Algorithm 1. SAMME Algorithm

Step 1. Initialize the observation weights $w_i=\frac{1}{n}, i=1,2,\dots , n.$   Step 2. For $m=1 to M$:   Step 2.1. fit a classifier $T^{\left(m\right)}\left(x\right)$ to the training data using weights $w_i$.   Step 2.2. compute:   $er{r}^{\left(m\right)}=\sum _{i=1}^n{w}_i\parallel \left(c_i\ne T^{\left(m\right)}\left(x_i\right)\right)/\sum _{i=1}^n{w}_i$.   Step 2.3. compute:   ${\alpha }^{\left(m\right)}=log\frac{1-er{r}^{\left(m\right)}}{er{r}^{\left(m\right)}}+log\left(K-1\right)$.   Step 2.4. set:   $w_i\leftarrow w_i.exp({\alpha }^{\left(m\right)}\parallel \left(c_i\ne T^{\left(m\right)}\left(x_i\right)\right), i=1, 2, \dots , n$.   Step 2.5. re-normalize $w_i$.   Step 3. Output   $C_{\left(x\right)}=arg\begin{array}{c}max\\ k\end{array}\sum _{m=1}^M({\alpha }^{\left(m\right)}\parallel \left(T^{\left(m\right)}\left(x\right)=k\right)$.   SAMME.R algorithm:   Step 1. Initialize the observation weights $w_i=\frac{1}{n}, i=1,2,\dots , n.$   Step 2. For $m=1 to M$:   Step 2.1. fit a classifier $T^{\left(m\right)}\left(x\right)$   to the training data using weights $w_i$.   Step 2.2. obtain the weighted class probability estimates:   $P_k^{\left(m\right)}\left(x\right)=Pro{b}_w\left(c=k\setminus x\right), k=1, 2, \dots , K$   Step 2.3. set:   $h_k^{\left(m\right)}\left(x\right)\leftarrow (K-1)\left(\log p_k^m\right(x)-1/K\sum _{k\prime }\log p_{k\prime }^{\left(m\right)}(x\left)\right),k=1,2,\dots ,K$.   Step 2.4. set:   $w_i\leftarrow w_i.exp (-\frac{K-1}{K}{y}_i^{T}log{p}^{\left(m\right)}\left(x_i\right), i=1, 2, \dots , n$.   Step 2.5. re-normalize $w_i$.   Step 3. Output   $C_{\left(x\right)}=arg\begin{array}{c}max\\ k\end{array}\sum _{m=1}^M{h}_k^{\left(m\right)}\left(x\right)$.