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 npimport pandas as pdimport matplotlib.pyplot as pltdef 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 xdef 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 xdef 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 xdef 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 0def predict2(x):    global theta    probability = np.asscalar(sigmoid(np.dot(x.T,theta)))    if(probability >= 0.5):        return 1    else:        return 0def 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 costdef 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