Given $10$ data distributed on the coordinates $($Figure $1),$ assume vectors $(2,6),(3,4),(3,8),(4,7),(6,7),(7,3),(8,5)$ are labeled $\text{'}+\text{'},$ and $(6,2),(6,3),(6,5),$ are labeled :$-.$ Using the linear classification model, $f(x_1,x_2)=w_0+w_1{x}_1+w_{2}2,$ with the categorical output is $\text{'}+\text{'}$ if $f(x1,x2)>0$ and $\text{'}-\text{'}$ if $f(x1,x2)0.$

Given initial weights of the linear model: $w_0=-3,w_1=2,$ and $w_2=3$ and learning rate $=0\mathrm{.}03,($a$)$ use batch gradient descent to train the weights $($show the detailed weight update for each epoch$).$ After how many epochs will the model converge? $($b$)$ Use stochastic gradient descent to train the weights $($show the detailed weight update for each epoch$),$ after how many epochs will the model converge?

Note that the vector data are not linear separable. So$,$ we set the convergence criteria to be: the error rate of the model is less than $30\%$