

In [1]:

    
%matplotlib inline

import numpy as np
import pandas as pd
import sklearn.svm
import seaborn as sns
import scipy.io as sio
import matplotlib.pyplot as plt



In [2]:

    
mat = sio.loadmat('./data/ex6data1.mat')
print(mat.keys())
data = pd.DataFrame(mat.get('X'), columns=['X1', 'X2'])
data['y'] = mat.get('y')

data.head()









    



dict_keys(['__globals__', 'X', 'y', '__version__', '__header__'])






    Out[2]:






  
    
      
      X1
      X2
      y
    
  
  
    
      0
      1.9643
      4.5957
      1
    
    
      1
      2.2753
      3.8589
      1
    
    
      2
      2.9781
      4.5651
      1
    
    
      3
      2.9320
      3.5519
      1
    
    
      4
      3.5772
      2.8560
      1

visualize data

pay attention to the edge case at the left hand side



In [3]:

    
fig, ax = plt.subplots(figsize=(8,6))
ax.scatter(data['X1'], data['X2'], s=50, c=data['y'], cmap='Reds')
ax.set_title('Raw data')
ax.set_xlabel('X1')
ax.set_ylabel('X2')









    Out[3]:





<matplotlib.text.Text at 0x112cee390>

try $C=1$

http://scikit-learn.org/stable/modules/generated/sklearn.svm.LinearSVC.html#sklearn.svm.LinearSVC



In [4]:

    
svc1 = sklearn.svm.LinearSVC(C=1, loss='hinge')
svc1.fit(data[['X1', 'X2']], data['y'])
svc1.score(data[['X1', 'X2']], data['y'])









    Out[4]:





0.98039215686274506



In [5]:

    
data['SVM1 Confidence'] = svc1.decision_function(data[['X1', 'X2']])



In [6]:

    
fig, ax = plt.subplots(figsize=(8,6))
ax.scatter(data['X1'], data['X2'], s=50, c=data['SVM1 Confidence'], cmap='RdBu')
ax.set_title('SVM (C=1) Decision Confidence')









    Out[6]:





<matplotlib.text.Text at 0x1151d5ac8>

try $C=100$

with large C, you try to overfit the data, so the left hand side edge case now is categorized right



In [7]:

    
svc100 = sklearn.svm.LinearSVC(C=100, loss='hinge')
svc100.fit(data[['X1', 'X2']], data['y'])
svc100.score(data[['X1', 'X2']], data['y'])









    Out[7]:





0.98039215686274506



In [8]:

    
data['SVM100 Confidence'] = svc100.decision_function(data[['X1', 'X2']])



In [9]:

    
fig, ax = plt.subplots(figsize=(8,6))
ax.scatter(data['X1'], data['X2'], s=50, c=data['SVM100 Confidence'], cmap='RdBu')
ax.set_title('SVM (C=100) Decision Confidence')









    Out[9]:





<matplotlib.text.Text at 0x115247b00>



In [10]:

    
data.head()









    Out[10]:






  
    
      
      X1
      X2
      y
      SVM1 Confidence
      SVM100 Confidence
    
  
  
    
      0
      1.9643
      4.5957
      1
      0.799366
      3.485448
    
    
      1
      2.2753
      3.8589
      1
      0.381775
      1.622359
    
    
      2
      2.9781
      4.5651
      1
      1.374058
      4.537510
    
    
      3
      2.9320
      3.5519
      1
      0.519575
      1.440891
    
    
      4
      3.5772
      2.8560
      1
      0.333060
      0.077828



In [ ]:

	X1	X2	y
0	1.9643	4.5957	1
1	2.2753	3.8589	1
2	2.9781	4.5651	1
3	2.9320	3.5519	1
4	3.5772	2.8560	1

	X1	X2	y	SVM1 Confidence	SVM100 Confidence
0	1.9643	4.5957	1	0.799366	3.485448
1	2.2753	3.8589	1	0.381775	1.622359
2	2.9781	4.5651	1	1.374058	4.537510
3	2.9320	3.5519	1	0.519575	1.440891
4	3.5772	2.8560	1	0.333060	0.077828