Topic
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.
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TL;DR: Evaluating Chidamber and Kemerer metrics by using Kitchenham's metric-evaluation framework and finds deficiencies in some of the C&K metrics, and proposes another metric suite for object-oriented programming.
159 citations
TL;DR: A new approach on defuzzification using the metric (distance) between two fuzzy numbers is introduced and an application of this new approach is investigated.
158 citations
TL;DR: A Bayesian methodology for assessing the confidence in model prediction by comparing the model output with experimental data when both are stochastic is developed.
158 citations
TL;DR: This paper proposes a new methodology for the semantic interpretation of 3D point clouds which involves feature relevance assessment in order to reduce both processing time and memory consumption and demonstrates the great potential of smaller subsets consisting of only the most relevant features with 4 different state-of-the-art classifiers.
Abstract: The automatic analysis of large 3D point clouds represents a crucial task in photogrammetry, remote sensing and computer vision. In this paper, we propose a new methodology for the semantic interpretation of such point clouds which involves feature relevance assessment in order to reduce both processing time and memory consumption. Given a standard benchmark dataset with 1.3 million 3D points, we first extract a set of 21 geometric 3D and 2D features. Subsequently, we apply a classifier-independent ranking procedure which involves a general relevance metric in order to derive compact and robust subsets of versatile features which are generally applicable for a large variety of subsequent tasks. This metric is based on 7 different feature selection strategies and thus addresses different intrinsic properties of the given data. For the example of semantically interpreting 3D point cloud data, we demonstrate the great potential of smaller subsets consisting of only the most relevant features with 4 different state-of-the-art classifiers. The results reveal that, instead of including as many features as possible in order to compensate for lack of knowledge, a crucial task such as scene interpretation can be carried out with only few versatile features and even improved accuracy.
158 citations
22 Oct 1990
TL;DR: Deterministic competitive k-server algorithms are given for all k and all metric spaces and the competitive ratio can be proved is exponential in the number of servers, which settles the k- server conjecture.
Abstract: Deterministic competitive k-server algorithms are given for all k and all metric spaces. This settles the k-server conjecture of M.S. Manasse et al. (1988) up to the competitive ratio. The best previous result for general metric spaces was a three-server randomized competitive algorithm and a nonconstructive proof that a deterministic three-server competitive algorithm exists. The competitive ratio the present authors can prove is exponential in the number of servers. Thus, the question of the minimal competitive ratio for arbitrary metric spaces is still open. The methods set forth here also give competitive algorithms for a natural generalization of the k-server problem, called the k-taxicab problem. >
158 citations