Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Quantum Minimum Distance Classifier

Version 1 : Received: 15 October 2017 / Approved: 16 October 2017 / Online: 16 October 2017 (05:59:18 CEST)

A peer-reviewed article of this Preprint also exists.

Santucci, E. Quantum Minimum Distance Classifier. Entropy 2017, 19, 659. Santucci, E. Quantum Minimum Distance Classifier. Entropy 2017, 19, 659.


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. In [34] a quantum counterpart of the NMC for two-dimensional problems was introduced, named "Quantum Nearest Mean Classifier" (QNMC), together with a possible generalization to arbitrary dimensions. In [33] 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 of n-dimensional patterns into density operators 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 to introduce a free parameter whose variation provides, in some cases, better classification results for the QNMC. The experimental section is devoted to: i) compare the NMC and QNMC performance on different datasets; ii) study the effects of the non-invariance under uniform rescaling for the QNMC.


quantum formalism applications; minimum distance classification; rescaling parameter


Physical Sciences, Mathematical Physics

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