In [1]:

    

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from pandas import Series, DataFrame

from numpy.random import multivariate_normal


    

In [2]:

    

def prepare_dataset(n1, mu1, variance1, n2, mu2, variance2):
    df1 = DataFrame(multivariate_normal(mu1, np.eye(2)*variance1 ,n1),
                    columns=['x','y'])
    df1['type'] = 1
    df2 = DataFrame(multivariate_normal(mu2, np.eye(2)*variance2, n2),
                    columns=['x','y'])
    df2['type'] = -1
    df = pd.concat([df1,df2], ignore_index=True)
    df = df.reindex(np.random.permutation(df.index)).reset_index(drop=True)
    return df


    

In [3]:

    

train_set = prepare_dataset(20, [15,10], 15, 30, [0,0], 15)


    

In [4]:

    

train_set.head(10)


    

    
Out[4]:






  

    

      

      
x
      
y
      
type
    
  
  

    

      
0
      
3.153045
      
3.130352
      
-1
    
    

      
1
      
15.825834
      
13.587521
      
1
    
    

      
2
      
12.813575
      
8.599196
      
1
    
    

      
3
      
0.675097
      
-1.206019
      
-1
    
    

      
4
      
-4.510967
      
-1.451511
      
-1
    
    

      
5
      
-10.572530
      
1.093595
      
-1
    
    

      
6
      
11.546414
      
10.606383
      
1
    
    

      
7
      
-2.420563
      
-1.865068
      
-1
    
    

      
8
      
6.110758
      
-0.954161
      
-1
    
    

      
9
      
7.666255
      
-1.576934
      
-1
    
  

In [5]:

    

def prepare_dataset_debug(n1, mu1, variance1, n2, mu2, variance2):
    df1 = DataFrame(multivariate_normal(mu1, np.eye(2)*variance1 ,n1),
                    columns=['x','y'])
    df1['type'] = 1
    
    print '\ndf1:'
    print df1.head()
    
    df2 = DataFrame(multivariate_normal(mu2, np.eye(2)*variance2, n2),
                    columns=['x','y'])
    df2['type'] = -1
    
    print '\ndf2:'
    print df2.head()
        
    df = pd.concat([df1,df2], ignore_index=True)
    df = df.reindex(np.random.permutation(df.index)).reset_index(drop=True)
    return df


    

In [6]:

    

train_set = prepare_dataset_debug(20, [15,10], 15, 30, [0,0], 15)


    

    




df1:
           x          y  type
0  14.477726   7.959437     1
1  13.690463   4.315477     1
2  16.258191   4.732707     1
3  22.279339  13.984933     1
4  15.553373   7.499926     1

df2:
          x         y  type
0 -1.280968 -1.464140    -1
1 -3.820834  1.561394    -1
2  1.613477  2.267638    -1
3 -4.554196 -3.150507    -1
4  2.430743  2.017678    -1

In [7]:

    

def run_train(train_set):
    # パラメータの初期値とbias項の設定
    w0 = w1 = w2 = 0.0
    bias = 0.5 * (train_set.x.mean() + train_set.y.mean())

    # Iterationを実施
    paramhist = DataFrame([[w0,w1,w2]], columns=['w0','w1','w2'])
    for i in range(30):
        for index, point in train_set.iterrows():
            x, y, type = point.x, point.y, point.type
            if type * (w0*bias + w1*x + w2*y) <= 0:
                w0 += type * bias
                w1 += type * x
                w2 += type * y
        paramhist = paramhist.append(Series([w0,w1,w2], ['w0','w1','w2']),
                                     ignore_index=True)
    
    # 判定誤差の計算
    err = 0
    for index, point in train_set.iterrows():
        x, y, type = point.x, point.y, point.type
        if type * (w0*bias + w1*x + w2*y) <= 0:
            err += 1
    err_rate = err * 100 / len(train_set)
    
    return paramhist, err_rate


    

In [8]:

    

paramhist, err_rate = run_train(train_set)
paramhist.head(10)


    

    
Out[8]:






  

    

      

      
w0
      
w1
      
w2
    
  
  

    

      
0
      
0.0
      
0.000000
      
0.000000
    
    

      
1
      
-7.0
      
10.226106
      
4.370980
    
    

      
2
      
-8.0
      
19.382292
      
10.881953
    
    

      
3
      
-11.0
      
23.252686
      
10.119207
    
    

      
4
      
-14.0
      
24.589077
      
10.408212
    
    

      
5
      
-17.0
      
25.925469
      
10.697217
    
    

      
6
      
-20.0
      
13.367002
      
-1.991919
    
    

      
7
      
-21.0
      
11.783361
      
-1.673432
    
    

      
8
      
-22.0
      
11.594949
      
0.357970
    
    

      
9
      
-22.0
      
14.976053
      
1.642384
    
  

In [9]:

    

def show_result(subplot, train_set, w0, w1, w2, err_rate):
    train_set1 = train_set[train_set['type']==1]
    train_set2 = train_set[train_set['type']==-1]
    bias = 0.5 * (train_set.x.mean() + train_set.y.mean())
    ymin, ymax = train_set.y.min()-5, train_set.y.max()+10
    xmin, xmax = train_set.x.min()-5, train_set.x.max()+10

    subplot.set_ylim([ymin-1, ymax+1])
    subplot.set_xlim([xmin-1, xmax+1])
    subplot.scatter(train_set1.x, train_set1.y, marker='o', label=None)
    subplot.scatter(train_set2.x, train_set2.y, marker='x', label=None)

    linex = np.arange(xmin-5, xmax+5)
    liney = - linex * w1 / w2 - bias * w0 / w2
    label = "ERR %.2f%%" % err_rate
    subplot.plot(linex, liney, label=label, color='red')
    subplot.legend(loc=1)


    

In [10]:

    

paramhist.plot().legend(loc=1)


    

    
Out[10]:





<matplotlib.legend.Legend at 0x4abe5d0>






    

In [11]:

    

fig = plt.figure()
subplot = fig.add_subplot(1,1,1)
params = paramhist[-1:]
w0, w1, w2 = float(params.w0), float(params.w1), float(params.w2)
show_result(subplot, train_set, w0, w1, w2, err_rate)