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GrassmannOptim: An R Package for Grassmann Manifold Optimization

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  • Adragni, Kofi Placid
  • Cook, R. Dennis
  • Wu, Seongho

Abstract

The optimization of a real-valued objective function f(U), where U is a p X d,p > d, semi-orthogonal matrix such that UTU=Id, and f is invariant under right orthogonal transformation of U, is often referred to as a Grassmann manifold optimization. Manifold optimization appears in a wide variety of computational problems in the applied sciences. In this article, we present GrassmannOptim, an R package for Grassmann manifold optimization. The implementation uses gradient-based algorithms and embeds a stochastic gradient method for global search. We describe the algorithms, provide some illustrative examples on the relevance of manifold optimization and finally, show some practical usages of the package.

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  • Adragni, Kofi Placid & Cook, R. Dennis & Wu, Seongho, 2012. "GrassmannOptim: An R Package for Grassmann Manifold Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(i05).
    • Handle: RePEc:jss:jstsof:v:050:i05
    DOI: http://hdl.handle.net/10.18637/jss.v050.i05
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    References listed on IDEAS

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    1. R. Dennis Cook & Liliana Forzani, 2008. "Covariance reducing models: An alternative to spectral modelling of covariance matrices," Biometrika, Biometrika Trust, vol. 95(4), pages 799-812.
    2. Lee, Eun-Kyung & Cook, Dianne & Klinke, Sigbert & Lumley, Thomas, 2005. "Projection pursuit for exploratory supervised classification," SFB 649 Discussion Papers 2005-026, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
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    Cited by:

    1. Ming-Yueh Huang & Kwun Chuen Gary Chan, 2017. "Joint sufficient dimension reduction and estimation of conditional and average treatment effects," Biometrika, Biometrika Trust, vol. 104(3), pages 583-596.

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