日拱一卒

import numpy as np
import matplotlib.pyplot as plt

# 训练数据
train = np.loadtxt('images1.csv', delimiter=',', skiprows=1)
train_x = train[:, 0:2]
train_y = train[:, 2]

# 权重初始化
w = np.random.rand(2)

# 判别函数
def f(x):
    if np.dot(w, x) >= 0:
        return 1
    else:
        return -1

# 重复次数
epoch = 10

# 更新次数
count = 0

# 学习权重
for _ in range(epoch):
    for x, y in zip(train_x, train_y):
        if f(x) != y:
            w = w + y * x
            # 输出日志
            count += 1
            print('第 {} 次 : w = {}'.format(count, w))

# 绘图确认
plt.plot(train_x[train_y == 1, 0], train_x[train_y == 1, 1], 'o')
plt.plot(train_x[train_y == -1, 0], train_x[train_y == -1, 1], 'x')
x1 = np.arange(0, 500)
plt.plot(x1, -w[0] / w[1] * x1, linestyle='dashed')
plt.show()

import numpy as np
import matplotlib.pyplot as plt

# 训练数据
train = np.loadtxt('click.csv', delimiter=',', dtype='int', skiprows=1)
train_x = train[:, 0]
train_y = train[:, 1]

# 标准化
mu = train_x.mean()
sigma = train_x.std()
def standardize(x):
    return (x - mu) / sigma
train_z = standardize(train_x)

# 创建训练数据的矩阵
def to_matrix(x):
    return np.vstack([np.ones(x.size), x, x ** 2]).T
X = to_matrix(train_z)

# 参数初始化
theta = np.random.rand(3)

# 预测函数
def f(x):
    return np.dot(x, theta)

# 均方误差
def MSE(x, y):
    return (1 / x.shape[0]) * np.sum((y - f(x)) ** 2)

# 学习率
ETA = 1e-3
# 误差的差值
diff = 1
# 更新次数
count = 0
# 直到误差的差值小于 0.01 为止，重复参数更新
error = MSE(X, train_y)
while diff > 1e-2:
    # 使用随机梯度下降法更新参数
    p = np.random.permutation(X.shape[0])
    for x, y in zip(X[p, :], train_y[p]):
        theta = theta - ETA * (f(x) - y) * x
    # 计算与上一次误差的差值
    current_error = MSE(X, train_y)
    diff = error - current_error
    error = current_error
    # 输出日志
    count += 1
    log = '第 {} 次 : theta = {}, 差值 = {:.4f}'
    print(log.format(count, theta, diff))

# 绘图确认
x = np.linspace(-3, 3, 100)
plt.plot(train_z, train_y, 'o')
plt.plot(x, f(to_matrix(x)))
plt.show()

import numpy as np
import matplotlib.pyplot as plt

# 训练数据
train = np.loadtxt('click.csv', delimiter=',', dtype='int', skiprows=1)
train_x = train[:, 0]
train_y = train[:, 1]

# 标准化
mu = train_x.mean()
sigma = train_x.std()
def standardize(x):
    return (x - mu) / sigma
train_z = standardize(train_x)

# 创建训练数据的矩阵
def to_matrix(x):
    return np.vstack([np.ones(x.size), x, x ** 2]).T
X = to_matrix(train_z)

# 参数初始化
theta = np.random.rand(3)

# 预测函数
def f(x):
    return np.dot(x, theta)

# 目标函数
def E(x, y):
    return 0.5 * np.sum((y - f(x)) ** 2)

# 学习率
ETA = 1e-3
# 误差的差值
diff = 1
# 更新次数
count = 0
# 直到误差的差值小于 0.01 为止，重复参数更新
error = E(X, train_y)
while diff > 1e-2:
    # 更新参数
    theta = theta - ETA * np.dot(f(X) - train_y, X)
    # 计算与上一次误差的差值
    current_error = E(X, train_y)
    diff = error - current_error
    error = current_error
    # 输出日志
    count += 1
    log = '第 {} 次 : theta = {}, 差值 = {:.4f}'
    print(log.format(count, theta, diff))

# 绘图确认
x = np.linspace(-3, 3, 100)
plt.plot(train_z, train_y, 'o')
plt.plot(x, f(to_matrix(x)))
plt.show()

import numpy as np
import matplotlib.pyplot as plt

# 训练数据
train = np.loadtxt('click.csv', delimiter=',', dtype='int', skiprows=1)
train_x = train[:, 0]
train_y = train[:, 1]

# 参数初始化
theta0 = np.random.rand()
theta1 = np.random.rand()

# 预测函数
def f(x):
    return theta0 + theta1 * x

# 目标函数
def E(x, y):
    return 0.5 * np.sum((y - f(x)) ** 2)

# 标准化
mu = train_x.mean()
sigma = train_x.std()
def standardize(x):
    return (x - mu) / sigma
train_z = standardize(train_x)

# 学习率
ETA = 1e-3
# 误差的差值
diff = 1
# 更新次数
count = 0
# 直到误差的差值小于 0.01 为止，重复参数更新
error = E(train_z, train_y)
while diff > 1e-2:
    # 更新结果保存到临时变量
    tmp_theta0 = theta0 - ETA * np.sum((f(train_z) - train_y))
    tmp_theta1 = theta1 - ETA * np.sum((f(train_z) - train_y) * train_z)
    # 更新参数
    theta0 = tmp_theta0
    theta1 = tmp_theta1
    # 计算与上一次误差的差值
    current_error = E(train_z, train_y)
    diff = error - current_error
    error = current_error
    # 输出日志
    count += 1
    log = '第 {} 次 : theta0 = {:.3f}, theta1 = {:.3f}, 差值 = {:.4f}'
    print(log.format(count, theta0, theta1, diff))

# 绘图确认
x = np.linspace(-3, 3, 100)
plt.plot(train_z, train_y, 'o')
plt.plot(x, f(x))
plt.show()