Algorithm 1 OPT-Seg

$$\begin{array}{ll}\underset{\mathbf{w},{\xi }_{i,m}}{\text{minimize}}& {\Vert \mathbf{w}\Vert }_1+{\displaystyle \sum _{i=1}^{N^{\text{train}}}{\displaystyle \sum _{m=1}^M{\xi }_{i,m}^2}}\\ \text{subject to}& {\displaystyle \sum _{k=k_{i,m}^{\text{start}}}^{k_{i,m}^{\text{end}}}{\displaystyle \sum _{j=1}^D{\mathbf{X}}_i}(k,j)\mathbf{w}(j)-{\mathbf{l}}_i(k)\le {\xi }_{i,m}}\\ & {\displaystyle \sum _{k=k_{i,m}^{\text{start}}}^{k_{i,m}^{\text{end}}}{\mathbf{l}}_i}(k)-{\displaystyle \sum _{j=1}^D{\mathbf{X}}_i}(k,j)\mathbf{w}(j)\le {\xi }_{i,m}\\ & \mathbf{w}\ge 0\end{array}$$