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ORTHOMAX rotation problem. a differential equation approach

Trendafilov, Nickolay T. and Chu, Moody T. (1998). ORTHOMAX rotation problem. a differential equation approach. Behaviormetrika, 25(1) pp. 13–23.

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In the present paper the ORTHOMAX rotation problem is reconsidered. It is shown that its solution can be presented as a steepest ascent flow on the manifold of orthogonal matrices. A matrix formulation of the ORTHOMAX problem is given as an initial value problem for matrix differential equation of first order. The solution can be found by any available ODE numerical integrator. Thus the paper proposes a convergent method for direct matrix solution of the ORTHOMAX problem. The well-known first order necessary condition for the VARIMAX maximizer is reestablished for the ORTHOMAX case without using Lagrange multipliers. Additionally new second order optimality conditions are derived and as a consequence an explicit second order necessary condition for further classification of the ORTHOMAX maximizer is obtained.

Item Type: Journal Item
Copyright Holders: 1998 The Behaviormetric Society of Japan
ISSN: 1349-6964
Keywords: ORTHOMAX rotation; matrix solution; projected gradient; optimality conditions
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 28349
Depositing User: Sarah Frain
Date Deposited: 15 Mar 2011 14:37
Last Modified: 07 Dec 2018 09:52
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