In [25]:

    

import numpy as np
import matplotlib.pyplot as plt

from sklearn.linear_model import LogisticRegression
from sklearn import datasets
from sklearn.preprocessing import StandardScaler


    

In [26]:

    

digits = datasets.load_digits()

X, y = digits.data, digits.target


    

In [27]:

    

len(X)
type(y)


    

    
Out[27]:





numpy.ndarray

In [28]:

    

X[0:2]


    

    
Out[28]:





array([[  0.,   0.,   5.,  13.,   9.,   1.,   0.,   0.,   0.,   0.,  13.,
         15.,  10.,  15.,   5.,   0.,   0.,   3.,  15.,   2.,   0.,  11.,
          8.,   0.,   0.,   4.,  12.,   0.,   0.,   8.,   8.,   0.,   0.,
          5.,   8.,   0.,   0.,   9.,   8.,   0.,   0.,   4.,  11.,   0.,
          1.,  12.,   7.,   0.,   0.,   2.,  14.,   5.,  10.,  12.,   0.,
          0.,   0.,   0.,   6.,  13.,  10.,   0.,   0.,   0.],
       [  0.,   0.,   0.,  12.,  13.,   5.,   0.,   0.,   0.,   0.,   0.,
         11.,  16.,   9.,   0.,   0.,   0.,   0.,   3.,  15.,  16.,   6.,
          0.,   0.,   0.,   7.,  15.,  16.,  16.,   2.,   0.,   0.,   0.,
          0.,   1.,  16.,  16.,   3.,   0.,   0.,   0.,   0.,   1.,  16.,
         16.,   6.,   0.,   0.,   0.,   0.,   1.,  16.,  16.,   6.,   0.,
          0.,   0.,   0.,   0.,  11.,  16.,  10.,   0.,   0.]])

In [29]:

    

X = StandardScaler().fit_transform(X)


    

In [30]:

    

len(y)


    

    
Out[30]:





1797

In [31]:

    

y[0:20]


    

    
Out[31]:





array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

In [32]:

    

y = (y > 4).astype(np.int)


    

In [33]:

    

type(y)


    

    
Out[33]:





numpy.ndarray

In [34]:

    

y[0:20]


    

    
Out[34]:





array([0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1])

In [36]:

    

for i, C in enumerate((100, 1, 0.01)):
    clf_l1_LR = LogisticRegression(C=C, penalty='l1', tol=0.01)
    clf_l2_LR = LogisticRegression(C=C, penalty='l2', tol=0.01)
    clf_l1_LR.fit(X, y)
    clf_l2_LR.fit(X, y)
    
    coef_l1_LR = clf_l1_LR.coef_.ravel()
    coef_l2_LR = clf_l2_LR.coef_.ravel()
    
    sparsity_l1_LR = np.mean(coef_l1_LR == 0) * 100
    sparsity_l2_LR = np.mean(coef_l2_LR == 0) * 100
    
    print("C=%.2f" % C)
    print("Sparsity with L1 penalty: %.2f%%" % sparsity_l1_LR)
    print("score with L1 penalty: %.4f" % clf_l1_LR.score(X, y))
    print("Sparsity with L2 penalty: %.2f%%" % sparsity_l2_LR)
    print("score with L2 penalty: %.4f" % clf_l2_LR.score(X, y))
    
    l1_plot = plt.subplot(3, 2, 2 * i + 1)
    l2_plot = plt.subplot(3, 2, 2*(i + 1))
    
    if i == 0:
        l1_plot.set_title("L1 penalty")
        l2_plot.set_title("L2 penalty")
    
    l1_plot.imshow(np.abs(coef_l1_LR.reshape(8, 8)), interpolation='nearest',
                   cmap='binary', vmax=1, vmin=0)
    l2_plot.imshow(np.abs(coef_l2_LR.reshape(8, 8)), interpolation='nearest',
                   cmap='binary', vmax=1, vmin=0)
    plt.text(-8, 3, "C = %.2f" % C)
    
    l1_plot.set_xticks(())
    l1_plot.set_yticks(())
    l2_plot.set_xticks(())
    l2_plot.set_yticks(())

plt.show()


    

    




C=100.00
Sparsity with L1 penalty: 6.25%
score with L1 penalty: 0.9098
Sparsity with L2 penalty: 4.69%
score with L2 penalty: 0.9098
C=1.00
Sparsity with L1 penalty: 9.38%
score with L1 penalty: 0.9093
Sparsity with L2 penalty: 4.69%
score with L2 penalty: 0.9093
C=0.01
Sparsity with L1 penalty: 85.94%
score with L1 penalty: 0.8631
Sparsity with L2 penalty: 4.69%
score with L2 penalty: 0.8915






    

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