A simple general procedure for orthogonal rotation
A simple general procedure for orthogonal rotation
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DOI：
10.1007/bf02294840
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发表时间：
2001-06-01
期刊：
影响因子：
3
通讯作者：
Jennrich, RI
中科院分区：
文献类型：
--
作者：
Jennrich, RI
一个非常普遍的算法正交旋转。它示出，当算法参数cr是足够大的算法单调收敛到一个稳定点的旋转准则从任何起始值。因为足够大的cu通常很难找到，所以引入了不需要它的修改。没有这个要求，修改后的算法不仅非常通用，而且非常简单。它的实现只涉及计算旋转准则的梯度。虽然修改后的算法从任何初始值单调收敛，但不能保证收敛到一个稳定点。然而，在我们所有的例子中都是这样。虽然在因子分析中的旋转问题的动机，所讨论的算法可以用来优化几乎任何函数的不一定正方形列的正交矩阵。一些这些更一般的应用程序被认为是。经验的例子表明，修改后的算法可以相当快，但其目的是节省调查人员的努力，而不是他或她的计算机。这使得它更适合作为研究工具，而不是作为既定方法的算法。
A very general algorithm for orthogonal rotation is identified. It is shown that when an algorithm parameter cr is sufficiently large the algorithm converges monotonically to a stationary point of the rotation criterion from any starting value. Because a sufficiently large cu is in general hard to find, a modification that does not require it is introduced. Without this requirement the modified algorithm is not only very general, but also very simple. Its implementation involves little more than computing the gradient of the rotation criterion. While the modified algorithm converges monotonically from any starting value, it is not guaranteed to converge to a stationary point. It, however, does so in all of our examples. While motivated by the rotation problem in factor analysis, the algorithms discussed may be used to optimize almost any function of a not necessarily square column-wise orthonormal matrix. A number of these more general applications are considered. Empirical examples show that the modified algorithm can be reasonably fast, but its purpose is to save an investigator's effort rather than that of his or her computer. This makes it more appropriate as a research tool than as an algorithm for established methods.