SDAAP | R Documentation |

Applies accelerated proximal gradient algorithm to the optimal scoring formulation of sparse discriminant analysis proposed by Clemmensen et al. 2011.

```
SDAAP(Xt, ...)
## Default S3 method:
SDAAP(
Xt,
Yt,
Om,
gam,
lam,
q,
PGsteps,
PGtol,
maxits,
tol,
selector = rep(1, dim(Xt)[2]),
initTheta,
bt = FALSE,
L,
eta,
rankRed = FALSE,
...
)
```

`Xt` |
n by p data matrix, (not a data frame, but a matrix) |

`Yt` |
n by K matrix of indicator variables (Yij = 1 if i in class j). This will later be changed to handle factor variables as well. Each observation belongs in a single class, so for a given row/observation, only one element is 1 and the rest is 0. |

`Om` |
p by p parameter matrix Omega in generalized elastic net penalty. |

`gam` |
Regularization parameter for elastic net penalty. |

`lam` |
Regularization parameter for l1 penalty, must be greater than zero. |

`q` |
Desired number of discriminant vectors. |

`PGsteps` |
Maximum number if inner proximal gradient algorithm for finding beta. |

`PGtol` |
Stopping tolerance for inner APG method. |

`maxits` |
Number of iterations to run |

`tol` |
Stopping tolerance for proximal gradient algorithm. |

`selector` |
Vector to choose which parameters in the discriminant vector will be used to calculate the regularization terms. The size of the vector must be *p* the number of predictors. The default value is a vector of all ones. This is currently only used for ordinal classification. |

`initTheta` |
Option to set the initial theta vector, by default it is a vector of all ones for the first theta. |

`bt` |
Boolean to indicate whether backtracking should be used, default false. |

`L` |
Initial estimate for Lipshitz constant used for backtracking. |

`eta` |
Scalar for Lipshitz constant. |

`rankRed` |
Boolean indicating whether Om is in factorized form, such that R^t*R = mO |

`SDAAP`

returns an object of `class`

"`SDAAP`

" including a list
with the following named components:

`call`

The matched call.

`B`

p by q matrix of discriminant vectors.

`Q`

K by q matrix of scoring vectors.

`subits`

Total number of iterations in proximal gradient subroutine.

`totalits`

Number coordinate descent iterations for all discriminant vectors

`NULL`

`SDAAPcv`

, `SDAP`

and `SDAD`

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