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.

Method, system and apparatus for targeting an offer

Abstract: A system, apparatus, means, computer code, and method may include receiving data indicative of information associated with a user, determining a value of a metric associated with the user based on the data indicative of information associated with the user, verifying that the value of the metric associated with the user is valid, selecting an offer from a plurality of offers where each of the offers has a score associated with the value of the metric, and providing data indicative of the selected offer.

A metric for odorant comparison.

Abstract: In studies of vision and audition, stimuli can be systematically varied by wavelength and frequency, respectively, but there is no equivalent metric for olfaction. Restricted odorant-feature metrics such as number of carbons and functional group do not account for response patterns to odorants varying along other structural dimensions. We generated a multidimensional odor metric, in which each odorant molecule was represented as a vector of 1,664 molecular descriptor values. Revisiting many studies, we found that this metric and a second optimized metric were always better at accounting for neural responses than the specific metric used in each study. These metrics were applicable across studies that differed in the animals studied, the type of olfactory neurons tested, the odorants applied and the recording methods used. We use this new metric to recommend sets of odorants that span the physicochemical space for use in olfaction experiments.

Transversing itemset lattices with statistical metric pruning

Abstract: We study how to efficiently compute significant association rules according to common statistical measures such as a chi-squared value or correlation coefficient. For this purpose, one might consider to use of the Apriori algorithm, but the algorithm needs major conversion, because none of these statistical metrics are anti-monotone, and the use of higher support for reducing the search space cannot guarantee solutions in its the search space. We here present a method of estimating a tight upper bound on the statistical metric associated with any superset of an itemset, as well as the novel use of the resulting information of upper bounds to prune unproductive supersets while traversing itemset lattices. Experimental tests demonstrate the efficiency of this method.

Metrics on states from actions of compact groups

Abstract: Let a compact Lie group act ergodically on a unital $C^*$-algebra $A$. We consider several ways of using this structure to define metrics on the state space of $A$. These ways involve length functions, norms on the Lie algebra, and Dirac operators. The main thrust is to verify that the corresponding metric topologies on the state space agree with the weak-$*$ topology.

HOTA: A Higher Order Metric for Evaluating Multi-Object Tracking

Abstract: Multi-Object Tracking (MOT) has been notoriously difficult to evaluate. Previous metrics overemphasize the importance of either detection or association. To address this, we present a novel MOT evaluation metric, HOTA (Higher Order Tracking Accuracy), which explicitly balances the effect of performing accurate detection, association and localization into a single unified metric for comparing trackers. HOTA decomposes into a family of sub-metrics which are able to evaluate each of five basic error types separately, which enables clear analysis of tracking performance. We evaluate the effectiveness of HOTA on the MOTChallenge benchmark, and show that it is able to capture important aspects of MOT performance not previously taken into account by established metrics. Furthermore, we show HOTA scores better align with human visual evaluation of tracking performance.