###Artificial Neural Network (Backpropagation)
This is a Python Multilayer Backpropagation ANN sample. The network has 3 neurons. The 2 inputs are N1, N2 and the output is N3. It calculates neurons' weights by the signum function. It stops learning by the number of iterations or error ratio value. It generates both text and graphical results (with decision boundaries) when the learning is finished.
####The Signum Function:
def sigma(x):
return 1 / (1 + math.exp(-x))
####Sample Input (XOR):
dataset = [[0, 0, 0], [0, 1, 1], [1, 0, 1], [1, 1, 0]]
####Sample Output (XOR):
initial weights
['0.30', '0.27', '0.75']
['0.92', '0.61', '0.54']
['0.98', '0.13', '0.01']
last weights
['5.18', '5.13', '2.25']
['4.92', '4.81', '7.48']
['7.47', '-7.72', '3.58']
outputs
['0.05', '0.96', '0.95', '0.04']
iteration: 3420, totalError: 0.19 / 4 = 0.05
decision boundaries (ax+by+c=0)
5.18x + 5.13y + 2.25 = 0
4.92x + 4.81y + 7.48 = 0
7.47x + -7.72y + 3.58 = 0
####Sample Input:
dataset = [[0.30, 3.5, 0], [0.35, 3.3, 0], [0.40, 3.6, 0], [1.20, 2.35, 0], [1.40, 2.15, 0], [1.40, 2.25, 0],
[1.55, 2.7, 0], [2.15, 1.45, 0], [3.00, 0.65, 0], [3.40, 0.8, 0], [4.20, 1, 0], [4.25, 1.2, 0],
[4.40, 1.45, 0], [4.60, 1.6, 0], [5.30, 1.9, 0], [5.55, 2.15, 0], [5.65, 2.2, 0], [5.85, 2.6, 0],
[5.90, 2.75, 0], [5.95, 2.1, 0], [2.80, 1.5, 1], [2.85, 2.45, 1], [2.90, 2, 1], [3.00, 1.75, 1],
[3.00, 2.25, 1], [3.10, 2.05, 1], [3.30, 1.55, 1], [3.35, 1.7, 1], [3.35, 1.85, 1], [3.45, 1.7, 1]]
####Sample Output:
initial weights
['0.77', '0.12', '0.73']
['0.92', '0.25', '0.55']
['0.10', '0.43', '0.58']
last weights
['3.53', '-5.07', '5.42']
['3.35', '-0.45', '7.17']
['-7.90', '8.03', '3.91']
outputs
['0.02', '0.02', '0.02', '0.02', '0.02', '0.02', '0.03', '0.24', '0.04', '0.03', '0.02', '0.03', '0.04', '0.04', '0.03', '0.03', '0.03', '0.06', '0.09', '0.02', '0.91', '0.91', '0.94', '0.96', '0.96', '0.97', '0.93', '0.95', '0.97', '0.95']
iteration: 349, totalError: 1.49 / 30 = 0.05
decision boundaries (ax+by+c=0)
3.53x + -5.07y + 5.42 = 0
3.35x + -0.45y + 7.17 = 0
-7.90x + 8.03y + 3.91 = 0
Absolutely, it is totally open source and under MIT License