Refine the Parameters of the Training Classifier

Refine the parameters

How should we use the classification error $E$ to guide us to a more refined parameter $A$? That’s the important question. Let’s take a step back from this task and think again. We want to use the error in $y$, which we call $E$, to inform the required change in parameter $A$. To do this, we need to know how the two are related. If we know their relationship, we can understand how changing one affects the other. Let’s start with the linear function for the classifier:

$$y = Ax$$

We know from our initial guesses of the value of $A$, that this gives the wrong answer for $y$, which should be the value given by the training data. Let’s call the correct desired value $t$ for the target value. To get that value $t$, we need to adjust $A$ by a small amount. Mathematicians use delta $Δ$, meaning “a small change in.”

$$t = (A + ΔA)x$$

Let’s graph this to make it easier to understand. You can see the new slope $(A + ΔA)$.