Learning on the compact Stiefel manifold by a cayley-transform-based pseudo-retraction map
Learning on the compact Stiefel manifold by a cayley-transform-based pseudo-retraction map
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通过基于凯莱变换的伪回缩图学习紧致 Stiefel 流形
DOI：
10.1109/ijcnn.2012.6252841
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Toshihisa Tanaka
中科院分区：
文献类型：
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作者：
S. Fiori;Tetsuya Kaneko;Toshihisa Tanaka
目前的研究采取了从以前的贡献，本作者在两个主题，即，神经学习微分流形上的流形收缩和平均微分流形。在可微流形上学习是一种通用理论，它允许坚持弯曲光滑空间的神经系统在不违反参数空间几何约束的情况下调整其参数。特别是，目前的贡献集中在学习上的紧凑Stiefel流形的流形收缩与应用平均“高瘦”矩阵，并概括了一些贡献最近出现在科学文献中关于这样一个话题。
The present research takes its moves from previous contributions by the present authors on two topics, namely, neural learning on differentiable manifolds by manifold retractions and averaging over differentiable manifolds. Learning on differentiable manifolds is a general theory that allows a neural system that insists on curved smooth spaces to adapt its parameters without violating the constraints on the geometry of the parameter spaces. In particular, the present contribution focuses on learning on the compact Stiefel manifold by manifold retraction with application to averaging `tall-skinny' matrices and generalizes some contributions recently appeared in the scientific literature about such a topic.