数据挖掘第二课笔记线性回归

weixin_51468604

已于 2023-03-14 23:32:13 修改

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文章标签：数据挖掘机器学习 python

于 2023-03-14 23:17:59 首次发布

本文链接：https://blog.youkuaiyun.com/weixin_51468604/article/details/129542328

版权

一、基础知识

二、线性回归和梯度下降算法

三、代码

数据集：200万条训练数据该数据集为一个出租车数据集的部分数据

通过for循环实现损失函数梯度下降

import numpy as np
import time

# 读入数据
data = np.matrix(np.loadtxt("taxi-data-sorted-small.csv", delimiter=",", usecols=(4, 5, 11, 12, 16)))

# 切分数据
x_data = np.insert(data[:, :-1], 0, 1, axis=1)  # 第0列插入1  对应于参数 theta0 即常数项
y_data = data[:, -1]

# 学习率learning rate
lr = 0.0001
# 参数
theta0 = 0
theta1 = 0
theta2 = 0
# 最大迭代次数
epochs = 2

# 最小二乘法
def compute_error(theta0, theta1, theta2, x_data, y_data):
    totalError = 0
    for i in range(0, len(x_data)):
        totalError += (y_data[i] - (theta1 * x_data[i, 0] + theta2 * x_data[i, 1] + theta0)) ** 2
    return totalError / (float(len(x_data))*2)


def gradient_descent_runner(x_data, y_data, theta0, theta1, theta2, lr, epochs):
    # 计算总数据量
    m = float(len(x_data))
    # 循环epochs次
    for i in range(epochs):
        theta0_grad = 0
        theta1_grad = 0
        theta2_grad = 0
        # 计算梯度的总和再求平均
        for j in range(0, len(x_data)):
            theta0_grad += -(1 / m) * (y_data[j] - (theta1 * x_data[j, 0] + theta2 * x_data[j, 1] + theta0))
            theta1_grad += -(1 / m) * x_data[j, 0] * (
                    y_data[j] - (theta1 * x_data[j, 0] + theta2 * x_data[j, 1] + theta0))
            theta2_grad += -(1 / m) * x_data[j, 1] * (
                    y_data[j] - (theta1 * x_data[j, 0] + theta2 * x_data[j, 1] + theta0))
        # 更新参数
        theta0 = theta0 - (lr * theta0_grad)
        theta1 = theta1 - (lr * theta1_grad)
        theta2 = theta2 - (lr * theta2_grad)
    return theta0, theta1, theta2


print("Starting theta0 = {0}, theta1 = {1}, theta2 = {2}, error = {3}".
      format(theta0, theta1, theta2, compute_error(theta0, theta1, theta2, x_data, y_data)))
print("Running...")
start = time.time()
theta0, theta1, theta2 = gradient_descent_runner(x_data, y_data, theta0, theta1, theta2, lr, epochs)
print('epoch=2 训练运行时间：', time.time()-start)
print("After {0} iterations theta0 = {1}, theta1 = {2}, theta2 = {3}, error = {4}".
      format(epochs, theta0, theta1, theta2, compute_error(theta0, theta1, theta2, x_data, y_data)))

运行结果：

2. 通过numpy矩阵优化


import numpy as np
import time

def compute_error(theta0, x, y):
    # 最小二乘法
    inner = np.power((x * theta0) - y, 2)
    return np.sum(inner) / (2 * len(x))
def gradient_descent_runner(x, y, theta0, l, epochs):
    for i in range(epochs):
        theta0 -= l / len(x) * x.T * ((x * theta0) - y)
    return theta0

# 读入数据
data = np.matrix(np.loadtxt("taxi-data-sorted-small.csv", delimiter=",", usecols=(4, 5, 11, 12, 16)))

# 切分数据
x_data = np.insert(data[:, :-1], 0, 1, axis=1)  # 第0列插入1  对应于参数 theta0 即常数项
y_data = data[:, -1]

lr = 0.0000001  # 学习率learning rate
theta = np.matrix([[0], [0], [0], [0], [0]],dtype='float64')  # 参数
epochs0 = 100  # 最大迭代次数

print("Starting theta0 = {0}, theta1 = {1}, theta2 = {2}, theta3 = {3}, theta4 = {4}, \n error = {5}".
      format(theta[0,0], theta[1,0], theta[2,0], theta[3,0], theta[4,0], compute_error(theta, x_data, y_data)))

print("Running...")
start = time.time()
theta = gradient_descent_runner(x_data, y_data, theta, lr, epochs0)  # 梯度下降
print('epoch=100 通过numpy矩阵优化的训练运行时间：', time.time()-start)
print("After {0} iterations theta0 = {1}, theta1 = {2}, theta2 = {3}, theta3 = {4}, theta4 = {5}, \n error = {6}".
      format(epochs0, theta[0,0], theta[1,0], theta[2,0], theta[3,0], theta[4,0], compute_error(theta, x_data, y_data)))

运行结果：

3. 正规方程

import numpy as np
import time
def compute_error(theta0, x, y):
    # 最小二乘法
    inner = np.power((x * theta0) - y, 2)
    return np.sum(inner) / (2 * len(x))

# 读入数据
data = np.matrix(np.loadtxt("taxi-data-sorted-small.csv", delimiter=",", usecols=(4, 5, 11, 12, 16)))

# 切分数据
x_data = np.insert(data[:, :-1], 0, 1, axis=1)  # 第0列插入1  对应于参数 theta0 即常数项
y_data = data[:, -1]

print("Running...")
start = time.time()
k = np.linalg.pinv(x_data.T * x_data) * x_data.T * y_data  # 正规方程
print('正规方程训练时间：', time.time()-start)
print("After iterations theta0 = {0}, theta1 = {1}, theta2 = {2}, theta3 = {3}, theta4 = {4},\n error = {5}".
      format(k[0,0], k[1,0], k[2,0], k[3,0], k[4,0], compute_error(k[:5], x_data, y_data)))

运行结果：