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Centroid

About: Centroid is a research topic. Over the lifetime, 4110 publications have been published within this topic receiving 53637 citations. The topic is also known as: barycenter (geometry) & geometric center of a plane figure.


Papers
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Journal ArticleDOI
TL;DR: In this article, the effects of Bose-Einstein or Fermi-Dirac quantum statistics within the centroid molecular dynamics formalism leads to additional correlations in the system due to exchange effects.
Abstract: We show that incorporating the effects of Bose–Einstein or Fermi–Dirac quantum statistics within the centroid molecular dynamics formalism leads to additional correlations in the system due to exchange effects. In the case of Bose–Einstein statistics they appear as an additional attraction between physical particles while an additional repulsion is observed for Fermi–Dirac statistics. We show that we can account for these correlations through the effective centroid Hamiltonian. Within the approach based on the phase space centroid density, this Hamiltonian depends on centroid momenta in a nonclassical way. We illustrate the above findings using a simple model of two bosons and fermions in a harmonic potential. The average of a centroid variable along centroid trajectories based on such an effective Hamiltonian can be used to study the equilibrium properties of quantum systems. Is is also shown that the dynamics of the centroid variables derived from the quantum mechanical dynamics of the corresponding physical observables does not depend on exchange effects for a harmonic system.

16 citations

Proceedings ArticleDOI
11 Dec 2011
TL;DR: An improved and robust centroid-based classifier that uses precise term-class distribution properties instead of simple presence or absence of terms in classes is proposed, which is called the CFC-KL centroid classifier.
Abstract: In centroid-based classification, each class is represented by a prototype or centroid document vector that is formed by averaging all member vectors during the training phase. In the prediction phase, the label of a test document vector is assigned to that of its nearest class prototype. Recently there has been revived interest in reformulating the prototype/centroid to improve classification performance. In this paper, we study the theoretical properties of the recently proposed Class Feature Centroid (CFC) classifier by considering the rate of change of each prototype vector with respect to individual dimensions (terms). The implication of our theoretical finding is that CFC is inherently biased towards large (dominant majority) classes, which means it is destined to perform poorly for highly class-imbalanced data. Another practical concern about CFC lies in its overly-aggressive design in weeding out terms that appear in all classes. To overcome these CFC limitations while retaining its intrinsic and worthy design goals, we propose an improved and robust centroid-based classifier that uses precise term-class distribution properties instead of simple presence or absence of terms in classes. Specifically, terms are weighted based on the Kullback-Leibler divergence measure between pairs of class-conditional term probabilities, we call this the CFC-KL centroid classifier. We then generalized CFC-KL to handle multi-class data by summing pair wise class-conditioned word probability ratios. Our proposed approach has been evaluated on 5 datasets, on which it consistently outperforms CFC and the baseline Support Vector Machine classifier. We also devise a word cloud visualization approach to highlight the important class-specific words picked out by our CFC-KL, and visually compare it with other popular term weigthing approaches. Our encouraging results show that the centroid based generalized CFC-KL classifier is both robust and efficient to deal with real-world text classification.

16 citations

Journal ArticleDOI
TL;DR: This study presents a method based on an irradiance model for computing the geometric PSF of an optical system by considering the energy conservation along a single light ray and shows that the proposed method obtains a reliable and accurate estimate of the PSF and enables the computation of the centroid and root-mean-square radius of the focus spot on the image plane.
Abstract: The distribution of the ray density of the spot diagram formed in the image plane is called the geometric point spread function (PSF). It plays an important role in the image formation theory, since it describes the impulse response of an optical system to a source point. However, the literature contains very few techniques for deriving the PSF of optical systems. Accordingly, this study presents a method based on an irradiance model for computing the geometric PSF of an optical system by considering the energy conservation along a single light ray. It is shown that the proposed method obtains a reliable and accurate estimate of the PSF and enables the computation of the centroid and root-mean-square radius of the focus spot on the image plane. In addition, compared to existing ray-counting methods presented in the literature, in which the quality of the PSF solution depends on the number of rays traced and the grid size used to mesh the image plane, the proposed irradiance-based method requires just one tracing operation. Overall, the results presented in this study confirm that the proposed method provides an ideal solution for calculating the merit function and modulation transfer function of an optical system.

16 citations

Proceedings ArticleDOI
21 Apr 2012
TL;DR: An improved DV-Hop location algorithm based on reduce the accumulation errors of the average hop distance of the unknown nodes in wireless sensor networks based on the weighted averaged method for calculate to the averageHop distance in the second stages is proposed.
Abstract: The localization of the unknown nodes is essential for many applications in wireless sensor networks (WSN). But the traditional DV-Hop algorithm has not high accuracy of the localization of the nodes. In this paper, we proposed an improved DV-Hop location algorithm based on reduce the accumulation errors of the average hop distance of the unknown nodes in wireless sensor networks. We have made detailed analysis of the DV-Hop algorithm, and have introduced the weighted averaged method for calculate to the average hop distance in the second stages. Then the estimates regional based on two beacon nodes is built, and the centroid of the region is the coordinates of the unknown node. Simulation experiments are conducted to compare the traditional DV-Hop algorithm and improved DV-Hop algorithm. The simulation results show that the proposed algorithm has better localization accuracy based on the same or different number of the sensor nodes and the communication radius.

16 citations

Journal ArticleDOI
TL;DR: In this paper, the authors developed the expressions that include the thresholding process in the relation between the wavefront derivative and the centroid of a thresholded intensity distribution and analyzed through numerical simulations the effective influence of thresholding on wavefront slope.

16 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023492
20221,001
2021184
2020202
2019269
2018271