machine learning in coding（python）：polynomial curve fitting，python拟合多项式

下面给出一个拟合多项式的例子：

 import pandas as pd
 import numpy as np
 import scipy as sp
 import matplotlib.pyplot as plt


 from sklearn.pipeline import Pipeline
 from sklearn.linear_model import LinearRegression
 from sklearn.preprocessing import PolynomialFeatures


 #RMS
 def rmse(y_test, y_true):
     return sp.sqrt(sp.mean((y_test - y_true) ** 2))

 # the sum of the squares of the errors
 def sse(y_test, y_true):
     return ((y_test - y_true) ** 2).sum() / 2.0




 # load training and test datasets
 data = pd.read_csv('fitting.csv')

 X = data.id.values
 y = data.dingdanshu.values
 X = np.array(X)
 y = np.array(y)
 X = X[2:20]
 y = y[2:20]
 #print X
 #print y


 # plot scatter of original data
 plt.scatter(X, y)

 degree = [1, 2, 3, 4, 5]
 for d in degree:
     clf = Pipeline([ ('poly', PolynomialFeatures(degree=d)), ('linear', LinearRegression(fit_intercept=False)) ])
     clf.fit(X[:, np.newaxis], y)
     y_test = clf.predict(X[:, np.newaxis])

     print(clf.named_steps['linear'].coef_)
     print('rmse=%.2f, sse=%.2f, clf.score=%.2f' % (rmse(y_test, y),  sse(y_test, y), clf.score(X[:, np.newaxis], y)) )

     # plot fit line of y_test
     plt.plot(X, y_test, linewidth=2)

 plt.grid()
 plt.legend(['1', '2', '3','4','5'], loc='upper right')
 plt.show()


 ''''' 对5次多项式求 每个点处的曲率
 aa=clf.named_steps['linear'].coef_
 for i in range(20):
     y1=aa[1]+aa[2]*2*i+aa[3]*3*i*i+aa[4]*4*i*i*i+aa[5]*5*i*i*i*i
     y2=aa[2]*2+aa[3]*6*i+aa[4]*12*i*i+aa[5]*20*i*i*i
     r = (y2*y2)/((1+y1*y1)*(1+y1*y1)*(1+y1*y1))
     print i, "---", y1, "---", y2, "---", r
 '''

结果如图所示：

提供部分数据：

id	dingdanshu
0	153880
1	246449
2	178882
3	120823
4	82616
5	60869
6	48609
7	39028
8	32532
9	28355
10	25058
11	22341
12	20822
13	19471
14	17555
15	16965
16	15134
17	14305
18	12716
19	11684
20	11274
21	10270
22	9139
23	8210
24	7848
25	6906