Can we start with the circle equation as decision boundary?

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Hi @tbhaxor,

in addition to @rmwkwok 's excellent answer.

I agree: Feature Engineering will do the trick: Of course you can also apply a transformation as we know it from polar coordinates to get rid of the non-linearity in the data and solve the problem with a linear classifier.

Bildschirm­foto 2023-01-14 um 20.36.23
Bildschirm­foto 2023-01-14 um 20.36.23696×994 42.8 KB 

import numpy as np
import math
import matplotlib.pyplot as plt 

# Some Parameters
dim = 100
noise = 0.2

#Create inner circle
x_1 = np.cos(np.linspace(0,2*math.pi, dim)) + noise*np.random.normal(0, 1, dim)
y_1 = np.sin(np.linspace(0,2*math.pi, dim)) + noise*np.random.normal(0, 1, dim)

#Create outer circle
x_2 = 2*np.cos(np.linspace(0,2*math.pi, dim)) + noise*np.random.normal(0, 1, dim)
y_2 = 2*np.sin(np.linspace(0,2*math.pi, dim)) + noise*np.random.normal(0, 1, dim)

# Plot of Circle data
ax = plt.gca()
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
plt.scatter(x_1,y_1)
plt.scatter(x_2,y_2)
plt.title('Before Transformation')
plt.show()


# Transformation function
def pol_transform(x, y):
    alpha = np.sqrt(x*x+y*y)
    beta = np.arctan2(y,x)
    return(alpha, beta)

# Apply transforation
alpha_1, beta_1 = pol_transform(x_1,y_1)
alpha_2, beta_2 = pol_transform(x_2,y_2)


# Plot of transformed data
ax = plt.gca()
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
plt.scatter(alpha_1,beta_1)
plt.scatter(alpha_2,beta_2)
plt.title('After Transformation')
plt.show()

After transformation, a generalized linear model, like a logistic regression will do the trick to solve this classification.

Best regards
Christian

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