# DWDLarge

## DWDLarge: a MATLAB software for large scale distance weighted discrimination.

#### Xin-Yee Lam, J. S. Marron, Defeng Sun, Kim-Chuan Toh corresponding author: Kim-Chuan Toh, email: mattohkc@nus.edu.sg

The software was last updated in 30 Jul 2017.

This software package is for solving the distance weighted discrimination problem of the following form:

$$\begin{eqnarray*} \begin{array}{rl} \mbox{(P)} \quad \min & \sum_{j=1}^n \frac{1}{r_j^q} + C \langle e,\,\xi \rangle \\[5pt] {\rm s.t.} & r = Z^T w + \beta y + \xi, \; r > 0,\; \xi \geq 0,\; \|w\|\leq 1 \\[5pt] w\in\mathbb{R}^d,\;r, x \in\mathbb{R}^n,\;\beta\in\mathbb{R} \end{array} \end{eqnarray*}$$
where $$n$$ is the sample size, $$d$$ is the feature dimension, and $$C$$ is the penalty parameter. Here, the input is a matrix $$X$$ whose columns are the feature vectors, and $$y$$ is an  $$n$$-vector containing binary classification label $$\{-1,1\}$$ . The notation $$Z$$ is defined to be $$Z:=X{\rm diag}(y)$$.

The main algorithm for solving (P) is a symmetric Gauss-Seidel based ADMM method. It will output the result
$$r,\xi,w,\beta$$ for which $$w^Tx+\beta = 0$$ is a hyperplane separating the two classes of data and $$\xi$$
is a slack variable to allow the possibility that the positive and negative data points may not be separated cleanly by the hyperplane.

##### Important note:
• The software is still under development. Thus it will invariably be buggy. We would appreciate your feedback and bugs’ report to the corresponding author: Kim-Chuan Toh, email: mattohkc@nus.edu.sg.
• This is a research software. It is not intended nor designed to be a general purpose software at the moment.

##### Citation:

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, 27(2), 368-379.