逻辑回归的决策边界图

Question

我正在尝试实现逻辑回归。我已将这些特征映射到 x1^2*x2^0 + x1^1*x2^1 + 形式的多项式......现在我想绘制相同的决策边界。经过这个答案后，我写了下面的代码来使用轮廓函数

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

def map_features(x, degree):

    x_old = x.copy()

    x = pd.DataFrame({"intercept" : [1]*x.shape[0]})

    column_index = 1

    for i in range(1, degree+1):

        for j in range(0, i+1):

            x.insert(column_index, str(x_old.columns[1]) + "^" + str(i-j) + str(x_old.columns[2]) + "^" + str(j), np.multiply(x_old.iloc[:,1]**(i-j), x_old.iloc[:,2]**(j)))

            column_index+=1

    return x

def normalize_features(x):

    for column_name in x.columns[1:]:

        mean = x[column_name].mean()

        std = x[column_name].std()

        x[column_name] = (x[column_name] - mean) / std

    return x

def normalize_features2(x):

    for column_name in x.columns[1:-1]:

        mean = x[column_name].mean()

        std = x[column_name].std()

        x[column_name] = (x[column_name] - mean) / std

    return x

def sigmoid(z):

    # print(z)

    return 1/(1+np.exp(-z))

def predict(x):

    global theta

    probability = np.asscalar(sigmoid(np.dot(x,theta)))

    if(probability >= 0.5):

        return 1

    else:

        return 0

def predict2(x):

    global theta

    probability = np.asscalar(sigmoid(np.dot(x.T,theta)))

    if(probability >= 0.5):

        return 1

    else:

        return 0

def cost(x, y, theta):

    m = x.shape[0]

    h_theta = pd.DataFrame(sigmoid(np.dot(x,theta)))

    cost = 1/m * ((-np.multiply(y,h_theta.apply(np.log)) - np.multiply(1-y, (1-h_theta).apply(np.log))).sum())

    return cost

def gradient_descent(x, y, theta):

    global cost_values

    m = x.shape[0]

    iterations = 1000

    alpha = 0.03

    cost_values = pd.DataFrame({'iteration' : [0], 'cost' : [cost(x,y,theta)]})

下面是我作为输出得到的图

我不确定我是否正确解释了这一点，但这条线应该更像是一条分隔这两个类的曲线。数据集在这里ex2data1.csv