Abstract
In this paper, we discuss a quantum approach for the all-pair multiclass classification problem. In an all-pair approach, there is one binary classification problem for each pair of classes, and so there are k(k − 1)/2 classifiers for a k-class classification problem. As compared to the classical multiclass support vector machine that can be implemented with polynomial run time complexity, our approach exhibits exponential speedup due to quantum computing. The quantum all-pair algorithm can also be used with other classification algorithms, and a speedup gain can be achieved as compared to their classical counterparts.
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References
MacKay, D.J.C.: Information Theory, Inference and Learning Algorithms. Cambridge University Press, Cambridge (2003)
Alpaydin, E.: Introduction to Machine Learning (Adaptive Computation and Machine Learning). MIT Press, Cambridge (2004)
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2007)
Murphy, K.P.: Machine Learning: A Probabilistic Perspective. MIT Press, Cambridge (2012)
Suykens, J.A.K., Vandewalle, J.: Multiclass least squares support vector machines. In: International Joint Conference on Neural Networks, 1999. IJCNN ‘99, vol. 2, pp. 900–903 (1999)
Hsu, C.-W., Lin, C.-J.: A comparison of methods for multiclass support vector machines. IEEE Trans. Neural Netw. 13(2), 415–425 (2002)
Rebentrost, P., Mohseni, M., Lloyd, S.: arXiv:1307.0471v3
Bishwas, A.K., Mani, A., Palade, V.: Conference Proceedings to IEEE 2nd International Conference on Contemporary Computing and Informatics (IC3I) (2016)
Suykens, J.A.K., Vandewalle, J.: Least squares support vector machine classifiers. Neural Process. Lett. 9(3), 293–300 (1999)
Giovannetti, V., Lloyd, S., Maccone, L.: Quantum random access memory. Phys. Rev. Lett. 100, 160501 (2008). arXiv:0708.1879
Giovannetti, V., Lloyd, S., Maccone, L.: Architectures for a quantum random access memory. Phys. Rev. A 78, 052310 (2008). arXiv:0807.4994
De Martini, F., Giovannetti, V., Lloyd, S., Maccone, L., Nagali, E., Sansoni, L., Sciarrino, F.: Experimental quantum private queries with linear optics. Phys. Rev. A 80, 010302(R) (2009). arXiv:0902.0222
Chiorescu, I., Groll, N., Bertaina, S., Mori, T., Miyashita, S.: Magnetic strong coupling in a spin–photon system and transition to classical regime. Phys. Rev. B 82, 024413 (2010)
Schuster, D.I., Sears, A.P., Ginossar, E., DiCarlo, L., Frunzio, L., Morton, J.J.L., Wu, H., Briggs, G.A.D., Buckley, B.B., Awschalom, D.D., Schoelkopf, R.J.: High-cooperativity coupling of electron-spin ensembles to superconducting cavities. Phys. Rev. Lett. 105, 140501 (2010)
Kubo, Y., Ong, F.R., Bertet, P., Vion, D., Jacques, V., Zheng, D., Drau, A., Roch, J.-F., Auffeves, A., Jelezko, F., Wrachtrup, J., Barthe, M.F., Bergonzo, P., Esteve, D.: Strong coupling of a spin ensemble to a superconducting resonator. Phys. Rev. Lett. 105, 140502 (2010)
Wu, H., George, R.E., Wesenberg, J.H., Mlmer, K., Schuster, D.I., Schoelkopf, R.J., Itoh, K.M., Ardavan, A., Morton, J.J.L., Briggs, G.A.D.: Storage of multiple coherent microwave excitations in an electron spin ensemble. Phys. Rev. Lett. 105, 140503 (2010)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum principal component analysis. Nat. Phys. 10, 631 (2014)
Harrow, A.W., Hassidim, A., Lloyd, S.: Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103, 150502 (2009)
Berry, D.W., Ahokas, G., Cleve, R., Sanders, B.C.: Efficient quantum algorithms for simulating sparse Hamiltonians. Commun. Math. Phys. 270, 359–371 (2007)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings, 28th Annual ACM Symposium on the Theory of Computing, p. 212 (1996)
Dürr, C., Høyer, P.: A quantum algorithm for finding the minimum. arXiv:quant-ph/9607014 (1999)
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, Berlin (2006)
Childs, A.: On the relationship between continuous-and discrete-time quantum walk. Commun. Math. Phys. 294, 581 (2010)
Tang, Y., Zhang, H.H.: Multiclass proximal support vector machines. J. Comput. Graph. Stat. 15(2), 339–355 (2006)
Huang, G.-B., Zhu, Q.-Y., Siew, C.-K.: Extreme learning machine: a new learning scheme of feedforward neural networks. In: Proceedings of IJCNN, Budapest, Hungary, July 25–29, vol. 2, pp. 985–990 (2004)
Kara, A.: https://www.researchgate.net/publication/242491626_A_Quantum_Algorithm_For_Finding_An_e-Approximate_Mode (2005)
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Bishwas, A.K., Mani, A. & Palade, V. An all-pair quantum SVM approach for big data multiclass classification. Quantum Inf Process 17, 282 (2018). https://doi.org/10.1007/s11128-018-2046-z
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DOI: https://doi.org/10.1007/s11128-018-2046-z