Algorithm 1. Multi-class AdaBoost learning algorithm. M hypothesis are constructed each using a single feature vector. The final hypothesis is a weighted linear combination of M hypothesis.

Initialize the observation weights w1,i=1/n, i=1,2,…,n. For m = 1 to M: Normalize the weights, $w_{m,i}\leftarrow w_{m,i}/{\sum }_{j=1}^n{w}_{m,j}$. Select the best week classifier with respect to the weighted error $$er{r}^{(m)}={min}_f{\sum }_{i=1}^n{w}_i\cdot \mathrm{I}\left(c_i\ne T\left(x_i,x^{(p)},f\right)\right)/{\sum }_{i=1}^n{w}_i.$$ Define T(m) (x) =T(x, x(p), fm)where fm is the minimize of err(m). Compute $${\alpha }^{(m)}=\text{log}\frac{1-{\mathit{\text{err}}}^{(m)}}{er{r}^{(m)}}+\text{log}(K-1).$$ (13) Update the weights: $w_{m,i}\leftarrow w_{m,i}\cdot \text{exp}\left({\alpha }^{(m)}\cdot \mathrm{I}\left(c_i\ne T^{(m)}(x_i)\right)\right),i=1,\dots ,n.$ The final strong classifier is: $$C(x)=\underset{k}{argmax}{\sum }_{m=1}^M{\alpha }^{(m)}\cdot \mathrm{I}\left(T^{(m)}(x)=k\right).$$ (14)