Topic
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.
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TL;DR: In this paper, the centroid dynamics formalism is extended to the calculation of time correlation functions of nonlinear operators via higher order Kubo-type transforms and a general methodology is developed to relate these Kubo type transforms to the desired quantum correlation functions.
Abstract: The centroid dynamics formalism is extended to the calculation of time correlation functions of nonlinear operators. It is shown that centroid correlation functions can be related to quantum mechanical ones via higher order Kubo-type transforms. A key step is the construction of the correlation functions from a mixed classical/semiclassical centroid representation of the operators. A general methodology is developed to relate these Kubo-type transforms to the desired quantum correlation functions. The approach is tested using a one-dimensional anharmonic potential for which the 〈x2x2(t)〉 and the 〈x3x3(t)〉 correlation functions are computed. Applications of this new approach are also outlined.
97 citations
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09 Oct 2018TL;DR: In this article, the authors propose an end-to-end clustering training schedule for neural networks that is direct, i.e., the output is a probability distribution over cluster memberships.
Abstract: We propose a novel end-to-end clustering training schedule for neural networks that is direct, i.e. the output is a probability distribution over cluster memberships. A neural network maps images to embeddings. We introduce centroid variables that have the same shape as image embeddings. These variables are jointly optimized with the network’s parameters. This is achieved by a cost function that associates the centroid variables with embeddings of input images. Finally, an additional layer maps embeddings to logits, allowing for the direct estimation of the respective cluster membership. Unlike other methods, this does not require any additional classifier to be trained on the embeddings in a separate step. The proposed approach achieves state-of-the-art results in unsupervised classification and we provide an extensive ablation study to demonstrate its capabilities.
96 citations
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TL;DR: A new definition for the neighbors of an arbitrary point P is proposed, free from any user-specified parameter and can be used for pattern classification, clustering and low-level description of dot patterns.
95 citations
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TL;DR: In this paper, a modified Bregman ADMM approach for computing the approximate discrete Wasserstein barycenter of large clusters is presented, where the support points of the barycenters are unknown and have low cardinality.
Abstract: In a variety of research areas, the weighted bag of vectors and the histogram are widely used descriptors for complex objects. Both can be expressed as discrete distributions. D2-clustering pursues the minimum total within-cluster variation for a set of discrete distributions subject to the Kantorovich–Wasserstein metric. D2-clustering has a severe scalability issue, the bottleneck being the computation of a centroid distribution, called Wasserstein barycenter, that minimizes its sum of squared distances to the cluster members. In this paper, we develop a modified Bregman ADMM approach for computing the approximate discrete Wasserstein barycenter of large clusters. In the case when the support points of the barycenters are unknown and have low cardinality, our method achieves high accuracy empirically at a much reduced computational cost. The strengths and weaknesses of our method and its alternatives are examined through experiments, and we recommend scenarios for their respective usage. Moreover, we develop both serial and parallelized versions of the algorithm. By experimenting with large-scale data, we demonstrate the computational efficiency of the new methods and investigate their convergence properties and numerical stability. The clustering results obtained on several datasets in different domains are highly competitive in comparison with some widely used methods in the corresponding areas.
95 citations
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14 Jun 2006TL;DR: In this paper, the authors extend previous work on oscillator models to meet the needs of multi-agent applications in which the motion of the collective centroid of the group must be dynamic.
Abstract: This paper extends previous work on oscillator models to meet the needs of multiagent applications in which the motion of the collective centroid of the group must be dynamic. Individual agents are modeled as unit speed planar kinematic unicycles. A steering control law is derived for each individual so that the velocity of the collective centroid matches a reference velocity, provided the reference speed is less than one. A framework for steering controls is presented such that the unicycles stay near the collective centroid even though the centroid is non-static. Finally, an outer loop controller is proposed to allow tracking of a target vehicle. Simulation results are shown to support analysis.
93 citations