吴恩达 机器学习课程 coursera 第二次编程作业（Logistic Regression Regularized） python实现

本文是吴恩达机器学习课程的第二次编程作业：Logistic Regression Regularized 的扩展作业，用python实现。

 

本作业包含5个文件，分别是：

ex2_reg.py 主程序入口

predict.py 预测函数

gradientReg.py 梯度下降算法

costFunctionReg.py 代价函数算法

sigmoid.py 函数计算方法

 

作业文件和训练集数据下载地址：https://github.com/toanoyx/MachineLearning-AndrewNg-coursera-python/tree/master/ex2%20Logistic%20Regression/ex2_reg

 

下文是文件的源代码：

ex2_reg.py 主程序入口

import pandas as pd
import matplotlib.pyplot as plt
import scipy.optimize as opt
from costFunctionReg import *
from gradientReg import *
from predict import *

""" 第1部分 可视化数据集 """

path = 'ex2data2.txt'
data2 = pd.read_csv(path, header=None, names=['Test 1', 'Test 2', 'Accepted'])

positive = data2[data2['Accepted'].isin([1])]
negative = data2[data2['Accepted'].isin([0])]

fig, ax = plt.subplots(figsize=(12,8))
ax.scatter(positive['Test 1'], positive['Test 2'], s=50, c='black', marker='+', label='y = 1')
ax.scatter(negative['Test 1'], negative['Test 2'], s=50, c='yellow', marker='o', label='y = 0')
ax.legend()
ax.set_xlabel('Microchip Test 1')
ax.set_ylabel('Microchip Test 2')
plt.show()

degree = 5
x1 = data2['Test 1']
x2 = data2['Test 2']

data2.insert(3, 'Ones', 1)

for i in range(1, degree):
    for j in range(0, i):
        data2['F' + str(i) + str(j)] = np.power(x1, i-j) * np.power(x2, j)

data2.drop('Test 1', axis=1, inplace=True)
data2.drop('Test 2', axis=1, inplace=True)

""" 第2部分 正则化代价函数 """

cols = data2.shape[1]
X2 = data2.iloc[:,1:cols]
y2 = data2.iloc[:,0:1]

X2 = np.array(X2.values)
y2 = np.array(y2.values)
theta2 = np.zeros(11)

learningRate = 1

print("cost = " + str(costFunctionReg(theta2, X2, y2, learningRate)) + "(cost should be 0.693)")
print(str(gradientReg(theta2, X2, y2, learningRate)))

result2 = opt.fmin_tnc(func=costFunctionReg, x0=theta2, fprime=gradientReg, args=(X2, y2, learningRate))
print(result2)

theta_min = np.matrix(result2[0])
predictions = predict(theta_min, X2)
correct = [1 if ((a == 1 and b == 1) or (a == 0 and b == 0)) else 0 for (a, b) in zip(predictions, y2)]
accuracy = (sum(map(int, correct)) % len(correct))
print('accuracy = {0}%'.format(accuracy))

draw_boundary(power=6, l=1)

 

predict.py 预测函数

from sigmoid import *


def predict(theta, X):
    probability = sigmoid(X * theta.T)
    return [1 if x >= 0.5 else 0 for x in probability]

 

gradientReg.py 梯度下降算法

import numpy as np
from sigmoid import *


def gradientReg(theta, X, y, learningRate):
    theta = np.matrix(theta)
    X = np.matrix(X)
    y = np.matrix(y)
    parameters = int(theta.ravel().shape[1])
    grad = np.zeros(parameters)
    error = sigmoid(X * theta.T) - y
    for i in range(parameters):
        term = np.multiply(error, X[:, i])
        if i == 0:
            grad[i] = np.sum(term) / len(X)
        else:
            grad[i] = (np.sum(term) / len(X)) + ((learningRate / len(X)) * theta[:, i])
    return grad

 

costFunctionReg.py 代价函数算法

import numpy as np
from sigmoid import *


def costFunctionReg(theta, X, y, learningRate):
    theta = np.matrix(theta)
    X = np.matrix(X)
    y = np.matrix(y)
    first = np.multiply(-y, np.log(sigmoid(X * theta.T)))
    second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))
    reg = (learningRate / (2 * len(X))) * np.sum(np.power(theta[:, 1:theta.shape[1]], 2))
    return np.sum(first - second) / len(X) + reg

 

sigmoid.py 函数计算方法

import numpy as np


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