Now, we want to separate the data using ellipsoid.

Its equation is:

$A{x}^2+B{y}^2+Cx+Dy+e=0$

Based on that equation, construct a mapping function into $4d$ space, such that the problem will become a linear $($

$w^t(x)+e=0).$

After the mapping, learn a linear classifier and print the hyperplane equation.

Note: after getting an output, I would recommend you to plot this equation on desmos, just to "see it$".$

$[]$ new$\_$features $=$# Implement here

model $=$ SVC $($kernel$=\text{'}$ linear', $C=10$

model.fit$($new$\_$features, y$\_$train$)$

# Get the hyperplane equation coefficients and intercept

coefficients $=$ model.coef$\_[0]$

intercept $=$ model. intercept$\_$

# Print the hyperplane equation

equation$\_$parts $=[]$

for $i$ in range$($len$($coefficients$))$:

equation$\_$parts.append$($ coefficients $\{$:$[i]$:$\mathrm{.}3f\}**x\{i+1\}$

equation $=+.$join$($equation$\_$parts$)$ intercept $[0]$:$\mathrm{.}3$f$\})"$

print$("$Hyperplane equation:"$)$

print $($f$"\{$equation $\}")$

Complete the missing lines to get plots on train and test

train$\_$features $=$ # Implement here

train$\_$preds $=$ # Implement here

train$\_$acc $=$ # Implement here

val$\_$features $=$# Implement here

val$\_$preds $=$ # Implement here

val$\_$acc $=$ # Implement here

$,yy=np.$ meshgrid $.$ arange$(-2,2\mathrm{.}2,0\mathrm{.}1),np.$ arange$(-2,2\mathrm{.}2,0\mathrm{.}1)$

data $=np*c_{-}[*ravel(),yy*ravel()]$

new$\_$features $=$ # Implement here the new features on 'data'

$z=$ # Implement here the predictions of data into $2$ classes, using $w,b$ you found

$Z=Z.$ reshape $($xx$.$shape$)$

fig, axs $=$ plt$.$subplots $,$ figsize $=(12,4)$

# Plot the training data on the first subplot

axs $[0].$ contourf $,$ alpha$=0\mathrm{.}8)$

scatter$1=$ axs $[0].$ scatter$($x$\_$train $[$: $,0],$ X$\_$train $[$:$,1],$ c$=$y$\_$train, cmap$=\text{'}$bwr$\text{'})$

axs $[0].$set$\_$xlabel $(\text{'}$X$\text{'})$

axs $[0].$ set$\_$ylabel$(\text{'}{Y}^{\text{'}}\text{'})$

axs$[0].$set$\_$title$($f$\text{'}$Train dataset $-\{$train$\_$acc:$\mathrm{.}4$f$\}$ accuracy'$)$

# Plot the validation data on the second subplot

axs $[1].$ contourf $(,yy,z,$ alpha $=0\mathrm{.}8)$

scatter$2=$ axs$[1].$scatter$($x$\_$val $[$:$,0],$ X$\_$val $[$:$,1],$ c$=$y$\_$val, cmap$=\text{'}$bwr$\text{'})$

axs $[1].$set$\_$xlabel $(\text{'}x\text{'})$

axs $[1].$ set$\_$ylabel$(\text{'}{Y}^{\text{'}}\text{'})$

axs$[1].$set$\_$title$($f$\text{'}$Validation dataset $-\{$val$\_$acc:$\mathrm{.}4$f$\}$ accuracy'$)$

plt$.$show$()$