对python实现二维函数高次拟合的示例详解

# coding=utf-8
import matplotlib.pyplot as plt
import numpy as np
import scipy as sp
import csv
from scipy.stats import norm
from sklearn.pipeline import Pipeline
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
from sklearn import linear_model

''''' 数据导入 '''
def loadDataSet(fileName):
 dataMat = []
 labelMat = []
 csvfile = file(fileName, 'rb')
 reader = csv.reader(csvfile)
 b = 0
 for line in reader:
  if line[50] is '':
   b += 1
  else:
   dataMat.append(float(line[41])/100*20+30)
   labelMat.append(float(line[25])*100)


 csvfile.close()
 print "absence time number: %d" % b
 return dataMat,labelMat

xArr,yArr = loadDataSet('data.csv')
x = np.array(xArr)
y = np.array(yArr)
# x = np.arange(0, 1, 0.002)
# y = norm.rvs(0, size=500, scale=0.1)
# y = y + x ** 2

def rmse(y_test, y):
 return sp.sqrt(sp.mean((y_test - y) ** 2))

def R2(y_test, y_true):
 return 1 - ((y_test - y_true) ** 2).sum() / ((y_true - y_true.mean()) ** 2).sum()

def R22(y_test, y_true):
 y_mean = np.array(y_true)
 y_mean[:] = y_mean.mean()
 return 1 - rmse(y_test, y_true) / rmse(y_mean, y_true)


plt.scatter(x, y, s=5)
#分别进行1,2,3,6次拟合
degree = [1, 2,3, 6]
y_test = []
y_test = np.array(y_test)

for d in degree:
 #普通
 # clf = Pipeline([('poly', PolynomialFeatures(degree=d)),
 #     ('linear', LinearRegression(fit_intercept=False))])
 # clf.fit(x[:, np.newaxis], y)

 # 岭回归
 clf = Pipeline([('poly', PolynomialFeatures(degree=d)),
     ('linear', linear_model.Ridge())])
 clf.fit(x[:, np.newaxis], y)
 y_test = clf.predict(x[:, np.newaxis])

 print('多项式参数%s' %clf.named_steps['linear'].coef_)
 print('rmse=%.2f, R2=%.2f, R22=%.2f, clf.score=%.2f' %
   (rmse(y_test, y),
   R2(y_test, y),
   R22(y_test, y),
   clf.score(x[:, np.newaxis], y)))

 plt.plot(x, y_test, linewidth=2)

plt.grid()
plt.legend(['1', '2','3', '6'], loc='upper left')
plt.show()