吴恩达机器学习作业（二）_python实现

一，必做部分

import pandas as pd
import numpy as np
import scipy.optimize as opt
import matplotlib.pyplot as plt
from sklearn.metrics import classification_report#这个包是评价报告


def get_X(df):#读取特征
    ones = pd.DataFrame({
     'ones': np.ones(len(df))})#ones是m行1列的dataframe
    data = pd.concat([ones, df], axis=1)  # 合并数据，根据列合并
    return data.iloc[:, :-1].values


def get_y(df):#读取标签
    return np.array(df.iloc[:, -1])#df.iloc[:, -1]是指df的最后一列


def normalize_feature(df):
    return df.apply(lambda column: (column - column.mean()) / column.std())#特征缩放


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


def cost(theta, X, y):
    return np.mean(-y * np.log(sigmoid(X @ theta)) - (1 - y) * np.log(1 - sigmoid(X @ theta)))


def gradient(theta, X, y):
    return (1 / len(X)) * X.T @ (sigmoid(X @ theta) - y)


def predict(x, theta):
    prob = sigmoid(x @ theta)
    return (prob >= 0.5).astype(int)#.astype方法前的数据类型为numpy.ndarray


theta=np.zeros(3)
data = pd.read_csv('ex2data1.txt', names=['exam 1', 'exam 2', 'admitted'])
X = get_X(data)
y = get_y(data)
res = opt.minimize(fun=cost, x0=theta, args=(X, y), method='Newton-CG', jac=gradient)
'''func：优化的目标函数
x0：初值
fprime：提供优化函数func的梯度函数，不然优化函数func必须返回函数值和梯度，或者设置approx_grad=True
args：元组，是传递给优化函数的参数'''
final_theta = res.x#res.x is final theta
y_pred = predict(X, final_theta)

#二维图
positive = data[data['admitted'].isin([1])]
negative = data[data['admitted'].isin([0])]
plt.scatter(positive['exam 1'], positive['exam 2'], s=50, c='b', marker='o', label='Admitted')
plt.scatter(negative['exam 1'], negative['exam 2'], s=50, c='r', marker='x', label='Not Admitted')
plt.legend(loc=0)#增加图例,0,1,2,3,4分别表示不同的位置
plt.xlabel('Exam 1 Score')
plt.ylabel('Exam 2 Score')
coef = -(res.x / res.x[2])  # find the equation
x = np.arange(130, step=0.1)
y2 = coef[0] + coef[1]*x#y = theta@X = sigmod(theta[0]*X[0]+theta[1]*X[1]+theta[2]*X[2])
plt.plot(x, y2, 'grey')
plt.show()


#三维图，注释掉了，看三维效果把下面的注释去掉，49-60加注释
"""x = plt.axes(projection='3d')
ax.scatter(X[:,1], X[:,2], y, alpha=0.3)
D = final_theta[0]
A = final_theta[1]
B = final_theta[2]
Z = A*X[:,1] + B*X[:,2] + D
ax.plot_trisurf(X[:,1], X[:,2], Z,
                       linewidth=0, antialiased=False,color='r')
ax.set_zlim(-2,2);"""
print(classification_report(y, y_pred))

二，选作部分

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import scipy.optimize as opt



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


def cost(theta, X, y, learningRate):
    theta = np.mat(theta)
    X = np.mat(X)
    y = np.mat(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


def gradientReg(theta, X, y, learningRate):
    theta = np.mat(theta)
    X = np.mat(X)
    y = np.mat(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


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


data2 = pd.read_csv("ex2data2.txt", header=None, names=['Test 1', 'Test 2', 'Accepted'])
df = data2[:]
#原始数据
positive = data2[data2['Accepted'].isin([1])]
negative = data2[data2['Accepted'].isin([0])]
plt.scatter(positive['Test 1'], positive['Test 2'], s=50, c='b', marker='o', label='Accepted')
plt.scatter(negative['Test 1'], negative['Test 2'], s=50, c='r', marker='x', label='Rejected')
plt.legend()
plt.xlabel('Test 1 Score')
plt.ylabel('Test 2 Score')
plt.show()


