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.

Effective Proximity Retrieval by Ordering Permutations

Abstract: We introduce a new probabilistic proximity search algorithm for range and A"-nearest neighbor (A"-NN) searching in both coordinate and metric spaces. Although there exist solutions for these problems, they boil down to a linear scan when the space is intrinsically high dimensional, as is the case in many pattern recognition tasks. This, for example, renders the A"-NN approach to classification rather slow in large databases. Our novel idea is to predict closeness between elements according to how they order their distances toward a distinguished set of anchor objects. Each element in the space sorts the anchor objects from closest to farthest to it and the similarity between orders turns out to be an excellent predictor of the closeness between the corresponding elements. We present extensive experiments comparing our method against state-of-the-art exact and approximate techniques, both in synthetic and real, metric and nonmetric databases, measuring both CPU time and distance computations. The experiments demonstrate that our technique almost always improves upon the performance of alternative techniques, in some cases by a wide margin.

Approximation of Metric Spaces by Partial Metric Spaces

Abstract: Partial metrics are generalised metrics with non-zero self-distances. We slightly generalise Matthews' original definition of partial metrics, yielding a notion of weak partial metric. After considering weak partial metric spaces in general, we introduce a weak partial metric on the poset of formal balls of a metric space. This weak partial metric can be used to construct the completion of classical metric spaces from the domain-theoretic rounded ideal completion.

Parsing in a Dynamical System: An Attractor-based Account of the Interaction of Lexical and Structural Constraints in Sentence Processing

Abstract: A dynamical systems approach to parsing is proposed in which syntactic hypotheses are associated with attractors in a metric space. These attractors have many of the properties of traditional syntactic categories, while at the same time encoding context-dependent, lexically specie c distinctions. Hypotheses motivated by the dynamical system theory were tested in four reading time experiments examining the interaction of simple lexica l frequencies, frequencies that are contingent on an environment deened by syntactic categories, and frequencies contingent on verb argument structure. The experiments documented a variety of contingent frequency effects that cut across traditional linguistic grains, each of which was predicted by the dynamical systems model. These effects were simulated in an implementation of the theory, employing a recurrent network trained from a corpus to construct metric representations and an algorithm implementing a gravitational dynamical system to model reading time as time to gravitate to an attractor.

In defence of metric learning for speaker recognition

Abstract: The objective of this paper is 'open-set' speaker recognition of unseen speakers, where ideal embeddings should be able to condense information into a compact utterance-level representation that has small intra-speaker and large inter-speaker distance. A popular belief in speaker recognition is that networks trained with classification objectives outperform metric learning methods. In this paper, we present an extensive evaluation of most popular loss functions for speaker recognition on the VoxCeleb dataset. We demonstrate that the vanilla triplet loss shows competitive performance compared to classification-based losses, and those trained with our proposed metric learning objective outperform state-of-the-art methods.