notebook.community

Edit and run 





In [1]:



    


%matplotlib inline

import numpy as np
import matplotlib.pyplot as plt
import scipy
import scipy.spatial



    











In [2]:



    


sigmoid = lambda x:1 / ( 1 + np.exp(-x) )



    











In [3]:



    


x = np.linspace( -10, 10)
y = np.array( [ sigmoid(v) for v in x ] )



    











In [4]:



    


plt.plot( x, y )
plt.savefig('../images/logistic_function.png')



    


















    
























In [10]:



    


# Hinton's Fish and Chips

wfish = 150
wchips = 50
wketchup = 100
target_weights = [ wfish, wchips, wketchup ]

weights = [ 50, 50, 50 ]
eta = 1/35.0



    











In [15]:



    


# One step example

inputs = [ 2, 5, 3 ]
target = sum( [ target_weights[k] * inputs[k] for k in range(3) ] )

output = sum( [ weights[k]*inputs[k] for k in range( 3 ) ] )

print( weights )
weights = [ weights[k] + eta*inputs[k] * ( target-output ) for k in range ( 3 ) ]
print( weights )



    


















    






[68.28571428571429, 95.71428571428571, 77.42857142857143]
[68.4326530612245, 96.08163265306123, 77.64897959183675]

















In [14]:



    






    


















    
Out[14]:








847.4285714285713

















In [22]:



    


# Multi-step example: runs over the the same input sets N times
weights = [ 50, 50, 50 ]

#input_sets = [ [ 2, 5, 3 ], [ 1, 1, 1], [3, 2, 1], [2, 4, 4], [5, 2, 3] ]
input_sets = [ [ 0, 5, 3 ] ]

for step in range( 200 ):
    print( "step " + str( step ) )
    print( weights )

    for inputs in input_sets:

        target = sum( [ target_weights[k] * inputs[k] for k in range(3) ] )

        output = sum( [ weights[k]*inputs[k] for k in range( 3 ) ] )

        weights = [ weights[k] + eta*inputs[k] * ( target-output ) for k in range ( 3 ) ]
    print( weights )



    


















    






step 0
[50, 50, 50]
[50.0, 71.42857142857143, 62.85714285714286]
step 1
[50.0, 71.42857142857143, 62.85714285714286]
[50.0, 72.0408163265306, 63.224489795918366]
step 2
[50.0, 72.0408163265306, 63.224489795918366]
[50.0, 72.05830903790088, 63.23498542274053]
step 3
[50.0, 72.05830903790088, 63.23498542274053]
[50.0, 72.05880882965431, 63.235285297792586]
step 4
[50.0, 72.05880882965431, 63.235285297792586]
[50.0, 72.0588231094187, 63.235293865651215]
step 5
[50.0, 72.0588231094187, 63.235293865651215]
[50.0, 72.05882351741197, 63.23529411044717]
step 6
[50.0, 72.05882351741197, 63.23529411044717]
[50.0, 72.05882352906893, 63.23529411744135]
step 7
[50.0, 72.05882352906893, 63.23529411744135]
[50.0, 72.05882352940196, 63.235294117641175]
step 8
[50.0, 72.05882352940196, 63.235294117641175]
[50.0, 72.05882352941148, 63.23529411764689]
step 9
[50.0, 72.05882352941148, 63.23529411764689]
[50.0, 72.05882352941175, 63.23529411764705]
step 10
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 11
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 12
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 13
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 14
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 15
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 16
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 17
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 18
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 19
[50.0, 72.05882352941175, 63.23529411764705]
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step 20
[50.0, 72.05882352941175, 63.23529411764705]
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step 21
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step 22
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step 23
[50.0, 72.05882352941175, 63.23529411764705]
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step 24
[50.0, 72.05882352941175, 63.23529411764705]
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step 25
[50.0, 72.05882352941175, 63.23529411764705]
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step 26
[50.0, 72.05882352941175, 63.23529411764705]
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step 27
[50.0, 72.05882352941175, 63.23529411764705]
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step 28
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step 29
[50.0, 72.05882352941175, 63.23529411764705]
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step 30
[50.0, 72.05882352941175, 63.23529411764705]
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step 31
[50.0, 72.05882352941175, 63.23529411764705]
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step 32
[50.0, 72.05882352941175, 63.23529411764705]
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step 33
[50.0, 72.05882352941175, 63.23529411764705]
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step 34
[50.0, 72.05882352941175, 63.23529411764705]
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step 35
[50.0, 72.05882352941175, 63.23529411764705]
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step 36
[50.0, 72.05882352941175, 63.23529411764705]
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step 37
[50.0, 72.05882352941175, 63.23529411764705]
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step 38
[50.0, 72.05882352941175, 63.23529411764705]
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step 39
[50.0, 72.05882352941175, 63.23529411764705]
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step 40
[50.0, 72.05882352941175, 63.23529411764705]
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step 41
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step 42
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step 43
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step 44
[50.0, 72.05882352941175, 63.23529411764705]
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step 46
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step 47
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 48
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 49
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 50
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 51
[50.0, 72.05882352941175, 63.23529411764705]
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step 52
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 53
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 54
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 55
[50.0, 72.05882352941175, 63.23529411764705]
[50.0, 72.05882352941175, 63.23529411764705]
step 56
[50.0, 72.05882352941175, 63.23529411764705]
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step 57
[50.0, 72.05882352941175, 63.23529411764705]
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step 58
[50.0, 72.05882352941175, 63.23529411764705]
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step 59
[50.0, 72.05882352941175, 63.23529411764705]
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step 60
[50.0, 72.05882352941175, 63.23529411764705]
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step 61
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step 62
[50.0, 72.05882352941175, 63.23529411764705]
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step 63
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step 64
[50.0, 72.05882352941175, 63.23529411764705]
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step 65
[50.0, 72.05882352941175, 63.23529411764705]
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step 66
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step 67
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step 68
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step 69
[50.0, 72.05882352941175, 63.23529411764705]
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step 70
[50.0, 72.05882352941175, 63.23529411764705]
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step 71
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step 72
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step 73
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step 74
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step 75
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step 76
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step 77
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step 78
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step 79
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step 80
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step 81
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step 84
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step 99
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step 100
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step 101
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step 102
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step 103
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step 104
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step 105
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step 109
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step 115
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step 128
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In [21]:



    


output



    


















    
Out[21]:








850.0

















In [ ]:

Content source: JoshuaW1990/TuftsCOMP135_Spring2016

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