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.

Disentangling by Factorising

Abstract: We define and address the problem of unsupervised learning of disentangled representations on data generated from independent factors of variation. We propose FactorVAE, a method that disentangles by encouraging the distribution of representations to be factorial and hence independent across the dimensions. We show that it improves upon $\beta$-VAE by providing a better trade-off between disentanglement and reconstruction quality. Moreover, we highlight the problems of a commonly used disentanglement metric and introduce a new metric that does not suffer from them.

Comparing Clusterings by the Variation of Information

Abstract: This paper proposes an information theoretic criterion for comparing two partitions, or clusterings, of the same data set. The criterion, called variation of information (VI), measures the amount of information lost and gained in changing from clustering \({\cal C}\) to clustering \({\cal C}'\). The criterion makes no assumptions about how the clusterings were generated and applies to both soft and hard clusterings. The basic properties of VI are presented and discussed from the point of view of comparing clusterings. In particular, the VI is positive, symmetric and obeys the triangle inequality. Thus, surprisingly enough, it is a true metric on the space of clusterings.

Geometry of the space of phylogenetic trees

Abstract: We consider a continuous space which models the set of all phylogenetic trees having a fixed set of leaves. This space has a natural metric of nonpositive curvature, giving a way of measuring distance between phylogenetic trees and providing some procedures for averaging or combining several trees whose leaves are identical. This geometry also shows which trees appear within a fixed distance of a given tree and enables construction of convex hulls of a set of trees. This geometric model of tree space provides a setting in which questions that have been posed by biologists and statisticians over the last decade can be approached in a systematic fashion. For example, it provides a justification for disregarding portions of a collection of trees that agree, thus simplifying the space in which comparisons are to be made.

Introduction to Functional Analysis

Abstract: Preliminaries 1. Banach spaces and Metric Linear Spaces 2. Spectral of Theory Linear Operators 3. Frechet Spaces and their Dual Spaces

A no-reference perceptual blur metric

Abstract: We present a no-reference blur metric for images and video. The blur metric is based on the analysis of the spread of the edges in an image. Its perceptual significance is validated through subjective experiments. The novel metric is near real-time, has low computational complexity and is shown to perform well over a range of image content. Potential applications include optimization of source coding, network resource management and autofocus of an image capturing device.