degree = 5
x1 = data2['Test 1']
x2 = data2['Test 2']
data2.insert(3, 'Ones', 1)#插入在第三列之前
for i in range(1, degree):#i:1~4
    for j in range(0, i):#i=4时，j为0到3
        data2['F' + str(i) + str(j)] = np.power(x1, i-j) * np.power(x2, j)
'''将F10，F20,F21这些列加在data2的最后，例如：data["ww"]=1    会在data2的列之后在格外加一列名字为ww'''
data2.drop('Test 1', axis=1, inplace=True)#删除方法，将index为Test 1，axis=1说明删除的是列
data2.drop('Test 2', axis=1, inplace=True)#如果手动设定为True（默认为False），那么原数组直接就被替换
#而采用inplace=False之后，原数组名对应的内存值并不改变，需要将新的结果赋给一个新的数组或者覆盖原数组的内存位置
cols = data2.shape[1]
X2 = data2.iloc[:, 1:cols].values#删除accepted列
y2 = data2.iloc[:, 0:1].values#仅保留accepted列
theta2 = np.zeros(11)
learningRate = 1
final_theta = opt.fmin_tnc(func=cost, x0=theta2, fprime=gradientReg, args=(X2, y2, learningRate))
'''或用
res = opt.minimize(fun=cost,
                       x0=theta2,
                       args=(X2, y2, learningRate),
                       method='TNC',
                       jac=gradientReg)
final_theta = res.x可得到相同的结果

func：优化的目标函数
x0：初值
fprime：提供优化函数func的梯度函数，不然优化函数func必须返回函数值和梯度，或者设置approx_grad=True
args：元组，是传递给优化函数的参数
'''
theta_min = np.mat(final_theta[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))

原始数据如图

画出决策边界：由于×是个11维的图，我们不能直观的表示出来
但可以找到所有 ×近似等于0的值以此来画出决策边界（是这么个思路，以下复制了国外大牛的代码）

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import scipy.optimize as opt
import seaborn as sns


def cost(theta, X, y):
    return np.mean(-y * np.log(sigmoid(X @ theta)) - (1 - y) * np.log(1 - sigmoid(X @ theta)))


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


def gradient(theta, X, y):
    return (1 / len(X)) * X.T @ (sigmoid(X @ theta) - y)


def feature_mapping(x, y, power, as_ndarray=False):
    data = {
     "f{}{}".format(i - p, p): np.power(x, i - p) * np.power(y, p)
            for i in np.arange(power + 1)
            for p in np.arange(i + 1)
            }
    if as_ndarray:
        return pd.DataFrame(data).values
    else:
        return pd.DataFrame(data)


def regularized_gradient(theta, X, y, l=1):
#     '''still, leave theta_0 alone'''
    theta_j1_to_n = theta[1:]
    regularized_theta = (l / len(X)) * theta_j1_to_n

    # by doing this, no offset is on theta_0
    regularized_term = np.concatenate([np.array([0]), regularized_theta])

    return gradient(theta, X, y) + regularized_term


def regularized_cost(theta, X, y, l=1):
#     '''you don't penalize theta_0'''
    theta_j1_to_n = theta[1:]
    regularized_term = (l / (2 * len(X))) * np.power(theta_j1_to_n, 2).sum()

    return cost(theta, X, y) + regularized_term


def feature_mapped_logistic_regression(power, l):
    df = pd.read_csv('ex2data2.txt', names=['test1', 'test2', 'accepted'])
    x1 = np.array(df.test1)
    x2 = np.array(df.test2)
    y = np.array(df.iloc[:, -1])
    X = feature_mapping(x1, x2, power, as_ndarray=True)
    theta = np.zeros(X.shape[1])
    res = opt.minimize(fun=regularized_cost,
                       x0=theta,
                       args=(X, y, l),
                       method='TNC',
                       jac=regularized_gradient)
    final_theta = res.x
    return final_theta


def find_decision_boundary(density, power, theta, threshhold):
    t1 = np.linspace(-1, 1.5, density)
    t2 = np.linspace(-1, 1.5, density)

    cordinates = [(x, y) for x in t1 for y in t2]
    x_cord, y_cord = zip(*cordinates)
    mapped_cord = feature_mapping(x_cord, y_cord, power)  # this is a dataframe

    inner_product = mapped_cord.values @ theta

    decision = mapped_cord[np.abs(inner_product) < threshhold]

    return decision.f10, decision.f01


def draw_boundary(power, l):

    density = 1000
    threshhold = 2 * 10**-3
    final_theta = feature_mapped_logistic_regression(power, l)
    x, y = find_decision_boundary(density, power, final_theta, threshhold)
    df = pd.read_csv('ex2data2.txt', names=['test1', 'test2', 'accepted'])
    sns.lmplot('test1', 'test2', hue='accepted', data=df, size=6, fit_reg=False, scatter_kws={
     "s": 100})
    plt.scatter(x, y, color='red', s=10)
    plt.title('Decision boundary')
    plt.show()


draw_boundary(6, 1)#第二个为lambda的值，lambda=0过拟合，lambda=100欠拟合

过拟合：draw_boundary(6, 0)

欠拟合：draw_boundary(6, 100)