Abstract
In the context of quantum-inspired machine learning, remarkable mathematical tools for solving classification problems are given by some methods of quantum state discrimination. In this respect, quantum-inspired classifiers based on nearest centroid and Helstrom discrimination have been efficiently implemented on classical computers. We present a local approach combining the kNN algorithm to some quantum-inspired classifiers.
Similar content being viewed by others
References
Leporini, R., Pastorello, D.: An efficient geometric approach to quantum-inspired classifications. Scientific Reports 12(1). https://doi.org/10.1038/s41598-022-12392-1 (2022)
Blanzieri, E., Melgani, F.: An Adaptive Svm Nearest Neighbor Classifier for Remotely Sensed Imagery. In: 2006 IEEE International Symposium on Geoscience and Remote Sensing, pp. 3931–3934. https://doi.org/10.1109/IGARSS.2006.1008 (2006)
Leporini, R., Pastorello, D.: Support vector machines with quantum state discrimination. Quantum Reports 3(3). https://doi.org/10.3390/quantum3030032 (2021)
Leporini, R., Pastorello, D.: Quantum-inspired classification based on voronoi tessellation and pretty-good measurements. Quantum Reports 4(4). https://doi.org/10.3390/quantum4040031 (2022)
Helstrom, C. W.: Quantum detection and estimation theory. J. Stat. Phys. 1, 231–252 (1969). https://doi.org/10.1007/BF01007479
Mochon, C.: Family of generalized pretty good measurements and the minimal-error pure-state discrimination problems for which they are optimal. Physical Review A 93(3). https://doi.org/10.1103/PhysRevA.73.032328https://doi.org/10.1103/PhysRevA.73.032328 (2006)
Bae, J.: Structure of minimum-error quantum state discrimination. New Journal of Physics 96(7). https://doi.org/10.1088/1367-2630/15/7/073037 (2013)
Kimura, G., Kossakowski, A.: The bloch-vector space for n-level systems: the spherical-coordinate point of view. Open Systems & Information Dynamics 12(3). https://doi.org/10.1007/s11080-005-0919-y (2005)
Sergioli, G., Giuntini, R., Freytes, H.: A new quantum approach to binary classification. PLoS ONE 14(5), 0216224 (2019). https://doi.org/10.1371/journal.pone.0216224
Giuntini, R., Freytes, H., Park, D. K., Blank, C., Holik, F., Chow, K. L., Sergioli, G.: Quantum state discrimination for supervised classification. arXiv:2104.00971v1 (2021)
Fix, E., Hodges, J.L.: Discriminatory Analysis, Nonparametric Discrimination: Consistency Properties. Technical Report 4, USAF School of Aviation Medicine, Randolph Field (1951)
Acknowledgements
This work was supported by Q@TN, the joint lab between University of Trento, FBK- Fondazione Bruno Kessler, INFN- National Institute for Nuclear Physics and CNR- National Research Council.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conceptualization, E.B, R.L. and D.P.; validation, E.B., D.P.; formal analysis, D.P.; writing—original draft preparation, R.L. and D.P.; writing—review and editing, E.B, D.P. All authors have read and agreed to this version of the manuscript.
Conflict of Interests
The authors declare no conflict of interest.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Enrico Blanzieri, Roberto Leporini and Davide Pastorello are contributed equally to this work.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Blanzieri, E., Leporini, R. & Pastorello, D. Local Approach to Quantum-inspired Classification. Int J Theor Phys 62, 4 (2023). https://doi.org/10.1007/s10773-022-05263-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10773-022-05263-y