The perceptron model y = f ( x ) = sign ( w T x + b ) y = f ( x ) =

The perceptron model $y=f\left(x\right)=\mathrm{sign}(w^{T}x+b)$ can be used to learn a binary classifier from training data.

a. Assume there are two training samples. The positive one is $x_1=(2,1{)}^T$; the negative one is $x_2=(1,0{)}^T$. The learning rate $\eta =1$. Starting from $w=(1,1{)}^T$ and $b=0$, solve the parameters of the classifier.

b. Assume there are four training samples. The positive samples are $x_1=(1,1{)}^T$ and $x_2=$ $(0,0{)}^T$; the negative samples are $x_3=(1,0{)}^T$ and $x_4=(0,1{)}^T$. Can we classify all training samples correctly using the perceptron model? Why?