在參加“資料探勘”比賽中遇到了關於函式高次擬合的問題，然後就整理了一下原始碼，以便後期的學習與改進。

在本次“資料探勘”比賽中感覺收穫最大的還是對於神經網路的認識，在接近一週的時間裡，研究了進40種神經網路模型，雖然在持續一週的挖掘比賽把自己折磨的慘不忍睹，但是收穫頗豐。現在想想也挺欣慰自己在這段時間裡接受新知識的能力。關於神經網路方面的理解會在後續博文中補充（剛提交完論文，還沒來得及整理），先分享一下高次擬合方面的知識。

# 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

''''' 資料匯入 '''
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)
#分別進行1,2,3,6次擬合
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)

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

    print('多項式引數%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()