Generalized weighted rules for principal components tracking
Generalized weighted rules for principal components tracking
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DOI：
10.1109/tsp.2005.843698
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发表时间：
2005-04
影响因子：
5.4
通讯作者：
Toshihisa Tanaka
中科院分区：
文献类型：
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作者：
Toshihisa Tanaka
我们研究了一类用于主成分分析(PCA)的一般加权子空间(WS)规则，以说明现有规则的差异。本文主要研究Oja和Xu提出的著名的加权主成分跟踪规则。我们将这些规则统一到由标量参数化的更一般的形式。证明了广义规则只在提取主成分的不动点稳定。此外，我们还找到了在跟踪过程中使估计主成分的动态保持正交性最强的规则的参数。最后，给出了玩具实例和在自适应图像压缩中的应用，以理解稳定性的理论分析。
We investigate a general class of weighted subspace (WS) rules for principal component analysis (PCA) in order to show the difference of the existing rules. We focus in this paper on the well-known weighted principal components tracking rules that are developed by Oja and Xu. We unify these rules to more generalized form that is parameterized by a scalar. It is then proved that the generalized rules are stable at only the fixed point from which the principal components are extracted. We moreover find the parameter of the rules that gives the dynamics preserving orthogonality of estimated principal components most strongly during the tracking. Finally, toy examples and application in adaptive image compression are illustrated to understand the theoretical analysis of the stability.