5.3 Hopfield Network

5.3.1 Recovery of Digits

In[]:=
session=StartExternalSession["Python"]
Out[]=
ExternalSessionObject
System: Python
EvaluationCount:
None
UUID: 276d967c-6d34-48b8-9e41-fceceb77940d

Test
〉
In[]:=
5+6
Out[]=
11
〉
In[]:=
import numpy as np
from neupy import algorithms
〉
In[]:=
zero=np.matrix([ 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0 ])
〉
In[]:=
zero
Out[]=
NumericArray
Type: Integer32
Dimensions: {1,30}

In[]:=
Normal[%]
Out[]=
{{0,1,1,1,0,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,0,1,1,1,0}}
In[]:=
zero=%;
In[]:=
Partition[zero//Flatten,5]//MatrixForm
Out[]//MatrixForm=
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
In[]:=
MatrixPlot[%,MeshTrue]
Out[]=
〉
In[]:=
one = np.matrix([ 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0 ])
〉
In[]:=
one
Out[]=
NumericArray
Type: Integer32
Dimensions: {1,30}

In[]:=
Normal[%]
Out[]=
{{0,0,1,0,0,0,1,1,0,0,1,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0}}
In[]:=
one=%;
In[]:=
Partition[one//Flatten,5]//MatrixForm
Out[]//MatrixForm=
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
In[]:=
MatrixPlot[%,MeshTrue]
Out[]=
〉
In[]:=
two = np.matrix([ 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, ])
〉
In[]:=
two
Out[]=
NumericArray
Type: Integer32
Dimensions: {1,30}

In[]:=
Normal[%]
Out[]=
{{0,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0,1,1,0,0,1,0,0,0,0,1,1,1,1,1}}
In[]:=
two=%;
In[]:=
Partition[two//Flatten,5]//MatrixForm
Out[]//MatrixForm=
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
In[]:=
MatrixPlot[%,MeshTrue]
〉
In[]:=
data = np.concatenate([zero, one,two], axis=0)
〉
In[]:=
dhnet = algorithms.DiscreteHopfieldNetwork(mode='sync')
dhnet.train(data)
〉
In[]:=
half_zero
〉
In[]:=
result = dhnet.predict(half_zero)
result
〉
In[]:=
half_two
〉
In[]:=
result = dhnet.predict(half_two)
result
〉
In[]:=
half_what
〉
In[]:=
result = dhnet.predict(half_what)
result
〉
In[]:=
from neupy import environment
environment.reproducible()
〉
In[]:=
dhnet.mode='async'
dhnet.n_times=1000
〉
In[]:=
result = dhnet.predict(half_what)
result

5.3.2 Reconstruction of Deteriorated Images

〉
In[]:=
​
from numpy import array, matrix
from scipy.io import mmread, mmwrite
〉
In[]:=
caki1=mmread('cuki1.mtx')
​
caki11=mmread('cuki11.mtx')
​
〉
In[]:=
data = caki1
〉
In[]:=
dhnet = algorithms.DiscreteHopfieldNetwork(mode='sync')
dhnet.train(data)
Reconstructed the deteriorated images, see Figs. 5.3.15 - 5.3.17
〉
In[]:=
t=dhnet.predict(caki11)
mmwrite('cico.mtx',t)
In[]:=
hopD = HopfieldFit[{H1b}]