Python3入门机器学习经典算法与应用——什么是多项式回归

浅浅的花香味﹌ 2022-12-21 15:50 159阅读 0赞

# 什么是多项式回归 #

# 线性回归 #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2U4OTEzNzc_size_16_color_FFFFFF_t_70_pic_center]  
多项式回归  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2U4OTEzNzc_size_16_color_FFFFFF_t_70_pic_center 1]  
把 x 2 x^\{2\} x2理解了一个特征，这样依然是一个线性回归的式子。

# 什么是多项式回归 #

import numpy as np 
    import matplotlib.pyplot as plt

x = np.random.uniform(-3, 3, size=100)
    X = x.reshape(-1, 1)
    y = 0.5 * x**2 + x + 2 + np.random.normal(0, 1, 100)

plt.scatter(x, y)
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2U4OTEzNzc_size_16_color_FFFFFF_t_70_pic_center 2]

### 线性回归？ ###

from sklearn.linear_model import LinearRegression
    
    lin_reg = LinearRegression()
    lin_reg.fit(X, y)
    y_predict = lin_reg.predict(X)

plt.scatter(x, y)
    plt.plot(x, y_predict, color='r')
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2U4OTEzNzc_size_16_color_FFFFFF_t_70_pic_center 3]

### 解决方案， 添加一个特征 ###

X2 = np.hstack([X, X**2])

X2.shape

(100, 2)

lin_reg2 = LinearRegression()
    lin_reg2.fit(X2, y)
    y_predict2 = lin_reg2.predict(X2)

plt.scatter(x, y)
    plt.plot(np.sort(x), y_predict2[np.argsort(x)], color='r')
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2U4OTEzNzc_size_16_color_FFFFFF_t_70_pic_center 4]

lin_reg2.coef_

array([ 0.99870163,  0.54939125])

lin_reg2.intercept_

1.8855236786516001

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