https://towardsdatascience.com/an-equation-to-code-machine-learning-project-walk-through-in-python-part-2-non-linear-d193c3c23bac

polynomial_logistic_regression.py

import numpy as np
import matplotlib.pyplot as plt

# read data
data = np.loadtxt("non_linear_data.csv", delimiter=',', skiprows=1)
train_x = data[:, 0:2]
train_y = data[:, 2]

# plot data points
# plt.plot(train_x[train_y == 1, 0], train_x[train_y == 1, 1], 'o')
# plt.plot(train_x[train_y == 0, 0], train_x[train_y == 0, 1], 'x')
# plt.show()

# initialize parameter
theta = np.random.randn(4)

# standardization
mu = train_x.mean(axis=0)
sigma = train_x.std(axis=0)

def standardizer(x):
    return (x - mu) / sigma
std_x = standardizer(train_x)

# add x0 and x3 to get matrix
def to_matrix(x):
    x0 = np.ones([x.shape[0], 1]) # (20, 1)
    x3 = x[:, 0, np.newaxis] ** 2 # (20, 1)
    return np.hstack([x0, x, x3])

mat_x = to_matrix(std_x) # (20, 4)


# sigmoid function
def f(x):
    """
    theta: (4,)
    x: (n, 4)
    return sigmoid(x) -> (4, 1)
    """
    return 1 / (1 + np.exp(-np.dot(x, theta)))

# classify sample to 0 or 1
def classify(x): 
    return (f(x) >= 0.5).astype(np.int)

# update times
epoch = 2000

# learning rate
ETA = 1e-3

# accuracy log
accuracies = []

# update parameter
for _ in range(epoch):
    """
    f(mat_x) - train_y: (20,)
    mat_x: (20, 4)
    theta: (4,)
    
    dot production: (20,) x (20, 4) -> (4,)
    """
    theta = theta - ETA * np.dot(f(mat_x) - train_y, mat_x)

    result = classify(mat_x) == train_y # result is [Ture, False, ...]
    accuracy = sum(result) / len(result)
    accuracies.append(accuracy)


## plot line
# x1 = np.linspace(-2, 2, 100)
# x2 = - (theta[0] + x1 * theta[1] + theta[3] * x1**2) / theta[2]

# plt.plot(std_x[train_y == 1, 0], std_x[train_y == 1, 1], 'o') # train data of class 1
# plt.plot(std_x[train_y == 0, 0], std_x[train_y == 0, 1], 'x') # train data of class 0
# plt.plot(x1, x2, linestyle='dashed') # plot the line we learned
# plt.show()

# plot accuracy line
x = np.arange(len(accuracies))
plt.plot(x, accuracies)
plt.show()