Algorithm for finding a L1-norm best-fit subspace of dimension m − 1.
Given a data matrix $X\in {\mathbb{R}}^{n\times m}$ with full column rank.
1: Set j* = 0, R0(X)=∞.	/* Initialization. */
2: for (j = 1; j ≤ m; j = j + 1) do
3: Solve $R_j\left(X\right)=\stackrel{\min }{\beta ,e^{+},e^{-}}{\Sigma }_{i=1}^n{e}_i^{+}+e_i^{-}$,  subject to $\begin{array}{c}\hfill {\beta }^T{x}_i+e_i^{+}-e_i^{-}=0,i=1,\dots ,n,\hfill \\ \hfill {\beta }_j=-1,\hfill \\ \hfill e_i^{+},e_i^{-}\ge 0,i=1,\dots ,n.\hfill \end{array}$	/*Find the L1 regression with variable j as the dependent variable.*/
4: if if Rj(X) < Rj* (X),  then	/* if the fitted subspace for variable j is better than that for j**/
5: j* = j, β* = β.	/* Update the coefficients defining the best fit subspace */
6: end if
7: end for