17,215 research outputs found
Classification Problem in a Quantum Framework
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 Sergioli et al. 2016, 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 Sergioli et al. 2017, 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 the first work. 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.Comment: 11 pages, 2 figure
SISSO: a compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates
The lack of reliable methods for identifying descriptors - the sets of
parameters capturing the underlying mechanisms of a materials property - is one
of the key factors hindering efficient materials development. Here, we propose
a systematic approach for discovering descriptors for materials properties,
within the framework of compressed-sensing based dimensionality reduction.
SISSO (sure independence screening and sparsifying operator) tackles immense
and correlated features spaces, and converges to the optimal solution from a
combination of features relevant to the materials' property of interest. In
addition, SISSO gives stable results also with small training sets. The
methodology is benchmarked with the quantitative prediction of the ground-state
enthalpies of octet binary materials (using ab initio data) and applied to the
showcase example of predicting the metal/insulator classification of binaries
(with experimental data). Accurate, predictive models are found in both cases.
For the metal-insulator classification model, the predictive capability are
tested beyond the training data: It rediscovers the available pressure-induced
insulator->metal transitions and it allows for the prediction of yet unknown
transition candidates, ripe for experimental validation. As a step forward with
respect to previous model-identification methods, SISSO can become an effective
tool for automatic materials development.Comment: 11 pages, 5 figures, in press in Phys. Rev. Material
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