Description Usage Arguments Details Value Author(s) References Examples

Solve the generalized DWD model by using a symmetric Gauss-Seidel based alternating direction method of multipliers (ADMM) method.

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`X` |
A |

`y` |
A vector of length |

`C` |
A number representing the penalty parameter for the generalized DWD model. |

`expon` |
A positive number representing the exponent |

`tol` |
The stopping tolerance for the algorithm. (Default = 1e-5) |

`maxIter` |
Maximum iteration allowed for the algorithm. (Default = 2000) |

`method` |
Method for solving generalized DWD model. The default is set to be 1 for the highly efficient sGS-ADMM algorithm. User can also select |

`printDetails` |
Switch for printing details of the algorithm. Default is set to be 0 (not printing). |

`rmzeroFea` |
Switch for removing zero features in the data matrix. Default is set to be 1 (removing zero features). |

`scaleFea` |
Switch for scaling features in the data matrix. This is to make the features having roughly similar magnitude. Default is set to be 1 (scaling features). |

This is a symmetric Gauss-Seidel based alternating method of multipliers (sGS-ADMM) algorithm for solving the generalized DWD model of the following formulation:

*\min ∑_i θ_q (r_i) + C e^T x_i*

subject to the constraints

*Z^T w + β y + ξ - r = 0, ||w||<=1, ξ>=0,*

where *Z = X diag(y)*, *e* is a given positive vector such that *||e||_∞ = 1*, and *θ_q*
is a function defined by *θ_q(t) = 1/t^q* if *t>0* and *θ_q(t)=∞* if *t<=0*.

A list consists of the result from the algorithm.

`w` |
The unit normal of hyperplane that distinguishes the two classes. |

`beta` |
The distance of the hyperplane to the origin ( |

`xi` |
A slack variable of length |

`r` |
The residual |

`alpha` |
Dual variable of the generalized DWD model. |

`info` |
A list consists of the information from the algorithm. |

`runhist` |
A list consists of the run history throughout the iterations. |

Xin-Yee Lam, J.S. Marron, Defeng Sun, and Kim-Chuan Toh

Lam, X.Y., Marron, J.S., Sun, D.F., and Toh, K.C. (2018)
“Fast algorithms for large scale generalized distance weighted discrimination", *Journal of Computational and Graphical Statistics*, forthcoming.

https://arxiv.org/abs/1604.05473

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