmRRdtDb6uDv9tNytGQ_n2fHZmpPvOgbw2kK36y4r-sjkMXoYDQk8CgB4gjrWraNHTZMOHGX2OnowbgvzVk8RiejAS3Rgjw4c0fEWj3DABm6w8Qx9fb872fmQxLYZiU7pYJ4InWoiSqYKywtf-0hLrUjGtPH2ZGqUzgaaUslNOZSGDXnJs0JLYhkzmTIsfY667szZDYRB4JfUCmNSC3ZqYQUFa0LTYcEzxRUjm2jQECTXsaa8b20yy5vgwZMcaJh7GuaBhptou51yHgqq_OnLtKFyHoEeNL0cIPH7aS_-bdpLdH-J5S3UnV8s7Ct0T1_Oj6uL1xE4vwDF8YIN |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Quantum+clustering+with+k-Means%3A+A+hybrid+approach&rft.jtitle=Theoretical+computer+science&rft.au=Poggiali%2C+Alessandro&rft.au=Berti%2C+Alessandro&rft.au=Bernasconi%2C+Anna&rft.au=Del+Corso%2C+Gianna+M.&rft.date=2024-04-21&rft.pub=Elsevier+B.V&rft.issn=0304-3975&rft.eissn=1879-2294&rft.volume=992&rft_id=info:doi/10.1016%2Fj.tcs.2024.114466&rft.externalDocID=S0304397524000811 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0304-3975&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0304-3975&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0304-3975&client=summon |