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.

Real-time status updating: Multiple sources

Abstract: We examine multiple independent sources providing status updates to a monitor through a first-come-first-served M/M/1 queue. We formulate a status-age timeliness metric and find the region of feasible average status ages for a pair of updating sources. In the presence of interfering traffic with a given offered load, we show the existence of an optimal rate at which a source should generate its updates.

No Fuss Distance Metric Learning using Proxies

Abstract: We address the problem of distance metric learning (DML), defined as learning a distance consistent with a notion of semantic similarity. Traditionally, for this problem supervision is expressed in the form of sets of points that follow an ordinal relationship -- an anchor point $x$ is similar to a set of positive points $Y$, and dissimilar to a set of negative points $Z$, and a loss defined over these distances is minimized. While the specifics of the optimization differ, in this work we collectively call this type of supervision Triplets and all methods that follow this pattern Triplet-Based methods. These methods are challenging to optimize. A main issue is the need for finding informative triplets, which is usually achieved by a variety of tricks such as increasing the batch size, hard or semi-hard triplet mining, etc. Even with these tricks, the convergence rate of such methods is slow. In this paper we propose to optimize the triplet loss on a different space of triplets, consisting of an anchor data point and similar and dissimilar proxy points which are learned as well. These proxies approximate the original data points, so that a triplet loss over the proxies is a tight upper bound of the original loss. This proxy-based loss is empirically better behaved. As a result, the proxy-loss improves on state-of-art results for three standard zero-shot learning datasets, by up to 15% points, while converging three times as fast as other triplet-based losses.

Gait recognition using static, activity-specific parameters

Abstract: A gait-recognition technique that recovers static body and stride parameters of subjects as they walk is presented. This approach is an example of an activity-specific biometric: a method of extracting identifying properties of an individual or of an individual's behavior that is applicable only when a person is performing that specific action. To evaluate our parameters, we derive an expected confusion metric (related to mutual information), as opposed to reporting a percent correct with a limited database. This metric predicts how well a given feature vector will filter identity in a large population. We test the utility of a variety of body and stride parameters recovered in different viewing conditions on a database consisting of 15 to 20 subjects walking at both an angled and frontal-parallel view with respect to the camera, both indoors and out. We also analyze motion-capture data of the subjects to discover whether confusion in the parameters is inherently a physical or a visual measurement error property.

Recursive MUSIC: A framework for EEG and MEG source localization

Abstract: The multiple signal classification (MUSIC) algorithm can be used to locate multiple asynchronous dipolar sources from electroencephalography (EEG) and magnetocncephalography (MEG) data. The algorithm scans a single-dipole model through a three-dimensional (3-D) head volume and computes projections onto an estimated signal subspace. To locate the sources, the user must search the head volume for multiple local peaks in the projection metric. This task is time consuming and subjective. Here, the authors describe an extension of this approach which they refer to as recursive MUSIC (R-MUSIC). This new procedure automatically extracts the locations of the sources through a recursive use of subspace projections. The new method is also able to locate synchronous sources through the use of a spatio-temporal independent topographies (IT) model. This model defines a source as one or more nonrotating dipoles with a single time course. Within this framework, the authors are able to locate fixed, rotating, and synchronous dipoles. The recursive subspace projection procedure that they introduce here uses the metric of canonical or subspace correlations as a multidimensional form of correlation analysis between the model subspace and the data subspace, by recursively computing subspace correlations, the authors build up a model for the sources which account for a given set of data. They demonstrate here how R-MUSIC can easily extract multiple asynchronous dipolar sources that are difficult to find using the original MUSIC scan. The authors then demonstrate R-MUSIC applied to the more general IT model and show results for combinations of fixed, rotating, and synchronous dipoles.