Quantum Minimum Distance Classifier

Abstract

Abstract:We propose a quantum version of the well known minimum distance classification model 1 called Nearest Mean Classifier (NMC). In this regard, we presented our first results in two previous 2 works. In [34] a quantum counterpart of the NMC for two-dimensional problems was introduced, 3 named Quantum Nearest Mean Classifier (QNMC), together with a possible generalization to arbitrary 4 dimensions. In [33] we studied the n-dimensional problem into detail and we showed a new 5 encoding for arbitrary n-feature vectors into density operators. In the present paper, another 6 promising encoding of n-dimensional patterns into density operators is considered, suggested by 7 recent debates on quantum machine learning. Further, we observe a significant property concerning 8 the non-invariance by feature rescaling of our quantum classifier. This fact, which represents a 9 meaningful difference between the NMC and the respective quantum version, allows to introduce a 10 free parameter whose variation provides, in some cases, better classification results for the QNMC. 11The experimental section is devoted to: i) compare the NMC and QNMC performance on different 12 datasets; ii) study the effects of the non-invariance under uniform rescaling for the QNMC.

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.…”

“…The paper is organized as follows: in the first section we briefly describe the formal structure of both the Nearest Mean Classifier and its quantum-inspired version (the QNMC). In the second section we briefly summarize some interesting results previously obtained in [31,33,28,27] by comparing the NMC and the QNMC on different datasets, and showing the advantages of the QNMC in terms of pattern classification accuracy.…”

“…Exhaustive surveys concerning the applications of quantum computing in computational intelligence and machine learning are provided in [19,35]. Even if these approaches suggest possible computational advantages of this sort [16,17], what we have proposed in [31,33,28,27] is based on a different approach that consists in using quantum formalism in order to reach remarkable benefits in the classical context. What we have provided is a model that allows to process any kind of classical dataset in a supervised system by i) translating each element of the dataset (pattern) into a density operator (that is the usual mathematical tool to formally describe a quantum state) that will be called density pattern; ii) defining, for any class of density patterns, a quantum centroid that is an object free of any counterpart in the initial classical dataset; iii) using the standard minimum distance procedure to classify an unlabeled density pattern; iv) decoding the result of the classification process in the classical pattern space.…”

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We face the problem of pattern classification by proposing a quantuminspired version of the widely used minimum distance classifier (i.e. the Nearest Mean Classifier (NMC)) already introduced in [31,33,28,27] and by applying this quantuminspired classifier in a biomedical context. In particular, we show and compare the NMC and our quantum model performance to solve a problem related to classify the probability of survival for patients affected by idiopathic pulmonary fibrosis (IPF).

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Sistem Prediksi Kualitas Santan Kelapa Menggunakan Nearest Mean Classifier (Nmc)

“…Pada citra digital dapat dilakukan klasifikasi berdasarkan fitur tertentu menggunkan algoritma tertentu. Nearest mean classifier (NMC) [2] merupakan salah satu algoritma klasifikasi. NMC merupakan pemilah linear sederhana yang menggunakan kemiripan antar pola untuk melakukan klasifikasi.…”