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.
Papers published on a yearly basis
Papers
More filters
TL;DR: A metric to estimate the optimal execution time of DO loops on particular processors is described, parameterized by the memory bandwidth and peak floating-point rate of the processor, as well as the length of the pipelines used in the functional units.
154 citations
30 Mar 2008
TL;DR: This work proposes an extension to the Discounted Cumulated Gain metric, the Session-based DCG (sDCG) metric, for evaluation scenarios involving multiple query sessions, graded relevance assessments, and open-ended user effort including decisions to stop searching.
Abstract: IR research has a strong tradition of laboratory evaluation of systems. Such research is based on test collections, pre-defined test topics, and standard evaluation metrics. While recent research has emphasized the user viewpoint by proposing user-based metrics and non-binary relevance assessments, the methods are insufficient for truly user-based evaluation. The common assumption of a single query per topic and session poorly represents real life. On the other hand, one well-known metric for multiple queries per session, instance recall, does not capture early (within session) retrieval of (highly) relevant documents. We propose an extension to the Discounted Cumulated Gain (DCG) metric, the Session-based DCG (sDCG) metric for evaluation scenarios involving multiple query sessions, graded relevance assessments, and open-ended user effort including decisions to stop searching. The sDCG metric discounts relevant results from later queries within a session. We exemplify the sDCG metric with data from an interactive experiment, we discuss how the metric might be applied, and we present research questions for which the metric is helpful.
153 citations
TL;DR: This study finds that landmarks and their geometry-based approach can account for variations of face expression and aging very well and can be used either in stand-alone mode or in conjunction with other approaches to reduce the search space a priori.
153 citations
24 Nov 2003
TL;DR: A novel solution to the inter-camera color calibration problem, which is very important for multicamera systems is presented and it is shown that the distance metric can be reduced to other commonly used metrics with suitable simplification.
Abstract: A novel solution to the inter-camera color calibration problem, which is very important for multicamera systems is presented. We propose a distance metric and a model function to evaluate the inter-camera radiometric properties. Instead of depending on the shape assumptions of brightness transfer function to find separate radiometric responses, we derive a nonparametric function to model color distortion for pair-wise camera combinations. Our method is based on correlation matrix analysis and dynamic programming. The correlation matrix is computed from three 1-D color histograms, and the model function is obtained from a minimum cost path traced within the matrix. The model function enables accurate compensation of color mismatches, which cannot be done with conventional distance metrics. Furthermore, we show that our metric can be reduced to other commonly used metrics with suitable simplification. Our simulations prove the effectiveness of the proposed method even for severe color distortions.
153 citations
01 Oct 2017
TL;DR: A new primal-dual approach is presented that allows to exploit the geometric structure of k-means and to satisfy the hard constraint that at most k clusters are selected without deteriorating the approximation guarantee.
Abstract: Clustering is a classic topic in optimization with k-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for k-means with a provable guarantee is a simple local search heuristic yielding an approximation guarantee of 9+≥ilon, a ratio that is known to be tight with respect to such methods.We overcome this barrier by presenting a new primal-dual approach that allows us to (1) exploit the geometric structure of k-means and (2) to satisfy the hard constraint that at most k clusters are selected without deteriorating the approximation guarantee. Our main result is a 6.357-approximation algorithm with respect to the standard LP relaxation. Our techniques are quite general and we also show improved guarantees for the general version of k-means where the underlying metric is not required to be Euclidean and for k-median in Euclidean metrics.
153 citations