Problem #$7$:

$(1$ point$)$ The perceptron algorithm is a fundamental algorithm for binary classification.

It iteratively updates the weight vector to find a linear decision boundary that separates

two classes.

Given a dataset $\{($xi

$,$ yi$)\}$

n

i$=1$ where xi in Rd and yi in $\{1,1\},$ the perceptron algorithm

aims to find a weight vector w in Rd and a bias term b in R such that the linear decision

boundary w

$$x $+$ b $=0$ separates the two classes.

Answer the following questions:

$$ Describe the update rule for the perceptron algorithm and explain the intuition

behind it$.$

$$ Prove that if the data is linearly separable, the perceptron algorithm will converge

to a solution that correctly classifies all training examples.Problem #$7$:

$(1$ point$)$ The perceptron algorithm is a fundamental algorithm for binary classification.

It iteratively updates the weight vector to find a linear decision boundary that separates

two classes.

Given a dataset $\{(x_i,y_i){\}}_i=1^n$ where $x_{i}in{R}^d$ and $y_{i}in\{-1,1\},$ the perceptron algorithm

aims to find a weight vector $win{R}^d$ and a bias term binR such that the linear decision

boundary $w^{TT}x+b=0$ separates the two classes.

Answer the following questions:

Describe the update rule for the perceptron algorithm and explain the intuition

behind it$.$

Prove that if the data is linearly separable, the perceptron algorithm will converge

to a solution that correctly classifies all training examples.