Algorithm 1. Algorithm for inserting and deleting processes of universal incremental LS-SVM.
Inserting			Deleting
Input: $S(l-1)={\left\{\left({\mathit{x}}_i,y_i\right)\right\}}_{i=1,i\ne p}^l$, $\mathit{R}(l-1)$, $\left({\mathit{x}}_p,y_p\right)$, $1\le p\le l$, C			Input: $S(l)={\left\{\left({\mathit{x}}_i,y_i\right)\right\}}_{i=1}^l$, $\mathit{R}(l)$, $1\le p\le l$
Output: $\mathit{R}(l)$, $\alpha (l)$, $b(l)$			Output: $\mathit{R}(l-1)$, $\alpha (l-1)$, $b(l-1)$
1	$\mathit{W}\leftarrow \mathit{R}(l-1)$		1	$\mathit{U}\leftarrow \mathit{R}(l)$
2	$\left[\begin{array}{cc}{\mathit{W}}_1& {\mathit{W}}_2\\ \mathit{O}& {\mathit{W}}_3\end{array}\right]\leftarrow \mathit{W}$	//divide at pth row and clomn	2	$\left[\begin{array}{ccc}{\mathit{U}}_1& {\mathit{u}}_1& {\mathit{U}}_2\\ 0^T& u_{pp}& {\mathit{u}}_2^T\\ \mathit{O}& 0& {\mathit{U}}_3\end{array}\right]\leftarrow \mathit{U}$	//divide at pth, p + 1st row and clomn
3	${\mathit{h}}_1\leftarrow {\left[k\left({\mathit{x}}_1,{\mathit{x}}_p\right),\dots ,k\left({\mathit{x}}_{p-1},{\mathit{x}}_p\right)\right]}^T$		3	${\mathit{W}}_1\leftarrow {\mathit{U}}_1,{\mathit{W}}_2\leftarrow {\mathit{U}}_2$
4	${\mathit{h}}_2\leftarrow {\left[k\left({\mathit{x}}_{p+1},{\mathit{x}}_p\right),\dots ,k\left({\mathit{x}}_l,{\mathit{x}}_p\right)\right]}^T$		4	${\mathit{W}}_3^T{\mathit{W}}_3\leftarrow {\mathit{U}}_3^T{\mathit{U}}_3+{\mathit{u}}_2{\mathit{u}}_2^T$ //low-rank update
5	$h_{pp}\leftarrow k\left({\mathit{x}}_p,{\mathit{x}}_p\right)+1/C$		5	$\mathit{W}\leftarrow \left[\begin{array}{cc}{\mathit{W}}_1& {\mathit{W}}_2\\ \mathit{O}& {\mathit{W}}_3\end{array}\right]$
6	${\mathit{U}}_1\leftarrow {\mathit{W}}_1,{\mathit{U}}_2\leftarrow {\mathit{W}}_2$		6	$b(l-1)\leftarrow \frac{{\mathit{E}}_V{}^T{\mathit{W}}^{-1}{\left({\mathit{W}}^T\right)}^{-1}\mathit{Y}}{{\mathit{E}}_V{}^T{\mathit{W}}^{-1}{\left({\mathit{W}}^T\right)}^{-1}{\mathit{E}}_V}$
7	${\mathit{u}}_1\leftarrow {({\mathit{U}}_1^T)}^{-1}{\mathit{h}}_1$ //forward substitution		7	$\alpha (l-1)\leftarrow {\mathit{W}}^{-1}{\left({\mathit{W}}^T\right)}^{-1}(\mathit{Y}-b{\mathit{E}}_V)$
8	${\mathit{u}}_2\leftarrow ({\mathit{h}}_2-{\mathit{U}}_2^T{\mathit{u}}_1)/u_{pp}$		8	$\mathit{R}(l-1)\leftarrow \mathit{W}$
9	${\mathit{U}}_3^T{\mathit{U}}_3\leftarrow {\mathit{W}}_3^T{\mathit{W}}_3-{\mathit{u}}_2{\mathit{u}}_2^T$ //low-rank downdate
10	$\mathit{U}\leftarrow \left[\begin{array}{ccc}{\mathit{U}}_1& {\mathit{u}}_1& {\mathit{U}}_2\\ 0^T& u_{pp}& {\mathit{u}}_2^T\\ \mathit{O}& 0& {\mathit{U}}_3\end{array}\right]$
11	$b(l)\leftarrow \frac{{\mathit{E}}_V{}^T{\mathit{U}}^{-1}{\left({\mathit{U}}^T\right)}^{-1}\mathit{Y}}{{\mathit{E}}_V{}^T{\mathit{U}}^{-1}{\left({\mathit{U}}^T\right)}^{-1}{\mathit{E}}_V}$	//forward substitution
12	$\alpha (l)\leftarrow {\mathit{U}}^{-1}{\left({\mathit{U}}^T\right)}^{-1}(\mathit{Y}-b{\mathit{E}}_V)$	//forward substitution
13	$\mathit{R}(l)\leftarrow \mathit{U}$