python – gitweixin

import numpy as np import matplotlib.pyplot as plt # 读入训练数据 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) # 参数初始化 theta = np.random.rand(3) # 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) # 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: # 更新结果保存到临时变量 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()

python, 数据挖掘 10月 8,2020

python源码实现线性回归并绘图

用python实现一次函数的线性回归。把fθ(x)作为一次函数来实现吧。我们要实现下面这样的fθ(x)和目标函数E(θ)。

要把下面的训练数据变成平均值为0、方差为1的数据。作用是参数的收敛会更快。这种做法也被称为标准化或者z-score规范化，变换表达式是这样的。µ是训练数据的平均值，σ是标准差。

参数更新表达式如下：

训练数据如下：

import numpy as np
import matplotlib.pyplot as plt

# 读入训练数据
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)

# 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)

# 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()

最终输出图形如下：

作者 east

分类归档python