Understanding Multiple Inputs in Neural Networks (With Python Examples) — Part 3

#machinelearning #ai

In the previous article, we plotted the surface for predicting Setosa.

Let’s get this in action. We will plug in 0.5 and 0.37 for the Setosa output.

import numpy as np

def setosa_output(petal, sepal):
    # Top (blue) hidden node
    top = max(0, (petal * -2.5) + (sepal * 0.6) + 1.6) * -0.1

    # Bottom (orange) hidden node
    bottom = max(0, (petal * -1.5) + (sepal * 0.4) + 0.7) * 1.5

    # Final output (bias = 0)
    return top + bottom


# Example
y = setosa_output(0.5, 0.37)
print(y)

This gives 0.09.

The Y-axis value is closer to 0 than 1, which means this iris is probably not Setosa.

Now let’s determine the output for the second species, Versicolor.

It’s similar, but the weights after applying ReLU are different.

import numpy as np
import matplotlib.pyplot as plt


def hidden_nodes(petal, sepal):
    """
    Returns (top_node, bottom_node) AFTER ReLU, BEFORE output weights
    Works for scalars or grids
    """
    top = np.maximum(0, (petal * -2.5) + (sepal * 0.6) + 1.6)
    bottom = np.maximum(0, (petal * -1.5) + (sepal * 0.4) + 0.7)
    return top, bottom


def output_surface(petal, sepal, top_w, bottom_w, bias=0):
    top, bottom = hidden_nodes(petal, sepal)
    return (top * top_w) + (bottom * bottom_w) + bias


# Setosa
def setosa_output(petal, sepal):
    return output_surface(petal, sepal, top_w=-0.1, bottom_w=1.5)


# Versicolor
def versicolor_output(petal, sepal):
    return output_surface(petal, sepal, top_w=2.4, bottom_w=-5.2)



p_dots = np.linspace(0, 1, 6)
s_dots = np.linspace(0, 1, 6)
P_grid, S_grid = np.meshgrid(p_dots, s_dots)

Y_final = versicolor_output(P_grid, S_grid)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

ax.plot_surface(
    P_grid,
    S_grid,
    Y_final,
    alpha=0.7
)

ax.set_xlabel('Petal Width')
ax.set_ylabel('Sepal Width')
ax.set_zlabel('Versicolor Output')

plt.show()

Similarly, we can do the same for Virginica.

def virginica_output(petal, sepal):
    return output_surface(petal, sepal, top_w=-2.2, bottom_w=-3.7, bias=1)


Y_final = virginica_output(P_grid, S_grid)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

ax.plot_surface(
    P_grid,
    S_grid,
    Y_final,
    alpha=0.7
)

ax.set_xlabel('Petal Width')
ax.set_ylabel('Sepal Width')
ax.set_zlabel('Virginica Output')

plt.show()

The value for Virginica is high when the petal width is close to 1.

Now let’s apply the petal and sepal widths and see which type of iris this is.

petal_width = 0.5
sepal_width = 0.37

setosa = setosa_output(petal_width, sepal_width)
versicolor = versicolor_output(petal_width, sepal_width)
virginica = virginica_output(petal_width, sepal_width)

print(setosa, versicolor, virginica)

We get the following output:

0.08979999999999996 0.8632000000000001 0.10419999999999974

Versicolor has the highest value (0.86), which means this iris is Versicolor.

And just like that, we made our neural network handy enough to do some prediction work.

Usually, when there are two or more output nodes, we send these values to Argmax or Softmax before making a final decision. We’ll explore that in the next article.

You can try the examples out in the Colab notebook.

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