逻辑回归代码详解版

 
 
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import os
 
path = 'C:/Users/Sherlock/data/LogiReg_data.csv'
pdData = pd.read_csv(path, header=None, names=['Exam1', 'Exam2', 'Admitted'])
pdData.head()
print(pdData.head())
print(pdData.shape)
positive = pdData[pdData['Admitted'] == 1]  # 定义正
nagative = pdData[pdData['Admitted'] == 0]  # 定义负
fig, ax = plt.subplots(figsize=(10, 5))#子图的行数为10，列数为5
ax.scatter(positive['Exam1'], positive['Exam2'], s=30, c='b', marker='o', label='Admitted')#s是标量或形如shape的数组，c显而易见是color，lable是标记、
ax.scatter(nagative['Exam1'], nagative['Exam2'], s=30, c='r', marker='x', label='not Admitted')
ax.legend()
ax.set_xlabel('Exam 1 score')#设置图标
ax.set_ylabel('Exam 2 score')
plt.show()  # 画图
 
 
##实现算法 the logistics regression 目标建立一个分类器 设置阈值来判断录取结果
##sigmoid 函数
def sigmoid(z):
    return 1 / (1 + np.exp(-z))  #sigmoid 函数，公式
 
 
# 画图
nums = np.arange(-10, 10, step=1)
fig, ax = plt.subplots(figsize=(12, 4))
ax.plot(nums, sigmoid(nums), 'r')  # 画图定义
plt.show()
 
 
# 按照理论实现预测函数
def model(X, theta):
    return sigmoid(np.dot(X, theta.T)) #X矩阵和theta的转置矩阵相乘
 
 
pdData.insert(0, 'ones', 1)  # 插入一列
orig_data = pdData.as_matrix()#将dataframe 转换成数组，
cols = orig_data.shape[1] #shape【0】是行数，【1】是列数
X = orig_data[:, 0:cols - 1]
y = orig_data[:, cols - 1:cols]
theta = np.zeros([1, 3]) #用0填充矩阵行数为1列数为3
print(X[:5])
print(X.shape, y.shape, theta.shape)
 
 
##损失函数
def cost(X, y, theta):
    left = np.multiply(-y, np.log(model(X, theta))) #0的情况下
    right = np.multiply(1 - y, np.log(1 - model(X, theta)))#1的情况下
    return np.sum(left - right) / (len(X))
 
 
print(cost(X, y, theta))
 
 
# 计算梯度
def gradient(X, y, theta):
    grad = np.zeros(theta.shape)#theta的维数进行填充0
    error = (model(X, theta) - y).ravel()#二维数组变一维数组
    for j in range(len(theta.ravel())):  # for each parmeter
        term = np.multiply(error, X[:, j])
        grad[0, j] = np.sum(term) / len(X)
 
    return grad
 
 
##比较3种不同梯度下降方法
STOP_ITER = 0
STOP_COST = 1
STOP_GRAD = 2
 
 
def stopCriterion(type, value, threshold):
    if type == STOP_ITER:
        return value > threshold
    elif type == STOP_COST:
        return abs(value[-1] - value[-2]) < threshold
    elif type == STOP_GRAD:
        return np.linalg.norm(value) < threshold
 
 
import numpy.random
 
 
# 打乱数据洗牌
def shuffledata(data):
    np.random.shuffle(data)
    cols = data.shape[1]
    X = data[:, 0:cols - 1]
    y = data[:, cols - 1:]
    return X, y
 
 
import time
 
 
def descent(data, theta, batchSize, stopType, thresh, alpha):
    # 梯度下降求解
 
    init_time = time.time()
    i = 0  # 迭代次数
    k = 0  # batch
    X, y = shuffledata(data)
    grad = np.zeros(theta.shape)  # 计算的梯度
    costs = [cost(X, y, theta)]  # 损失值
 
    while True:
        grad = gradient(X[k:k + batchSize], y[k:k + batchSize], theta)
        k += batchSize  # 取batch数量个数据
        if k >= n:
            k = 0
            X, y = shuffledata(data)  # 重新洗牌
        theta = theta - alpha * grad  # 参数更新
        costs.append(cost(X, y, theta))  # 计算新的损失
        i += 1
 
        if stopType == STOP_ITER:
            value = i
        elif stopType == STOP_COST:
            value = costs
        elif stopType == STOP_GRAD:
            value = grad
        if stopCriterion(stopType, value, thresh): break
 
    return theta, i - 1, costs, grad, time.time() - init_time
 
 
# 选择梯度下降
def runExpe(data, theta, batchSize, stopType, thresh, alpha):
    # import pdb; pdb.set_trace();
    theta, iter, costs, grad, dur = descent(data, theta, batchSize, stopType, thresh, alpha)
    name = "Original" if (data[:, 1] > 2).sum() > 1 else "Scaled"
    name += " data - learning rate: {} - ".format(alpha)
    if batchSize == n:
        strDescType = "Gradient"
    elif batchSize == 1:
        strDescType = "Stochastic"
    else:
        strDescType = "Mini-batch ({})".format(batchSize)
    name += strDescType + " descent - Stop: "
    if stopType == STOP_ITER:
        strStop = "{} iterations".format(thresh)
    elif stopType == STOP_COST:
        strStop = "costs change < {}".format(thresh)
    else:
        strStop = "gradient norm < {}".format(thresh)
    name += strStop
    print("***{}\nTheta: {} - Iter: {} - Last cost: {:03.2f} - Duration: {:03.2f}s".format(
        name, theta, iter, costs[-1], dur))
    fig, ax = plt.subplots(figsize=(12, 4))
    ax.plot(np.arange(len(costs)), costs, 'r')
    ax.set_xlabel('Iterations')
    ax.set_ylabel('Cost')
    ax.set_title(name.upper() + ' - Error vs. Iteration')
    return theta
 
 
n = 100
runExpe(orig_data, theta, n, STOP_ITER, thresh=5000, alpha=0.000001)
plt.show()
runExpe(orig_data, theta, n, STOP_GRAD, thresh=0.05, alpha=0.001)
plt.show()
runExpe(orig_data, theta, n, STOP_COST, thresh=0.000001, alpha=0.001)
plt.show()
# 对比
runExpe(orig_data, theta, 1, STOP_ITER, thresh=5000, alpha=0.001)
plt.show()
runExpe(orig_data, theta, 1, STOP_ITER, thresh=15000, alpha=0.000002)
plt.show()
runExpe(orig_data, theta, 16, STOP_ITER, thresh=15000, alpha=0.001)
plt.show()
##对数据进行标准化 将数据按其属性(按列进行)减去其均值，然后除以其方差。
# 最后得到的结果是，对每个属性/每列来说所有数据都聚集在0附近，方差值为1
 
from sklearn import preprocessing as pp
 
scaled_data = orig_data.copy()
scaled_data[:, 1:3] = pp.scale(orig_data[:, 1:3])
 
runExpe(scaled_data, theta, n, STOP_ITER, thresh=5000, alpha=0.001)
 
 
# 设定阈值
def predict(X, theta):
    return [1 if x >= 0.5 else 0 for x in model(X, theta)]
 
 
# if __name__=='__main__':
 
scaled_X = scaled_data[:, :3]
y = scaled_data[:, 3]
predictions = predict(scaled_X, theta)
correct = [1 if ((a == 1 and b == 1) or (a == 0 and b == 0)) else 0 for (a, b) in zip(predictions, y)]
accuracy = (sum(map(int, correct)) % len(correct))
print('accuracy = {0}%'.format(accuracy))