標準方程法的改進--嶺迴歸算法的python實現

標準方程法的改進–嶺迴歸算法的python實現實現

前言： 嶺迴歸相比標準方程法就是多了一個嶺係數，目的是防止數據不可逆導致的參數無法估計的問題，關於嶺迴歸的具體理論請點擊此處，到我的一篇博文中查看

一、嶺迴歸公式推導

二、嶺迴歸算法python實現代碼

此處嶺係數默認爲0.2，對於程序中的數據比較合適，而具體應用中需要結合交叉驗證法，試驗多次才能找到合適的嶺係數

import numpy as np
from numpy import genfromtxt
import matplotlib.pyplot as plt

# 讀取數據
data = genfromtxt(r'longley.csv', delimiter=',')

# 切分數據
x_data = data[1:, 2:]
y_data = data[1:, 1, np.newaxis]

# 給樣本添加偏置項
X_data = np.concatenate((np.ones((16, 1)), x_data), axis=1)

# 嶺迴歸求解線性模型參數值
def weights(xArr, yArr, lam=0.2):
    xMat = np.mat(xArr)
    yMat = np.mat(yArr)
    xTx = xMat.T * xMat
    rxTx = xTx + np.eye(xMat.shape[1]) * lam
    if np.linalg.det(rxTx) == 0.0:
        print('數據不可逆，不能求解權重（參數）值')
        return
    ws = rxTx.I * xMat.T * yMat
    return ws

ws = weights(X_data, y_data)
print(ws)

# 計算預測值
print(np.mat(X_data) * np.mat(ws))
print(y_data) # 真實值
print(y_data - (np.mat(X_data) * np.mat(ws)))  # 真實值和預測值之差

三、算法運行結果

[[ 7.38107538e-04]
 [ 2.07703836e-01]
 [ 2.10076376e-02]
 [ 5.05385441e-03]
 [-1.59173066e+00]
 [ 1.10442920e-01]
 [-2.42280461e-01]]
[[ 83.55075226]
 [ 86.92588689]
 [ 88.09720228]
 [ 90.95677622]
 [ 96.06951002]
 [ 97.81955375]
 [ 98.36444357]
 [ 99.99814266]
 [103.26832266]
 [105.03165135]
 [107.45224671]
 [109.52190685]
 [112.91863666]
 [113.98357055]
 [115.29845063]
 [117.64279933]]
[[ 83. ]
 [ 88.5]
 [ 88.2]
 [ 89.5]
 [ 96.2]
 [ 98.1]
 [ 99. ]
 [100. ]
 [101.2]
 [104.6]
 [108.4]
 [110.8]
 [112.6]
 [114.2]
 [115.7]
 [116.9]]
[[-5.50752262e-01]
 [ 1.57411311e+00]
 [ 1.02797725e-01]
 [-1.45677622e+00]
 [ 1.30489977e-01]
 [ 2.80446252e-01]
 [ 6.35556429e-01]
 [ 1.85733868e-03]
 [-2.06832266e+00]
 [-4.31651346e-01]
 [ 9.47753293e-01]
 [ 1.27809315e+00]
 [-3.18636658e-01]
 [ 2.16429451e-01]
 [ 4.01549370e-01]
 [-7.42799331e-01]]

Process finished with exit code 0

由結果可知模型的擬合效果較好

四、數據下載
鏈接：https://pan.baidu.com/s/14xi9nAW4DyY3mWFp_GTb0w
提取碼：3kf3