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A Quantum Approach to Pattern Recognition and Machine Learning. Part II

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Abstract

Different classifier functions can be defined in the framework of a quantum approach to machine learning. While the fidelity-classifier is based on a measure of similarity between quantum states, other classifiers refer to the possibility of an empirical discrimination between different states. An important example is represented by the Helstrom-classifier that has been successfully applied to some empirical simulations, for instance to the study of bio-medical images. An interesting case is represented by the evaluation of clonogenic assays: a technique whose aim is measuring the survival-degree of in vitro-cell cultures, based on the ability of a single cell to grow and to form a colony. In this field a quantum approach allows us to increase the classification-accuracy, in comparison with the corresponding results that are currently obtained in the case of most classical approaches. Some open problems and some possible further developments are mentioned in the conclusion of the article.

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Notes

  1. See [3].

  2. See Def. 1.1 of Part I.

  3. See [1].

  4. See Section 2 of Part I.

  5. See [1] and [2].

  6. See [5].

  7. Notice that in Fig. 2 (as well in Fig. 3) our four Helstrom-classifiers are termed: “HelstromQuantumCentroid1”, “HelstromQuantumCentroid2”, “HelstromQuantumCentroid3”, “HelstromQuantumCentroid4”.

  8. See [4].

  9. Details can be found in [7].

References

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  2. Giuntini, R., Holik, F., Park, D.K., Freytes, H., Blank, C., Sergioli, G.: Quantum-inspired algorithm for direct multi-class classification. Appl. Soft Comput. 134, 109956, ISSN: 1568-4946, (2023)

  3. Helstrom, C.W.: Quantum detection and estimation theory. J. Stat. Soc. Lond. 1, 231–252 (1969)

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  4. Militello, C., et al.: MF2C3: Multi-feature fuzzy clustering to enhance cell colony detection in automated clonogenic assay evaluation. Symmetry 12(5), 773 (2020). https://doi.org/10.3390/sym12050773

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Acknowledgements

R. Giuntini and G. Sergioli are partially supported by the projects: i) “Ubiquitous Quantum Reality (UQR): understanding the natural processes under the light of quantum-like structures”, funded by Fondazione di Sardegna (code: F73C22001360007); ii) “CORTEX The COst of Reasoning: Theory and EXperiments”, funded by the Ministry of University and Research (Prin 2022, cod. 2022ZLLR3T): iii) “Quantum Models for Logic, Computation and Natural Processes (Qm4Np)” funded by the Ministry of University and Research (Prin-Pnrr 2022 cod. P2022A52CR). R. Giuntini is partially funded by the TÜV SÜD Foundation, the Federal Ministry of Education and Research (BMBF) and the Free State of Bavaria under the Excellence Strategy of the Federal Government and theLänder, as well as by the Technical University of Munich-Institute for Advanced Study.

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Authors and Affiliations

  1. Dipartimento di Lettere e Filosofia, Università di Firenze, Via della Pergola 60, I-50121, Firenze, Italy

    Maria Luisa Dalla Chiara

  2. Dipartimento di Pedagogia, Psicologia, Università di Cagliari, Via Is Mirrionis 1, I-09123, Cagliari, Italy

    Roberto Giuntini & Giuseppe Sergioli

Authors
  1. Maria Luisa Dalla Chiara
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  2. Roberto Giuntini
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  3. Giuseppe Sergioli
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All authors contributed equally to the conceptualization of the work, the execution of the experiments, and the writing of the manuscript

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Correspondence to Giuseppe Sergioli.

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Dalla Chiara, M.L., Giuntini, R. & Sergioli, G. A Quantum Approach to Pattern Recognition and Machine Learning. Part II. Int J Theor Phys 63, 44 (2024). https://doi.org/10.1007/s10773-024-05567-1

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