<b>GrassmannOptim</b>: An<i>R</i>Package for Grassmann Manifold Optimization

Adragni, Kofi P.; Cook, R. Dennis; Wu, Seongho

doi:10.18637/jss.v050.i05

Cited by 13 publications

(15 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, µ p . This is essentially an eigenvalue problem reminiscent of the generalized Rayleigh quotient for discriminant analysis (Adragni and Wu, 2010). It will be later used in section 3 to illustrate practical use of the package.…”

Section: Optimization On Manifoldsmentioning

confidence: 99%

“…Other manifold optimization software packages are found in the literature: sg min written by Lippert (2000) which was adapted from Edelman et al (1998), and Manopt of Boumal et al (2014) are available in Matlab. In R, Adragni and Wu (2010) developed GrassmannOptim specifically for the Grassmann manifold. To our knowledge, there are no other publicly available R packages for manifold optimization.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

ManifoldOptim: An R Interface to the ROPTLIB Library for Riemannian Manifold Optimization

Martin¹,

Raim²,

Huang³

et al. 2020

J. Stat. Soft.

Self Cite

View full text Add to dashboard Cite

Manifold optimization appears in a wide variety of computational problems in the applied sciences. In recent statistical methodologies such as sufficient dimension reduction and regression envelopes, estimation relies on the optimization of likelihood functions over spaces of matrices such as the Stiefel or Grassmann manifolds. Recently, Huang, Absil, Gallivan, and Hand (2016) have introduced the library ROPTLIB, which provides a framework and state of the art algorithms to optimize real-valued objective functions over commonly used matrix-valued Riemannian manifolds. This article presents ManifoldOptim, an R package that wraps the C++ library ROPTLIB. ManifoldOptim enables users to access functionality in ROPTLIB through R so that optimization problems can easily be constructed, solved, and integrated into larger R codes. Computationally intensive problems can be programmed with Rcpp and RcppArmadillo, and otherwise accessed through R. We illustrate the practical use of ManifoldOptim through several motivating examples involving dimension reduction and envelope methods in regression.

show abstract

Section: Optimization On Manifoldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

ManifoldOptim: An R Interface to the ROPTLIB Library for Riemannian Manifold Optimization

Martin¹,

Raim²,

Huang³

et al. 2020

J. Stat. Soft.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Covariance reduction, LAD, and extended PFC rely on an external R package called Grass-mannOptim (Adragni et al 2012) for the optimization. Additional optional arguments may be provided for the optimization, especially arguments related to simulated annealing for global optimization.…”

Section: Overview and Use Of The Packagementioning

confidence: 99%

“…Optimization on the Grassmann manifold adds a layer of difficulty to the estimation procedure. Fortunately, a recent R package called GrassmannOptim (Adragni, Cook, and Wu 2012) has been made available for such optimization, which allows the current implementation of ldr in R. The implementation of GrassmannOptim uses gradient-based algorithms and embeds a stochastic gradient method for global search.…”

Section: Introductionmentioning

confidence: 99%

ldr: AnRSoftware Package for Likelihood-Based Sufficient Dimension Reduction

Adragni¹,

Raim²

2014

J. Stat. Soft.

Self Cite

View full text Add to dashboard Cite

In regression settings, a sufficient dimension reduction (SDR) method seeks the core information in a p-vector predictor that completely captures its relationship with a response. The reduced predictor may reside in a lower dimension d < p, improving ability to visualize data and predict future observations, and mitigating dimensionality issues when carrying out further analysis. We introduce ldr, a new R software package that implements three recently proposed likelihood-based methods for SDR: covariance reduction, likelihood acquired directions, and principal fitted components. All three methods reduce the dimensionality of the data by projection into lower dimensional subspaces. The package also implements a variable screening method built upon principal fitted components which makes use of flexible basis functions to capture the dependencies between the predictors and the response. Examples are given to demonstrate likelihood-based SDR analyses using ldr, including estimation of the dimension of reduction subspaces and selection of basis functions. The ldr package provides a framework that we hope to grow into a comprehensive library of likelihood-based SDR methodologies.

show abstract

“…For more background in Grassmann manifolds and Grassmann optimizations, see Edelman, Tomas, and Smith (1998). There are two currently available packages for Grassmann manifold optimization: R package GrassmannOptim by Adragni, Cook, and Wu (2012) and the MATLAB package sg min by Ross A. Lippert (http://web.mit.edu/˜ripper/www/software/).…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Envelopes for Multivariate Linear Regression

Cook

Zhang

2015

Technometrics

Self Cite

View full text Add to dashboard Cite

We introduce envelopes for simultaneously reducing the predictors and the responses in multivariate linear regression, so the regression then depends only on estimated linear combinations of X and Y. We use a likelihood-based objective function for estimating envelopes and then propose algorithms for estimation of a simultaneous envelope as well as for basic Grassmann manifold optimization. The asymptotic properties of the resulting estimator are studied under normality and extended to general distributions. We also investigate likelihood ratio tests and information criteria for determining the simultaneous envelope dimensions. Simulation studies and real data examples show substantial gain over the classical methods, like partial least squares, canonical correlation analysis, and reduced-rank regression. This article has supplementary material available online.

show abstract

GrassmannOptim: AnRPackage for Grassmann Manifold Optimization

Cited by 13 publications

References 21 publications

ManifoldOptim: An R Interface to the ROPTLIB Library for Riemannian Manifold Optimization

ManifoldOptim: An R Interface to the ROPTLIB Library for Riemannian Manifold Optimization

ldr: AnRSoftware Package for Likelihood-Based Sufficient Dimension Reduction

Simultaneous Envelopes for Multivariate Linear Regression

Contact Info

Product

Resources

About