CS$5402$ Homework $-2$

$($Deadline: $03-15-202411$:$59$pm$)$

Instructor: Huiyuan Yang

Theory questions $[30\%]$ :

Q$1.[30\%]$ Perceptron algorithm with SGD and Hard$-$SVM$.$

Given the data points:

POSITIVE data points $x_1=[1,2{]}^T,x_2=[2,3{]}^T,x_1=[3,3{]}^T$;

NEgAtIVE data points $x_4=[2,1{]}^T,x_s=[3,2{]}^T$

Use SGD algorithm to find a perceptron model $h_{w,b}(x)=w^{}x+b$ with different initialization and

learning rate.

Q$1)$ Use initial value $w_0=[0,0{]}^{},b_0=0$ and learning rate $=1[9\%]$

Q$2)$ Use initial value $w_0=[1,1{]}^{TT},b_0=-4$ and learning rate $=0\mathrm{.}5.\{$:$9\%]$