

In [1]:

    
%matplotlib inline
import matplotlib.pyplot as plt

from sklearn import svm

import numpy as np
import pandas as pd
import seaborn as sns
import scipy.io as sio



In [2]:

    
# kernek function
def gaussian_kernel(x1, x2, sigma):
    return np.exp(- np.power(x1 - x2, 2).sum() / (2 * (sigma ** 2)))



In [3]:

    
x1 = np.array([1, 2, 1])
x2 = np.array([0, 4, -1])
sigma = 2

gaussian_kernel(x1, x2, sigma)









    Out[3]:





0.32465246735834974

load data



In [4]:

    
mat = sio.loadmat('./data/ex6data2.mat')
print(mat.keys())
data = pd.DataFrame(mat.get('X'), columns=['X1', 'X2'])
data['y'] = mat.get('y')

data.head()









    



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






    Out[4]:






  
    
      
      X1
      X2
      y
    
  
  
    
      0
      0.107143
      0.603070
      1
    
    
      1
      0.093318
      0.649854
      1
    
    
      2
      0.097926
      0.705409
      1
    
    
      3
      0.155530
      0.784357
      1
    
    
      4
      0.210829
      0.866228
      1



In [5]:

    
data.shape









    Out[5]:





(863, 3)

visualize data



In [6]:

    
sns.set(context="notebook", style="white", palette=sns.diverging_palette(240, 10, n=2))
sns.lmplot('X1', 'X2', hue='y', data=data, 
           size=5, 
           fit_reg=False, 
           scatter_kws={"s": 10}
          )









    Out[6]:





<seaborn.axisgrid.FacetGrid at 0x106c59710>

try built-in Gaussian Kernel of sklearn



In [7]:

    
svc = svm.SVC(C=100, kernel='rbf', gamma=10, probability=True)
svc









    Out[7]:





SVC(C=100, cache_size=200, class_weight=None, coef0=0.0,
  decision_function_shape=None, degree=3, gamma=10, kernel='rbf',
  max_iter=-1, probability=True, random_state=None, shrinking=True,
  tol=0.001, verbose=False)



In [8]:

    
svc.fit(data[['X1', 'X2']], data['y'])
svc.score(data[['X1', 'X2']], data['y'])









    Out[8]:





0.9698725376593279

the predict_proba will give you ndarray (data size, class)
so if you just want to plot the decision contour of this binary example, choose one class and plot it



In [9]:

    
predict_prob = svc.predict_proba(data[['X1', 'X2']])[:, 0]



In [10]:

    
fig, ax = plt.subplots(figsize=(8,6))
ax.scatter(data['X1'], data['X2'], s=30, c=predict_prob, cmap='Reds')









    Out[10]:





<matplotlib.collections.PathCollection at 0x1151ec978>



In [ ]:

	X1	X2	y
0	0.107143	0.603070	1
1	0.093318	0.649854	1
2	0.097926	0.705409	1
3	0.155530	0.784357	1
4	0.210829	0.866228	1