If you want to experiment with one neuron

xxxxxxxxxx

 

1

import numpy as np,pylab as pl

2

# functions for neuron construction

3

def sigmoid(x): return 1.0/(1+np.exp(-x))

4

def sigmoid_derivation(x): return x*(1.0-x)

5

# artificial data for the experiment

6

X=np.array([[.11,.05,.95],[.09,.03,.08],[.01,.09,.91],

7

            [.04,.92,.07],[.05,.02,.04],[.07,.97,.05],

8

            [.06,.02,.98],[.02,.06,.03],[.01,.09,.03],

9

            [.02,.94,.01],[.06,.03,.95],[.04,.91,.09]])

10

Y=np.array([[1,0,1,2,0,2,1,0,1,2,1,2]]).T

11

fig,ax=pl.subplots(nrows=2,ncols=1,figsize=(6.5,4))

12

ax[0].imshow(X.T,cmap=pl.cm.cool)

13

ax[0].set_xticks([])

14

ax[0].text(-.3,1,str(Y.T)[2:-2],color='white',fontsize=32)

15

ax[0].set_title('Real Labels with One Error')

16

# the start point for iterations

17

synapse0=np.random.randn(3,1); layer0=X

18

# the steps of iterations

19

for iter in range(100):

20

    layer1=sigmoid(np.dot(layer0,synapse0))

21

    # finding errors and directions for correction

22

    layer1_error=layer1-Y

23

    layer1_delta=layer1_error*sigmoid_derivation(layer1)

24

    # correction values & coefficients

25

    synapse0_derivative=np.dot(layer0.T,layer1_delta)

26

    synapse0-=synapse0_derivative

27

# comparing predictions and real data

28

# the error in the start labeling (the 9th image) had been corrected

29

def labeling(x):

30

    if (x<.7): return 0

31

    if (x>.7) and (x<.99): return 1

32

    else: return 2

33

predict_Y=np.array([[labeling(layer1[i,0]) for i in range(12)]]).T

34

ax[1].imshow(X.T,cmap=pl.cm.cool)

35

ax[1].set_xticks([])

36

ax[1].text(-.3,1,str(predict_Y.T)[2:-2],color='white',fontsize=32)

37

ax[1].set_title('Predicted Labels'); pl.show()

38

print(np.hstack((np.hstack((X,Y)),(layer1.round(3)),(predict_Y))))

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

---

Messages