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.

A comparison of algorithms for maximum entropy parameter estimation

Abstract: Conditional maximum entropy (ME) models provide a general purpose machine learning technique which has been successfully applied to fields as diverse as computer vision and econometrics, and which is used for a wide variety of classification problems in natural language processing. However, the flexibility of ME models is not without cost. While parameter estimation for ME models is conceptually straightforward, in practice ME models for typical natural language tasks are very large, and may well contain many thousands of free parameters. In this paper, we consider a number of algorithms for estimating the parameters of ME models, including iterative scaling, gradient ascent, conjugate gradient, and variable metric methods. Sur-prisingly, the standardly used iterative scaling algorithms perform quite poorly in comparison to the others, and for all of the test problems, a limited-memory variable metric algorithm outperformed the other choices.

Discriminative Deep Metric Learning for Face Verification in the Wild

Abstract: This paper presents a new discriminative deep metric learning (DDML) method for face verification in the wild. Different from existing metric learning-based face verification methods which aim to learn a Mahalanobis distance metric to maximize the inter-class variations and minimize the intra-class variations, simultaneously, the proposed DDML trains a deep neural network which learns a set of hierarchical nonlinear transformations to project face pairs into the same feature subspace, under which the distance of each positive face pair is less than a smaller threshold and that of each negative pair is higher than a larger threshold, respectively, so that discriminative information can be exploited in the deep network. Our method achieves very competitive face verification performance on the widely used LFW and YouTube Faces (YTF) datasets.

A comparison of extrinsic clustering evaluation metrics based on formal constraints

Abstract: There is a wide set of evaluation metrics available to compare the quality of text clustering algorithms. In this article, we define a few intuitive formal constraints on such metrics which shed light on which aspects of the quality of a clustering are captured by different metric families. These formal constraints are validated in an experiment involving human assessments, and compared with other constraints proposed in the literature. Our analysis of a wide range of metrics shows that only BCubed satisfies all formal constraints. We also extend the analysis to the problem of overlapping clustering, where items can simultaneously belong to more than one cluster. As Bcubed cannot be directly applied to this task, we propose a modified version of Bcubed that avoids the problems found with other metrics.

Statistical Models for Text Segmentation

Abstract: This paper introduces a new statistical approach to automatically partitioning text into coherent segments. The approach is based on a technique that incrementally builds an exponential model to extract features that are correlated with the presence of boundaries in labeled training text. The models use two classes of features: topicality features that use adaptive language models in a novel way to detect broad changes of topic, and cue-word features that detect occurrences of specific words, which may be domain-specific, that tend to be used near segment boundaries. Assessment of our approach on quantitative and qualitative grounds demonstrates its effectiveness in two very different domains, Wall Street Journal news articles and television broadcast news story transcripts. Quantitative results on these domains are presented using a new probabilistically motivated error metric, which combines precision and recall in a natural and flexible way. This metric is used to make a quantitative assessment of the relative contributions of the different feature types, as well as a comparison with decision trees and previously proposed text segmentation algorithms.

A No-Reference Objective Image Sharpness Metric Based on the Notion of Just Noticeable Blur (JNB)

Abstract: This work presents a perceptual-based no-reference objective image sharpness/blurriness metric by integrating the concept of just noticeable blur into a probability summation model. Unlike existing objective no-reference image sharpness/blurriness metrics, the proposed metric is able to predict the relative amount of blurriness in images with different content. Results are provided to illustrate the performance of the proposed perceptual-based sharpness metric. These results show that the proposed sharpness metric correlates well with the perceived sharpness being able to predict with high accuracy the relative amount of blurriness in images with different content.