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linear_regression.py
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linear_regression.py
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# -*- coding: utf-8 -*-
"""
@Create DATE: 2021/3/27
@Author: Cao Zihang
@File: linear_regression.py
@Software: PyCharm
@Target: 实现一元线性回归模型
@Status: done
"""
import time
import numpy as np
import matplotlib.pyplot as plt
# generate data
x = 10*np.random.random((1, 100)) # np.random.random 生成1个100维的随机浮点数阵列
epsilon = np.random.normal(0, 1, 100)
y = 3*x + 11 + epsilon # 真实回归曲线
print('True result: y = 3*x + 11')
time_start = time.time()
# Github: MachineLearningModels-master version_change —— 使用梯度下降法
# initialize parameters
a = 0
b = 0
# performance measure
performance = 0
gra_a = 5
gra_b = 5
# iterations
iteration_max = 100000 # 最大迭代次数
learning_rate = 0.001 # 学习率
j = 0
# calculate
while j < iteration_max:
# timer
num = round((j/iteration_max)*100, 2)
process = "\r[%3s%%]: |%-100s|" % (num, '|' * int(num))
print(process, end='', flush=True)
# calculate the performance
for i in range(len(x[0, ])):
# 最小二乘法计算代价函数值
performance += ((y[0, i] - a*x[0, i] - b)**2)
performance = performance/(2*len(x[0, ]))
# 除以m为消除样本数影响；除以2为便于求导时化简，无实际意义
# 迭代终止判断
if performance <= 0.5: # 我猜是自由设置的一个标准
print('\n')
print('The result is: y=', round(a, 2), 'x+', round(b, 2))
break
elif j == (iteration_max-1):
print('\n')
print('The result is (unsolved): y=', a, 'x+', b)
break
else:
# 计算a b的梯度
for i in range(len(x[0, ])):
gra_a += -(y[0, i] - a * x[0, i] - b) * x[0, i]
gra_b += -(y[0, i] - a * x[0, i] - b)
gra_a = gra_a / len(x[0, ])
gra_b = gra_b // len(x[0, ])
a = a - learning_rate*gra_a
b = b - learning_rate*gra_b
# 重置参数
j += 1
gra_a = 0
gra_b = 0
performance = 0
# show
x_hat = np.arange(0, 10, 0.1)
y_hat = a*x_hat+b
plt.scatter(x, y)
plt.plot(x_hat, y_hat, c='blue')
plt.show()
time_end = time.time()
print('time cost', round(time_end-time_start, 2), 's')
print('---'*10)
# ______________________________________________________________________________________________________________________
# sklearn version
from sklearn import linear_model
time_start = time.time()
x_data = x[0, ]
y_data = y[0, ]
x_data = x_data[:, np.newaxis]
y_data = y_data[:, np.newaxis]
model = linear_model.LinearRegression()
model.fit(x_data, y_data)
w = model.coef_ # 斜率w
b = model.intercept_
print('The result is: y=', float(w), "x + ", float(b))
x_hat = np.arange(0, 10, 0.1)
y_hat = float(w)*x_hat+float(b)
plt.scatter(x, y)
plt.plot(x_hat, y_hat, c='blue')
plt.show()
time_end = time.time()
print('time cost', round(time_end-time_start, 2), 's')
print('---'*10)
# ______________________________________________________________________________________________________________________
# my version
time_start = time.time()
w_h = 0
b_tmp = 0
for i in range(len(x[0, ])):
w_h += y[0, i]*(x[0, i]-np.mean(x[0, ]))
w = w_h/(np.sum((x[0, ]**2))-np.sum(x[0, ])**2/len(x[0, ]))
for i in range(len(x[0, ])):
b_tmp += y[0, i] - w*x[0, i]
b = b_tmp/len(x[0, ])
print('The result is: y=', w, 'x+', b)
x_hat = np.arange(0, 10, 0.1)
y_hat = w*x_hat+b
plt.scatter(x, y)
plt.plot(x_hat, y_hat, c='blue')
plt.show()
time_end = time.time()
print('time cost', round(time_end-time_start, 2), 's')