• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Extended Hamiltonian Learning on Riemannian Manifolds: Numerical Aspects
【24h】

Extended Hamiltonian Learning on Riemannian Manifolds: Numerical Aspects

机译：黎曼流形上的扩展哈密顿学：数值方面

获取原文
获取原文并翻译 | 示例
       
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

This paper is the second part of a study initiated with the paper S. Fiori, “Extended Hamiltonian learning on Riemannian manifolds: Theoretical aspects,” IEEE Trans. Neural Netw., vol. 22, no. 5, pp. 687–700, May 2011, which aimed at introducing a general framework to develop a theory of learning on differentiable manifolds by extended Hamiltonian stationary-action principle. This paper discusses the numerical implementation of the extended Hamiltonian learning paradigm by making use of notions from geometric numerical integration to numerically solve differential equations on manifolds. The general-purpose integration schemes and the discussion of several cases of interest show that the implementation of the dynamical learning equations exhibits a rich structure. The behavior of the discussed learning paradigm is illustrated via several numerical examples and discussions of case studies. The numerical examples confirm the theoretical developments presented in this paper as well as in its first part.
机译：本文是论文S. Fiori发起的研究的第二部分，S。Fiori，“关于黎曼流形的扩展哈密顿学习：理论方面”，IEEE Trans。神经网络，第一卷22号第五卷，第687–700页，2011年5月，其目的是引入一个通用框架，以扩展的哈密顿静力学原理发展关于微分流形的学习理论。本文利用几何数值积分的概念对流形上的微分方程进行数值求解，讨论了扩展哈密顿学习范式的数值实现。通用积分方案和感兴趣的几种情况的讨论表明，动态学​​习方程的实现具有丰富的结构。通过几个数值示例和案例研究的讨论来说明所讨论的学习范例的行为。数值例子证实了本文及其第一部分中提出的理论发展。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

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