scispace - formally typeset
Search or ask a question
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
More filters
Posted Content
TL;DR: This work introduces a novel architecture where class representations are conditioned for each few-shot trial based on a target image, and deviates from traditional metric-learning approaches by training a network to perform comparisons between classes rather than relying on a static metric comparison.
Abstract: Learning high quality class representations from few examples is a key problem in metric-learning approaches to few-shot learning To accomplish this, we introduce a novel architecture where class representations are conditioned for each few-shot trial based on a target image We also deviate from traditional metric-learning approaches by training a network to perform comparisons between classes rather than relying on a static metric comparison This allows the network to decide what aspects of each class are important for the comparison at hand We find that this flexible architecture works well in practice, achieving state-of-the-art performance on the Caltech-UCSD birds fine-grained classification task

145 citations

Journal ArticleDOI
TL;DR: A theoretical analysis of metric-based SAR autofocus techniques using simple image models shows that the objective function has a special separble property through which it can be well approximated locally by a sum of 1-D functions of each phase error component simultaneously.
Abstract: Synthetic aperture radar (SAR) autofocus techniques that optimize sharpness metrics can produce excellent restorations in comparison with conventional autofocus approaches. To help formalize the understanding of metric-based SAR autofocus methods, and to gain more insight into their performance, we present a theoretical analysis of these techniques using simple image models. Specifically, we consider the intensity-squared metric, and a dominant point-targets image model, and derive expressions for the resulting objective function. We examine the conditions under which the perfectly focused image models correspond to stationary points of the objective function. A key contribution is that we demonstrate formally, for the specific case of intensity-squared minimization autofocus, the mechanism by which metric-based methods utilize the multichannel defocusing model of SAR autofocus to enforce the stationary point property for multiple image columns. Furthermore, our analysis shows that the objective function has a special separble property through which it can be well approximated locally by a sum of 1-D functions of each phase error component. This allows fast performance through solving a sequence of 1-D optimization problems for each phase component simultaneously. Simulation results using the proposed models and actual SAR imagery confirm that the analysis extends well to realistic situations.

145 citations

Journal ArticleDOI
26 Sep 2018
TL;DR: In this article, a new and highly efficient tagger for hadronically decaying top quarks, based on a deep neural network working with Lorentz vectors and the Minkowski metric, is introduced.
Abstract: We introduce a new and highly efficient tagger for hadronically decaying topquarks, based on a deep neural network working with Lorentz vectors and theMinkowski metric. With its novel machine learning setup and architecture itallows us to identify boosted top quarks not only from calorimeter towers, butalso including tracking information. We show how the performance of our taggercompares with QCD-inspired and image-recognition approaches and find that itsignificantly increases the performance for strongly boosted top quarks.

144 citations

Proceedings Article
05 Dec 2016
TL;DR: This paper proposes an efficient technique to learn a supervised metric, which it is called the Supervised-WMD (S-W MD) metric, and provides an arbitrarily close approximation of the original WMD distance that results in a practical and efficient update rule.
Abstract: Recently, a new document metric called the word mover's distance (WMD) has been proposed with unprecedented results on kNN-based document classification. The WMD elevates high-quality word embeddings to a document metric by formulating the distance between two documents as an optimal transport problem between the embedded words. However, the document distances are entirely un-supervised and lack a mechanism to incorporate supervision when available. In this paper we propose an efficient technique to learn a supervised metric, which we call the Supervised-WMD (S-WMD) metric. The supervised training minimizes the stochastic leave-one-out nearest neighbor classification error on a per-document level by updating an affine transformation of the underlying word embedding space and a word-imporance weight vector. As the gradient of the original WMD distance would result in an inefficient nested optimization problem, we provide an arbitrarily close approximation that results in a practical and efficient update rule. We evaluate S-WMD on eight real-world text classification tasks on which it consistently outperforms almost all of our 26 competitive baselines.

144 citations

Book
01 Jan 1971

144 citations


Network Information
Related Topics (5)
Cluster analysis
146.5K papers, 2.9M citations
83% related
Optimization problem
96.4K papers, 2.1M citations
83% related
Fuzzy logic
151.2K papers, 2.3M citations
83% related
Robustness (computer science)
94.7K papers, 1.6M citations
83% related
Support vector machine
73.6K papers, 1.7M citations
82% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202253
20213,191
20203,141
20192,843
20182,731
20172,341