python的numpy模塊實現邏輯回歸模型

def initial_para(nums_feature):
    """initial the weights and bias which is zero"""
    #nums_feature是輸入數據的屬性數目，因此權重w是[1, nums_feature]維
    #且w和b均初始化為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_))"""
    #線性方程，輸入的x是[batch, 2]維，輸出是[1, batch]維，batch是模型優化迭代一次輸入數據的數目
    #[1, 2] * [2, batch] = [1, batch], 所以是w * x.T（x的轉置）
    #np.dot是矩陣乘法
    x_ = np.dot(w, x.T) + b
    #np.exp是實現e的x次冪
    sigmoid = 1 / (1 + np.exp(-x_))
    return sigmoid

def gradient_descent_batch(x, w, b, label, learning_rate):
    #獲取輸入數據的數目，即batch大小
    n = len(label)
    #進行邏輯回歸預測
    sigmoid = activation(x, w, b)
    #損失函數，np.sum是將矩陣求和
    cost = -np.sum(label.T * np.log(sigmoid) + (1-label).T * np.log(1-sigmoid)) / n
    #求對w和b的偏導(即梯度值)
    g_w = np.dot(x.T, (sigmoid - label.T).T) / n
    g_b = np.sum((sigmoid - label.T)) / n
    #根據梯度更新參數
    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):
        #隨機獲取一個batch數目的數據
        num = randint(0, length - 1 - batch_size)
        x_batch = x[num:(num+batch_size), :]
        label_batch = label[num:num+batch_size]
        #進行一次梯度更新(優化)
        w, b, cost = gradient_descent_batch(x_batch, w, b, label_batch, 0.0001)
        #每1000次打印一下損失值
        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():
    #讀取csv格式的數據data_path是數據的路徑
    data = pd.read_csv('data_path')
    #獲取樣本屬性和標簽
    x = data.iloc[:, 2:4].values
    y = data.iloc[:, 4].values
    #將數據集分為測試集和訓練集
    x_train, x_test, y_train, y_test = train_test_split(x, y, test_size = 0.2, random_state=0)
    #數據預處理，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)
    #訓練模型
    w, b = optimal_model_batch(x_train, y_train, 2, 50000, 64)
    print('trian is over')
    #對測試集進行預測，並計算精度
    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)])
    #將預測結果以散點圖的形式可視化
    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()