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arXiv:1803.02749 · International Journal of Quantum Information

Quantum-inspired minimum distance classification in a biomedical context

Giuseppe Sergioli, Giorgio Ivan Russo, Enrica Santucci, Alessandro Stefano, Sebastiano Emanuele Torrisi, Stefano Palmucci, Carlo Vancheri, Roberto Giuntini

Published Dec 1, 2018• 19 citations

Abstract

We propose an application of a quantum-inspired version of the Nearest Mean Classifier (NMC) (G. Sergioli, E. Santucci, L. Didaci, J. A. Miszczak and R. Giuntini, A quantum inspired version of the NMC classifier, Soft Comput. 22(3) (2018) 691. G. Sergioli, G. M. Bosyk, E. Santucci and R. Giuntini, A quantum-inspired version of the classification problem, Int. J. Theo. Phys. 56(12) (2017) 3880. E. Santucci and G. Sergioli, Classification problem in a quantum framework, in quantum foundations, probability and information, Proc. Quantum and Beyond Conf., 13–16 June 2016, Vaxjo, Sweden, A. Khrennikov and T. Bourama, Springer-Berlin, Germany, 2018 (in press, 2018). E. Santucci, Quantum minimum distance classifier, Entropy 19(12) (2017) 659.) to a biomedical context. In particular, we benchmark the performances of such a quantum-variant of NMC against NMC and other (nonlinear) classifiers with respect to the problem of classifying the probability of survival for patients affected by idiopathic pulmonary fibrosis (IPF).

DOI: 10.1142/s0219749918400117

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We propose an application of a quantum-inspired version of the Nearest Mean Classifier (NMC) (G. Sergioli, E. Santucci, L. Didaci, J. A. Miszczak and R. Giuntini, A quantum inspired version of the NMC classifier, Soft Comput. 22(3) (2018) 691. G. Sergioli, G. M. Bosyk, E. Santucci and R. Giuntini, A quantum-inspired version of the classification problem, Int. J. Theo. Phys. 56(12) (2017) 3880. E. Santucci and G. Sergioli, Classification problem in a quantum framework, in quantum foundations, probability and information, Proc. Quantum and Beyond Conf., 13–16 June 2016, Vaxjo, Sweden, A. Khrennikov and T. Bourama, Springer-Berlin, Germany, 2018 (in press, 2018). E. Santucci, Quantum minimum distance classifier, Entropy 19(12) (2017) 659.) to a biomedical context. In particular, we benchmark the performances of such a quantum-variant of NMC against NMC and other (nonlinear) classifiers with respect to the problem of classifying the probability of survival for patients affected by idiopathic pulmonary fibrosis (IPF).

The aim of this paper is to provide a quantum counterpart of the well known minimum-distance classifier named Nearest Mean Classifier (NMC). In particular, we refer to the following previous works: i) in Sergioli et al. 2016, we have introduced a detailed quantum version of the NMC, named Quantum Nearest Mean Classifier (QNMC), for two-dimensional problems and we have proposed a generalization to abitrary dimensions; ii) in Sergioli et al. 2017, the n-dimensional problem was analyzed in detail and a particular encoding for arbitrary n-feature vectors into density operators has been presented. In this paper, we introduce a new promizing encoding of arbitrary n-dimensional patterns into density operators, starting from the two-feature encoding provided in the first work. Further, unlike the NMC, the QNMC shows to be not invariant by rescaling the features of each pattern. This property allows us to introduce a free parameter whose variation provides, in some case, an improvement of the QNMC performance. We show experimental results where: i) the NMC and QNMC performances are compared on different datasets; ii) the effects of the non-invariance under uniform rescaling for the QNMC are investigated.

We propose a quantum version of the well known minimum distance classification model called Nearest Mean Classifier (NMC). In this regard, we presented our first results in two previous works. First, a quantum counterpart of the NMC for two-dimensional problems was introduced, named Quantum Nearest Mean Classifier (QNMC), together with a possible generalization to any number of dimensions. Secondly, we studied the n-dimensional problem into detail and we showed a new encoding for arbitrary n-feature vectors into density operators. In the present paper, another promising encoding is considered, suggested by recent debates on quantum machine learning. Further, we observe a significant property concerning the non-invariance by feature rescaling of our quantum classifier. This fact, which represents a meaningful difference between the NMC and the respective quantum version, allows us to introduce a free parameter whose variation provides, in some cases, better classification results for the QNMC. The experimental section is devoted: (i) to compare the NMC and QNMC performance on different datasets; and (ii) to study the effects of the non-invariance under uniform rescaling for the QNMC.

Optimal measurements for the discrimination of quantum states are useful tools for classification problems. In order to exploit the potential of quantum computers, feature vectors have to be encoded into quantum states represented by density operators. However, quantum-inspired classifiers based on nearest mean and on Helstrom state discrimination are implemented on classical computers. We show a geometric approach that improves the efficiency of quantum-inspired classification in terms of space and time acting on quantum encoding and allows one to compare classifiers correctly in the presence of multiple preparations of the same quantum state as input. We also introduce the nearest mean classification based on Bures distance, Hellinger distance and Jensen-Shannon distance comparing the performance with respect to well-known classifiers applied to benchmark datasets.