Axis parameter in the keras normalization function- keras.utils.normalization()

Question

I spent a lot of time trying to understand how the axis argument works in the keras.utils.normalization() function. Can someone please explain it to me by using the concept of np.array by making a random (2,2) np array and explain how the normalization actually works for different axes.

Answer 1

Let's consider a 2*2 Numpy Array,

x = np.array([[1,2],
              [3,4]])

Axis = 0 indicates that the Operation is done Row-wise. Code with Axis = 0:

x_norm_rows_axis = tf.keras.utils.normalize(x, axis= 0)
print(x_norm_rows_axis)

Output of the above code is:

[[0.31622777 0.4472136 ]
 [0.9486833  0.89442719]]

The output of Axis = 0 can be elaborated as shown below:

print('x_norm_rows_axis[0][0] = {}'.format(1/np.sqrt(1 ** 2 + 3 ** 2)))
print('x_norm_rows_axis[0][1] = {}'.format(2/np.sqrt(2 ** 2 + 4 ** 2)))
print('x_norm_rows_axis[1][0] = {}'.format(3/np.sqrt(1 ** 2 + 3 ** 2)))
print('x_norm_rows_axis[1][1] = {}'.format(4/np.sqrt(2 ** 2 + 4 ** 2)))

Output of the above Print Statements is shown below:

x_norm_rows_axis[0][0] = 0.31622776601683794
x_norm_rows_axis[0][1] = 0.4472135954999579
x_norm_rows_axis[1][0] = 0.9486832980505138
x_norm_rows_axis[1][1] = 0.8944271909999159

Axis = 1 indicates that the Operation is done Column-wise. Code with axis = 1. In this case, since we have only 2 Dimensions, we can consider this as axis = -1 as well:

x_norm_col_axis = tf.keras.utils.normalize(x, axis= 1)
print(x_norm_col_axis)

Output of the above code is:

[[0.4472136  0.89442719]
 [0.6        0.8       ]]

The output of axis = 1 or axis = -1 (in this case) can be elaborated as shown below:

print('x_norm_col_axis[0][0] = {}'.format(1/np.sqrt(1 ** 2 + 2 ** 2)))
print('x_norm_col_axis[0][1] = {}'.format(2/np.sqrt(2 ** 2 + 1 ** 2)))
print('x_norm_col_axis[1][0] = {}'.format(3/np.sqrt(4 ** 2 + 3 ** 2)))
print('x_norm_col_axis[1][1] = {}'.format(4/np.sqrt(3 ** 2 + 4 ** 2)))

Output of the above Print Statements is shown below:

x_norm_col_axis[0][0] = 0.4472135954999579
x_norm_col_axis[0][1] = 0.8944271909999159
x_norm_col_axis[1][0] = 0.6
x_norm_col_axis[1][1] = 0.8

To understand how the Order argument works, refer this Stack Overflow Answer.

Hope this helps. Happy Learning!