one_hump_ann.py

# affine transformation of an input x
# using weight w and biais b
def affine(x, w, b):
    return w * x + b
    
# sigmoidal activation 
# on output from affine transformation 
def sigmoid(z):
    return 1.0 / (1.0 + np.exp(-z))
    
# neuron that takes input x
# applies affine transformation
# and activation
def perceptron(x, w, b):
    z = affine(x, w, b) # Affine transformation
    h = sigmoid(z) # Sigmoid activation
    return h

# first neuron
one_hump_h1 = perceptron(one_hump_df.x, w=14, b=-28.0)

# second neuron
one_hump_h2 = perceptron(one_hump_df.x, w=-8.9, b=54.3) 

# third neuron
wout = [1, 1] 
bout = -1
one_hump_yout = wout[0] * one_hump_h1 + wout[1] * one_hump_h2 + bout

# plot data vs ANN prediction

def plot_data(x, y, ax, label, title):
    SIZE = 10
    ax.scatter(x, y, lw=0.5, label=label)
    ax.set_xlabel('$x$', fontsize=SIZE) 
    ax.set_ylabel('$y$', fontsize=SIZE)
    ax.tick_params(labelsize=SIZE) 
    ax.legend(fontsize=SIZE, loc='best')
    ax.set_title(title)
    
fig, ax = plt.subplots(1,1, figsize=(11,5))
plot_data(one_hump_df.x, one_hump_df.y, ax=ax, title='', label='Original Data')
plot_data(one_hump_df.x, one_hump_yout, ax=ax, title='', label='ANN prediction')