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()