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Open AccessArticle

Quantum Minimum Distance Classifier

Department of Electrical and Electronic Engineering, University of Cagliari, Cagliari 09123, Italy
Entropy 2017, 19(12), 659; https://doi.org/10.3390/e19120659
Received: 15 October 2017 / Revised: 21 November 2017 / Accepted: 29 November 2017 / Published: 1 December 2017
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
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. View Full-Text
Keywords: quantum formalism applications; minimum distance classification; rescaling parameter quantum formalism applications; minimum distance classification; rescaling parameter
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Santucci, E. Quantum Minimum Distance Classifier. Entropy 2017, 19, 659.

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