Santucci, E. Quantum Minimum Distance Classifier. Entropy2017, 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  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  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.
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