python实现二维函数高次拟合

在参加“数据挖掘”比赛中遇到了关于函数高次拟合的问题，然后就整理了一下源码，以便后期的学习与改进。在本次“数据挖掘”比赛中感觉收获最大的还是对于神经网络的认识，在接近一周的时间里，研究了进40种神经网络模型，虽然在持续一周的挖掘比赛把自己折磨的惨不忍睹，但是收获颇丰。现在想想也挺欣慰自己在这段时间里接受新知识的能力。关于神经网络方面的理解会在后续博文中补充（刚提交完论文，还没来得及整理），先分享一下高次拟合方面的知识。

# coding=utf-8import matplotlib.pyplot as pltimport numpy as npimport scipy as spimport csvfrom scipy.stats import normfrom sklearn.pipeline import Pipelinefrom sklearn.linear_model import LinearRegressionfrom sklearn.preprocessing import PolynomialFeaturesfrom 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,labelMatxArr,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 ** 2def 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()