SZVD_ADMM

Iteratively solves the problem
$$\min(-1/2*x^TB^Tx + \gamma p(y): ||x||_2 \leq 1, DNx = y)$$

internal

Implementation of sparse linear discriminant analysis, which is a supervised
classification method for multiple classes. Various novel optimization approaches to
this problem are implemented including alternating direction method of multipliers ('ADMM'),
proximal gradient (PG) and accelerated proximal gradient ('APG') (See Atkins 'et al'. <arXiv:1705.07194>).
Functions for performing cross validation are also supplied along with basic prediction
and plotting functions.
Sparse zero variance discriminant analysis ('SZVD') is also included in the package
(See Ames and Hong, <arXiv:1401.5492>). See the 'github' wiki for a more extended description.

Gudmundur Einarsson

accSDA

Accelerated Sparse Discriminant Analysis

Line Clemmensen

Brendan Ames

Summer Atkins

SZVD_ADMM function

<dl><dt>B</dt>
<dd>Between class covariance matrix for objective (in space defined by N).</dd>
<dt>N</dt>
<dd>basis matrix for null space of covariance matrix W.</dd>
<dt>D</dt>
<dd>penalty dictionary/basis.</dd>
<dt>sols0</dt>
<dd>initial solutions sols0$x, sols0$y, sols0$z</dd>
<dt>pen_scal</dt>
<dd>penalty scaling term.</dd>
<dt>gamma</dt>
<dd>l1 regularization parameter</dd>
<dt>beta</dt>
<dd>penalty term controlling the splitting constraint.</dd>
<dt>tol</dt>
<dd>tol$abs = absolute error, tol$rel = relative error to be
achieved to declare convergence of the algorithm.</dd>
<dt>maxits</dt>
<dd>maximum number of iterations of the algorithm to run.</dd>
<dt>quiet</dt>
<dd>toggles between displaying intermediate statistics.</dd></dl>

Arguments

Alternating Direction Method of Multipliers for SZVD — SZVD_ADMM

<dl>

<dt>B</dt>
<dd>Between class covariance matrix for objective (in space defined by N).</dd>


<dt>N</dt>
<dd>basis matrix for null space of covariance matrix W.</dd>


<dt>D</dt>
<dd>penalty dictionary/basis.</dd>


<dt>sols0</dt>
<dd>initial solutions sols0$x, sols0$y, sols0$z</dd>


<dt>pen_scal</dt>
<dd>penalty scaling term.</dd>


<dt>gamma</dt>
<dd>l1 regularization parameter</dd>


<dt>beta</dt>
<dd>penalty term controlling the splitting constraint.</dd>


<dt>tol</dt>
<dd>tol$abs = absolute error, tol$rel = relative error to be
achieved to declare convergence of the algorithm.</dd>


<dt>maxits</dt>
<dd>maximum number of iterations of the algorithm to run.</dd>


<dt>quiet</dt>
<dd>toggles between displaying intermediate statistics.</dd>

</dl>

SZVD_ADMM: Alternating Direction Method of Multipliers for SZVD

Description

Usage

Value

Arguments

Details

See Also