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Metric (mathematics)

About: Metric (mathematics) is a research topic. Over the lifetime, 42617 publications have been published within this topic receiving 836571 citations. The topic is also known as: distance function & metric.


Papers
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Journal ArticleDOI
01 Oct 1994
TL;DR: A fast and exact planner for the mobile robot model, based upon recursive subdivision of a collision-free path generated by a lower-level geometric planner that ignores the motion constraints, is presented.
Abstract: This paper considers the problem of motion planning for a car-like robot (i.e., a mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We present a fast and exact planner for our mobile robot model, based upon recursive subdivision of a collision-free path generated by a lower-level geometric planner that ignores the motion constraints. The resultant trajectory is optimized to give a path that is of near-minimal length in its homotopy class. Our claims of high speed are supported by experimental results for implementations that assume a robot moving amid polygonal obstacles. The completeness and the complexity of the algorithm are proven using an appropriate metric in the configuration space R/sup 2//spl times/S/sup 1/ of the robot. This metric is defined by using the length of the shortest paths in the absence of obstacles as the distance between two configurations. We prove that the new induced topology and the classical one are the same. Although we concentrate upon the car-like robot, the generalization of these techniques leads to new theoretical issues involving sub-Riemannian geometry and to practical results for nonholonomic motion planning. >

604 citations

Proceedings ArticleDOI
23 Jun 2013
TL;DR: A new approach for matching images observed in different camera views with complex cross-view transforms and apply it to person re-identification that jointly partitions the image spaces of two camera views into different configurations according to the similarity of cross- view transforms.
Abstract: In this paper, we propose a new approach for matching images observed in different camera views with complex cross-view transforms and apply it to person re-identification. It jointly partitions the image spaces of two camera views into different configurations according to the similarity of cross-view transforms. The visual features of an image pair from different views are first locally aligned by being projected to a common feature space and then matched with softly assigned metrics which are locally optimized. The features optimal for recognizing identities are different from those for clustering cross-view transforms. They are jointly learned by utilizing sparsity-inducing norm and information theoretical regularization. This approach can be generalized to the settings where test images are from new camera views, not the same as those in the training set. Extensive experiments are conducted on public datasets and our own dataset. Comparisons with the state-of-the-art metric learning and person re-identification methods show the superior performance of our approach.

602 citations

Proceedings ArticleDOI
Xiaoqiang Luo1
06 Oct 2005
TL;DR: The paper proposes a Constrained Entity-Alignment F-Measure (CEAF) for evaluating coreference resolution and shows that the best alignment is a maximum bipartite matching problem which can be solved by the Kuhn-Munkres algorithm.
Abstract: The paper proposes a Constrained Entity-Alignment F-Measure (CEAF) for evaluating coreference resolution. The metric is computed by aligning reference and system entities (or coreference chains) with the constraint that a system (reference) entity is aligned with at most one reference (system) entity. We show that the best alignment is a maximum bipartite matching problem which can be solved by the Kuhn-Munkres algorithm. Comparative experiments are conducted to show that the widely-known MUC F-measure has serious flaws in evaluating a coreference system. The proposed metric is also compared with the ACE-Value, the official evaluation metric in the Automatic Content Extraction (ACE) task, and we conclude that the proposed metric possesses some properties such as symmetry and better interpretability missing in the ACE-Value.

591 citations

Journal ArticleDOI
TL;DR: Space-time Riemann metric for scalar-tensor gravitational theories with arbitrary omega parameter was proposed in this article, where the omega parameter is defined as a Gaussian.
Abstract: Space-time Riemann metric for scalar-tensor gravitational theories with arbitrary omega parameter

590 citations

Journal Article
TL;DR: This paper reviews the proper construction of offline experiments for deciding on the most appropriate algorithm, and discusses three important tasks of recommender systems, and classify a set of appropriate well known evaluation metrics for each task.
Abstract: Recommender systems are now popular both commercially and in the research community, where many algorithms have been suggested for providing recommendations. These algorithms typically perform differently in various domains and tasks. Therefore, it is important from the research perspective, as well as from a practical view, to be able to decide on an algorithm that matches the domain and the task of interest. The standard way to make such decisions is by comparing a number of algorithms offline using some evaluation metric. Indeed, many evaluation metrics have been suggested for comparing recommendation algorithms. The decision on the proper evaluation metric is often critical, as each metric may favor a different algorithm. In this paper we review the proper construction of offline experiments for deciding on the most appropriate algorithm. We discuss three important tasks of recommender systems, and classify a set of appropriate well known evaluation metrics for each task. We demonstrate how using an improper evaluation metric can lead to the selection of an improper algorithm for the task of interest. We also discuss other important considerations when designing offline experiments.

580 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202253
20213,191
20203,141
20192,843
20182,731
20172,341