Calculating Errors

5.5. Calculating Errors#

Recall that our aim was to solve the following problem:

Given the RGB values for a colour, calculate the corresponding hue and saturation.

../../_images/problem.png

This is what our neural network predicted a hue of 107 and a saturation of 32 for the input (150, 25, 150).

../../_images/flow12.png

Is this correct? No it isn’t. You can see that what we wanted was a hue of 300 and a saturation of 71.

Let’s try another input.

../../_images/example2.png

Again, it’s not quite correct. The network predicted a hue of 124.3 and a saturation of 38.8, but what we wanted was a huge of 235 and a saturation of 57.

Let’s try one more!

../../_images/example3.png

Again, it’s still not correct. The network predicted a hue of 170 and a saturation of 50, but what we wanted was a huge of 23 and a saturation of 89.

Let’s calculate the error for each sample. Since we predict two values, we calculate the error for both values in each sample.

Sample

Predicted

Actual

Error (Predicted - Actual)

(150, 25, 150)

(107, 32)

(300, 71)

(-193, -39)

(50, 60, 180)

(124.3, 38.8)

(235, 57)

(-110.7, -18.2)

(250, 200, 170)

(170, 50)

(23, 89)

(147, -39)

Now we’ll calculate the mean squared error across all samples. This means we take all the error values, square them and then take the average.

\[\text{MSE} =\cfrac{1}{6}\left( (-193)^2 + (-39)^2 + (-110.7)^2 + (-18.2)^2 + (147)^2 + (-39)^2\right) = 12414.29 \text{ (2 d.p.)}\]