python的numpy模块实现逻辑回归模型

def initial_para(nums_feature):
    """initial the weights and bias which is zero"""
    #nums_feature是输入数据的属性数目，因此权重w是[1, nums_feature]维
    #且w和b均初始化为0
    w = np.zeros((1, nums_feature))
    b = 0
    return w, b

def activation(x, w , b):
    """a linear function and then sigmoid activation function: 
    x_ = w*x +b,y = 1/(1+exp(-x_))"""
    #线性方程，输入的x是[batch, 2]维，输出是[1, batch]维，batch是模型优化迭代一次输入数据的数目
    #[1, 2] * [2, batch] = [1, batch], 所以是w * x.T（x的转置）
    #np.dot是矩阵乘法
    x_ = np.dot(w, x.T) + b
    #np.exp是实现e的x次幂
    sigmoid = 1 / (1 + np.exp(-x_))
    return sigmoid

def gradient_descent_batch(x, w, b, label, learning_rate):
    #获取输入数据的数目，即batch大小
    n = len(label)
    #进行逻辑回归预测
    sigmoid = activation(x, w, b)
    #损失函数，np.sum是将矩阵求和
    cost = -np.sum(label.T * np.log(sigmoid) + (1-label).T * np.log(1-sigmoid)) / n
    #求对w和b的偏导(即梯度值)
    g_w = np.dot(x.T, (sigmoid - label.T).T) / n
    g_b = np.sum((sigmoid - label.T)) / n
    #根据梯度更新参数
    w = w - learning_rate * g_w.T
    b = b - learning_rate * g_b
    return w, b, cost

def optimal_model_batch(x, label, nums_feature, step=10000, batch_size=1):
    """train the model with batch"""
    length = len(x)
    w, b = initial_para(nums_feature)
    for i in range(step):
        #随机获取一个batch数目的数据
        num = randint(0, length - 1 - batch_size)
        x_batch = x[num:(num+batch_size), :]
        label_batch = label[num:num+batch_size]
        #进行一次梯度更新(优化)
        w, b, cost = gradient_descent_batch(x_batch, w, b, label_batch, 0.0001)
        #每1000次打印一下损失值
        if i%1000 == 0:
            print('step is : ', i, ', cost is: ', cost)
    return w, b

import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from random import randint
from sklearn.preprocessing import StandardScaler
 
def _main():
    #读取csv格式的数据data_path是数据的路径
    data = pd.read_csv('data_path')
    #获取样本属性和标签
    x = data.iloc[:, 2:4].values
    y = data.iloc[:, 4].values
    #将数据集分为测试集和训练集
    x_train, x_test, y_train, y_test = train_test_split(x, y, test_size = 0.2, random_state=0)
    #数据预处理，去均值化
    standardscaler = StandardScaler()
    x_train = standardscaler.fit_transfORM(x_train)
    x_test = standardscaler.transform(x_test)
    #w, b = optimal_model(x_train, y_train, 2, 50000)
    #训练模型
    w, b = optimal_model_batch(x_train, y_train, 2, 50000, 64)
    print('trian is over')
    #对测试集进行预测，并计算精度
    predict = activation(x_test, w, b).T
    n = 0
    for i, p in enumerate(predict):
        if p >=0.5:
            if y_test[i] == 1:
                n += 1
        else:
            if y_test[i] == 0:
                n += 1
    print('accuracy is : ', n / len(y_test))

predict = np.reshape(np.int32(predict), [len(predict)])
    #将预测结果以散点图的形式可视化
    for i, j in enumerate(np.unique(predict)):
        plt.scatter(x_test[predict == j, 0], x_test[predict == j, 1], 
        c = ListedColormap(('red', 'blue'))(i), label=j)
    plt.show()