scikit-learn 之岭回归

scikit-learn 之岭回归

基本语句

from sklearn import linear_model
reg = linear_model.Ridge(alpha = 0.5)
reg.fit([[0,0],[1,1],[2,2]],[0,1,2])
reg.coef_ #coeficients
reg.intercept_

Plot Ridge coefficients as a function of the regularization

from sklearn import linear_model
reg = linear_model.Ridge(alpha = 0.5)
reg.fit([[0,0],[1,1],[2,2]],[0,1,2])
reg.coef_ #coeficients
reg.intercept_
#Plot Ridge coefficients as a function of the regularization
import numpy as np
import matplotlib.pyplot as plt
from sklearn import linear_model
x = 1/(np.arange(1,11)+np.arange(0,10)[:,np.newaxis])#生成一个希尔伯特矩阵
(np.arange(1,11)+np.arange(0,10)[:,np.newaxis])#看一下这个矩阵
Out[65]: 
array([[ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10],
       [ 2,  3,  4,  5,  6,  7,  8,  9, 10, 11],
       [ 3,  4,  5,  6,  7,  8,  9, 10, 11, 12],
       [ 4,  5,  6,  7,  8,  9, 10, 11, 12, 13],
       [ 5,  6,  7,  8,  9, 10, 11, 12, 13, 14],
       [ 6,  7,  8,  9, 10, 11, 12, 13, 14, 15],
       [ 7,  8,  9, 10, 11, 12, 13, 14, 15, 16],
       [ 8,  9, 10, 11, 12, 13, 14, 15, 16, 17],
       [ 9, 10, 11, 12, 13, 14, 15, 16, 17, 18],
       [10, 11, 12, 13, 14, 15, 16, 17, 18, 19]])

一个ndarray( shape is m * 1) + ndarray(shape is n * 1) 变成了一个新的ndarray(shape is m * n)
运算过程是range（1,11）的矩阵每一行，加上range（0，10）的每个数生成一个新的行，最后生成10行矩阵

希尔伯特矩阵，来自360百科…了解一下hh：

y = np.ones(10)
n_alpha = 200#我们的alpha取值有200个，用于做图看趋势
alphas = np.logspace(-10,-2,n_alpha)#生成alpha

#np.logspace(起点，终点，数量)
np.logspace(2.0, 3.0, num=4)#表示以10^2为起点,10^3为终点，生成4个数
Out[67]: array([ 100.        ,  215.443469  ,  464.15888336, 1000.        ])

coefs =[]
for a in alphas:
    ridge = linear_model.Ridge(alpha=a,fit_intercept=False)
    ridge.fit(x,y)
    coefs.append(ridge.coef_)
ax = plt.gca()#画个坐标轴先
ax.plot(alphas,coefs)#这个时候的图挤到了一起

ax.set_xscale('log')#把x值取log

ax.set_xlim(ax.get_xlim()[::-1])  # 把x轴从大到小排列
#a = [1,3,4]则a[::-1]是[4，3，2]逆序
plt.xlabel('alpha')
plt.ylabel('coef')
plt.axes('tight')
#Classification of text documents using sparse features
#这个例子我没看，因为还没学这么多。。。。

留一交叉验证(leave-one-out cross-validation)确定alpha

reg = linear_model.RidgeCV(alphas=[0.1,1,10],cv=3)
reg.fit([[0, 0], [0, 0], [1, 1]], [0, .1, 1])
reg.alpha_#获得最好的alpha值