Classification Problem in a Quantum Framework

Abstract

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 [13] 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 [12] 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 [13]. 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.

Quantum-inspired minimum distance classification in a biomedical context

“…Obviously, all these points require a very interdisciplinary investigation and some partial result will be introduced in a future work. Finally, we think that even if our investigation is in a preliminary stage, the actual results introduced in the present paper (and in the previously mentioned ones [31,33,28,27]) are promising enough to suggest to carry on with this research.…”

A quantum-inspired classifier for clonogenic assay evaluations

“…On the other hand, the AE is based on the idea of keeping the information about the amplitude of the vector by considering this as a particular feature 34 . Both the SE and AE were previously detailed 35 . The third hyperparameter was given by taking a certain number of copies for each row vector of the encoded training set (which has now been encoded into density matrices).…”

“…On the other hand, the AE is based on the idea of keeping the information about the amplitude of the vector by considering this as a particular feature 34 . Both the SE and AE were previously detailed 35 .…”

Quantum State Discrimination for Supervised Classification

“…However, the quantum centroid ρ (i) related to the object quantum-states {ρ x j : x j ∈ S i tr } turns out to be non-translational invariant. This characteristic is shown to be beneficial for classification tasks [16,20].…”