Refine the Parameters of the Training Classifier

Learn how to refine our slope parameter based on the error value.

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Refine the parameters

How should we use the classification error EE to guide us to a more refined parameter AA? That’s the important question. Let’s take a step back from this task and think again. We want to use the error in yy, which we call EE, to inform the required change in parameter AA. 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=Axy = Ax

We know from our initial guesses of the value of AA, that this gives the wrong answer for yy, which should be the value given by the training data. Let’s call the correct desired value tt for the target value. To get that value tt, we need to adjust AA by a small amount. Mathematicians use delta ΔΔ, meaning “a small change in.”

t=(A+ΔA)xt = (A + ΔA)x

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

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