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.
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TL;DR: A novel filter method for feature selection, called Multivariate Relative Discrimination Criterion (MRDC), is proposed for text classification, which focuses on the reduction of redundant features using minimal-redundancy and maximal-relevancy concepts.
162 citations
TL;DR: A new transportation-related distance between pairs of images is described, which is described as linear optimal transportation (LOT), which can be used directly on pixel intensities, and is based on a linearized version of the Kantorovich-Wasserstein metric.
Abstract: Transportation-based metrics for comparing images have long been applied to analyze images, especially where one can interpret the pixel intensities (or derived quantities) as a distribution of `mass' that can be transported without strict geometric constraints. Here we describe a new transportation-based framework for analyzing sets of images. More specifically, we describe a new transportation-related distance between pairs of images, which we denote as linear optimal transportation (LOT). The LOT can be used directly on pixel intensities, and is based on a linearized version of the Kantorovich-Wasserstein metric (an optimal transportation distance, as is the earth mover's distance). The new framework is especially well suited for computing all pairwise distances for a large database of images efficiently, and thus it can be used for pattern recognition in sets of images. In addition, the new LOT framework also allows for an isometric linear embedding, greatly facilitating the ability to visualize discriminant information in different classes of images. We demonstrate the application of the framework to several tasks such as discriminating nuclear chromatin patterns in cancer cells, decoding differences in facial expressions, galaxy morphologies, as well as sub cellular protein distributions.
162 citations
TL;DR: A generalization of learning vector quantization with three additional features: it directly integrates neighborhood cooperation, hence is less affected by local optima, and the method can be combined with any differentiable similarity measure.
Abstract: Prototype based classification offers intuitive and sparse models with excellent generalization ability. However, these models usually crucially depend on the underlying Euclidian metric; moreover, online variants likely suffer from the problem of local optima. We here propose a generalization of learning vector quantization with three additional features: (I) it directly integrates neighborhood cooperation, hence is less affected by local optima; (II) the method can be combined with any differentiable similarity measure whereby metric parameters such as relevance factors of the input dimensions can automatically be adapted according to the given data; (III) it obeys a gradient dynamics hence shows very robust behavior, and the chosen objective is related to margin optimization.
162 citations
11 Dec 2013
TL;DR: Metric structures for Riemannian and non-Riemannians in space as mentioned in this paper, Metric structures of Riemanian space for non-residual space.
Abstract: Metric structures for Riemannian and non-Riemannian space , Metric structures for Riemannian and non-Riemannian space , کتابخانه دیجیتال جندی شاپور اهواز
162 citations
TL;DR: This paper introduces an ensemble method to compare MOEAs by combining a number of performance metrics using double elimination tournament selection and shows that the proposed metric ensemble can provide a more comprehensive comparison among variousMOEAs than what could be obtained from a single performance metric alone.
Abstract: Evolutionary algorithms have been successfully exploited to solve multiobjective optimization problems. In the literature, a heuristic approach is often taken. For a chosen benchmark problem with specific problem characteristics, the performance of multiobjective evolutionary algorithms (MOEAs) is evaluated via some heuristic chosen performance metrics. The conclusion is then drawn based on statistical findings given the preferable choices of performance metrics. The conclusion, if any, is often indecisive and reveals no insight pertaining to which specific problem characteristics the underlying MOEA could perform the best. In this paper, we introduce an ensemble method to compare MOEAs by combining a number of performance metrics using double elimination tournament selection. The double elimination design allows characteristically poor performance of a quality algorithm to still be able to win it all. Experimental results show that the proposed metric ensemble can provide a more comprehensive comparison among various MOEAs than what could be obtained from a single performance metric alone. The end result is a ranking order among all chosen MOEAs, but not quantifiable measures pertaining to the underlying MOEAs.
162 citations