• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文OA文献 >Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences
【2h】

Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences

机译：再次探讨对数决定因素的分歧：Alpha-Beta和Gamma对数偏差的分歧

代理获取
本网站仅为用户提供外文OA文献查询和代理获取服务，本网站没有原文。下单后我们将采用程序或人工为您竭诚获取高质量的原文，但由于OA文献来源多样且变更频繁，仍可能出现获取不到、文献不完整或与标题不符等情况，如果获取不到我们将提供退款服务。请知悉。
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

This work reviews and extends a family of log-determinant (log-det) divergencesfor symmetric positive definite (SPD) matrices and discusses their fundamental properties.We show how to use parameterized Alpha-Beta (AB) and Gamma log-det divergencesto generate many well-known divergences; in particular, we consider the Stein’s loss,the S-divergence, also called Jensen-Bregman LogDet (JBLD) divergence, Logdet Zero(Bhattacharyya) divergence, Affine Invariant Riemannian Metric (AIRM), and otherdivergences. Moreover, we establish links and correspondences between log-det divergencesand visualise them on an alpha-beta plane for various sets of parameters. We use thisunifying framework to interpret and extend existing similarity measures for semidefinitecovariance matrices in finite-dimensional Reproducing Kernel Hilbert Spaces (RKHS). Thispaper also shows how the Alpha-Beta family of log-det divergences relates to the divergencesof multivariate and multilinear normal distributions. Closed form formulas are derivedfor Gamma divergences of two multivariate Gaussian densities; the special cases of theKullback-Leibler, Bhattacharyya, Rényi, and Cauchy-Schwartz divergences are discussed.Symmetrized versions of log-det divergences are also considered and briefly reviewed.Finally, a class of divergences is extended to multiway divergences for separable covariance(or precision) matrices.
机译：这项工作回顾并扩展了对称正定（SPD）矩阵的对数行列式（log-det）散度的族，并讨论了它们的基本特性。我们展示了如何使用参数化的Alpha-Beta（AB）和Gamma对数散度来产生许多众所周知的分歧；特别是，我们考虑了Stein的损失，S散度，也称为Jensen-Bregman LogDet（JBLD）散度，Logdet零（Bhattacharyya）散度，仿射不变黎曼度量（AIRM）和其他散度。此外，我们建立了log-det散度之间的链接和对应关系，并在alpha-beta平面上可视化了各种参数集。我们使用这个统一框架来解释和扩展有限维再现内核希尔伯特空间（RKHS）中半确定协方差矩阵的现有相似性度量。本文还展示了log-det散度的Alpha-Beta系列与多元和线性正态分布散度的关系。对于两个多元高斯密度的伽玛散度，得出封闭式公式；讨论了Kullback-Leibler，Bhattacharyya，Rényi和Cauchy-Schwartz散度的特殊情况，并考虑并简要介绍了log-det散度的对称形式。精度）矩阵。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
代理获取

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号