Previous code:

# Some settings.

learning$\_$rate $=0\mathrm{.}0001$

iterations $=10000$

losses $=[]$

# Gradient descent algorithm for linear SVM classifier.

# Step $1.$ Initialize the parameters W$,$ b$.$

W $=$ np$.$zeros$(2)$

b $=0$

C $=1000$

for i in range$($iterations$)$:

# Step $2.$ Compute the partial derivatives.

grad$\_$W$,$ grad$\_$b $=$ grad$\_$L$\_$W$\_$b$($X$\_$train, Y$\_$train, W$,$ b$,$ C$)$

# Step $3.$ Update the parameters.

W $=$ W $-$ learning$\_$rate $*$ grad$\_$W

b $=$ b $-$ learning$\_$rate $*$ grad$\_$b

# Track the training losses.

losses.append$($L$\_$W$\_$b$($X$\_$train, Y$\_$train, W$,$ b$,$ C$))$

In $[17]$: # Some settings.

learning$\_$rate $=0\mathrm{.}0001$

iterations $=10000$

losses $=[]$

Gradient descent algorithm for linear SVM classifier.

Step $1.$ Initialize the parameters W$,$ b$.$

W $=$ np$.$zeros$(2)$

b $=0$

C $=1000$

for i in range$($iterations$)$:

Step $2.$ Compute the partial derivatives.

grad$\_$W$,$ grad$\_$b $=$ grad$\_$L$\_$W$\_$b$($X$\_$train, Y$\_$train, W$,$ b$,$ C$)$

Step $3.$ Update the parameters.

W $=$ W $-$ learning$\_$rate $*$ grad$\_$W

b $=$ b $-$ learning$\_$rate $*$ grad$\_$b

Track the training losses.

losses.append$($L$\_$W$\_$b$($X$\_$train, Y$\_$train, W$,$ b$,$ C$))$

Visualize the results

Please complete the following codes to visualize the decision boundary of the perceptron model. You may use the vis function defined above.

Also, please plot the training error curve with respect to the number of iterations.

You should only insert your code in the part.

Points: $4$

In $[]$: # Show decision boundary, training error and test error.

print$(\text{'}$Decision boundary: $\{$:$\mathrm{.}3$f$\}\backslash$times$0+\{$:$\mathrm{.}3$f$\}$x$1+\{$:$\mathrm{.}3$f$\}=0\text{'}.$format$($W$[0],$W$[1],$b$))$

$...$

print$(\text{'}$Training error: $\{\}\text{'}.$format$($calc$\_$error$($X$\_$train, Y$\_$train, W$,$ b$)))$

$...$

print$(\text{'}$Test error: $\{\}\text{'}.$format$($calc$\_$error$($X$\_$test, Y$\_$test, W$,$ b$)))|```$

In $[17]$: # Some settings.

learning$\_$rate $=0\mathrm{.}0001$

iterations $=10000$

losses $=[]$

# Gradient descent algorithm for linear SVM classifier.

# Step $1.$ Initialize the parameters W$,$ b$.$

W $=$ np$.$zeros$(2)$

b $=0$

C $=1000$

for i in range$($iterations$)$:

# Step $2.$ Compute the partial derivatives.

grad$\_$W$,$ grad$\_$b $=$ grad$\_$L$\_$W$\_$b$($X$\_$train, Y$\_$train, W$,$ b$,$ C$)$

# Step $3.$ Update the parameters.

W $=$ W $-$ learning$\_$rate $*$ grad$\_$W

b $=$ b $-$ learning$\_$rate $*$ grad$\_$b

# Track the training losses.

losses.append$($L$\_$W$\_$b$($X$\_$train, Y$\_$train, W$,$ b$,$ C$))$

$```$