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.

Space-time decoding with imperfect channel estimation

Abstract: Under the assumption of a frequency-flat slow Rayleigh fading channel with multiple transmit and receive antennas, we examine the effects on system performance of imperfect estimation of the channel parameters when the receiver either assumes that the estimate is perfect or uses a proper maximum-likelihood decision metric. An algorithm for the recursive calculation of the maximum-likelihood decision metric is developed for application to trellis space-time codes.

A Boosting Framework for Visuality-Preserving Distance Metric Learning and Its Application to Medical Image Retrieval

Abstract: Similarity measurement is a critical component in content-based image retrieval systems, and learning a good distance metric can significantly improve retrieval performance. However, despite extensive study, there are several major shortcomings with the existing approaches for distance metric learning that can significantly affect their application to medical image retrieval. In particular, ldquosimilarityrdquo can mean very different things in image retrieval: resemblance in visual appearance (e.g., two images that look like one another) or similarity in semantic annotation (e.g., two images of tumors that look quite different yet are both malignant). Current approaches for distance metric learning typically address only one goal without consideration of the other. This is problematic for medical image retrieval where the goal is to assist doctors in decision making. In these applications, given a query image, the goal is to retrieve similar images from a reference library whose semantic annotations could provide the medical professional with greater insight into the possible interpretations of the query image. If the system were to retrieve images that did not look like the query, then users would be less likely to trust the system; on the other hand, retrieving images that appear superficially similar to the query but are semantically unrelated is undesirable because that could lead users toward an incorrect diagnosis. Hence, learning a distance metric that preserves both visual resemblance and semantic similarity is important. We emphasize that, although our study is focused on medical image retrieval, the problem addressed in this work is critical to many image retrieval systems. We present a boosting framework for distance metric learning that aims to preserve both visual and semantic similarities. The boosting framework first learns a binary representation using side information, in the form of labeled pairs, and then computes the distance as a weighted Hamming distance using the learned binary representation. A boosting algorithm is presented to efficiently learn the distance function. We evaluate the proposed algorithm on a mammographic image reference library with an interactive search-assisted decision support (ISADS) system and on the medical image data set from ImageCLEF. Our results show that the boosting framework compares favorably to state-of-the-art approaches for distance metric learning in retrieval accuracy, with much lower computational cost. Additional evaluation with the COREL collection shows that our algorithm works well for regular image data sets.

Multiple model adaptive control. Part 1: Finite controller coverings

Abstract: We consider the problem of determining an appropriate model set on which to design a set of controllers for a multiple model switching adaptive control scheme. We show that, given mild assumptions on the uncertainty set of linear time-invariant plant models, it is possible to determine a "nite set of controllers such that for each plant in the uncertainty set, satisfactory performance will be obtained for some controller in the "nite set. We also demonstrate how such a controller set may be found. The analysis exploits the Vinnicombe metric and the fact that the set of approximately bandand time-limited transfer functions is approximately "nite-dimensional. Copyright ( 2000 John Wiley & Sons, Ltd.

Equilibrium maps between metric spaces

Abstract: We show the existence of harmonic mappings with values in possibly singular and not necessarily locally compact complete metric length spaces of nonpositive curvature in the sense of Alexandrov. As a technical tool, we show that any bounded sequence in such a space has a subsequence whose mean values converge. We also give a general definition of harmonic maps between metric spaces based on mean value properties andΓ-convergence.

Learning topological maps with weak local odometric information

Abstract: Topological maps provide a useful abstraction for robotic navigation and planning. Although stochastic maps can theoretically be learned using the Baum-Welch algorithm, without strong prior constraint on the structure of the model it is slow to converge, requires a great deal of data, and is often stuck in local minima. In this paper, we consider a special case of hidden Markov models for robot-navigation environments, in which states are associated with points in a metric configuration space. We assume that the robot has some odometric ability to measure relative transformations between its configurations. Such odometry is typically not precise enough to suffice for building a global map, but it does give valuable local information about relations between adjacent states. We present an extension of the Baum-Welch algorithm that takes advantage of this local odometric information, yielding faster convergence to better solutions with less data.