机器学习，吴恩达逻辑回归

一

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
#路径来源
path = 'ex2data1.txt'
data = pd.read_csv(path, header=None, names=['Exam1 score', 'Exam2 score', 'Admitted'])
data.head()
data.describe()

#积极为1，消极为0
pos = data[data['Admitted'].isin([1])]
neg = data[data['Admitted'].isin([0])]
#画出图像
fig, ax = plt.subplots(figsize=(12, 8))
ax.scatter(pos['Exam1 score'], pos['Exam2 score'], s=50, c='black', marker='+', label='Admitted')
ax.scatter(neg['Exam1 score'], neg['Exam2 score'], s=50, c='y', marker='o', label='Not Admitted')
ax.legend()
ax.set_xlabel('Exam1 Score')
ax.set_ylabel('Exam2 Score')
plt.show()

二、sigmoid函数

def sigmoid(z):
    return 1 / (1 + np.exp(-z))

nums = np.arange(-10, 10, step=0.5)

fig, ax = plt.subplots(figsize=(12, 8))
ax.plot(nums, sigmoid(nums), 'r')
plt.show()

三、代价函数

def cost(theta, X, Y):
    first = Y * np.log(sigmoid([email protected].T))
    second = (1 - Y) * np.log(1 - sigmoid([email protected].T))
    return -1 * np.mean(first + second)

#预处理数据
# add ones column
data.insert(0, 'Ones', 1)

# set X(training data) and Y(target variable)
X = data.iloc[:, 0: -1].values
Y = data.iloc[:, -1].values
theta = np.zeros(3)

print(cost(theta, X, Y))#0.6931471805599453

四、梯度下降

#偏导公式
# 计算步长
def gradient(theta, X, Y):
    return (1/len(X) * X.T @ (sigmoid(X @ theta.T) - Y))
print(gradient(theta, X, Y))#[ -0.1 -12.00921659 -11.26284221]

#gradient只是计算了梯度下降$\theta$更新的步长，使用Scipy.optimize.fmin_tnc拟合最优的$\theta$

#拟合参数

#拟合参数

import scipy.optimize as opt
result = opt.fmin_tnc(func=cost, x0=theta, fprime=gradient, args=(X, Y))
#print(result)#(array([-25.1613187 , 0.20623159, 0.20147149]), 36, 0)

type(result)

cost(result[0], X, Y)
#使用Scipy.optimize.minimize拟合最优的$\theta$公式
res = opt.minimize(fun=cost, x0=np.array(theta), args=(X, np.array(Y)), method='Newton-CG', jac=gradient)



cost(res.x, X, Y)

五、决策边界

coef = -res.x / res.x[2]
x = np.arange(30, 100, 0.5)
y = coef[0] + coef[1] * x

fig, ax = plt.subplots(figsize=(12, 8))
ax.scatter(pos['Exam1 score'], pos['Exam2 score'], s=50, c='black', marker='+', label='Admitted')
ax.scatter(neg['Exam1 score'], neg['Exam2 score'], s=50, c='y', marker='o', label='Not Admitted')
ax.plot(x, y, label='Decision Boundary', c='grey')
ax.legend()
ax.set_xlabel('Exam1 Score')
ax.set_ylabel('Exam2 Score')
plt.show()