Formalizing a Parameter Selection Problem in Machine Learning

Question

I have a simple problem,

I have an array (say of length 300), which gives me the fraction of importance of some value.

I plot it and see that the value becomes flat after some index.

So, I select the index after which the importance fraction just becomes flatter by just plotting the value.

So, my question is how should I formalize the problem of selecting this index.

The curve is like: Example Curve

How should I select the index? What mathematical condition is guaranteed to allow me to find that index after which the values become flat?

Answer 1

Why not slope of the curve? $dy/dx$? Consider value at the consecutive indices then $dx=1$. From figure

            @ index 1, value= 3.5
            @ index 2, value= 1.8
                     etc
            @ index 7, value= 0.5
            @ index 8, value= 0.3

search through the array and find out when the slope is less than the required...so that the curve is flat ...close to $dy/dx=0$

for i=1:300
       check=value(i)-value(i+1); %dy, dx=1
          if check<=0.2
             display('index value')
             i
             break
          end
end%end for loop

Isnt this you are asking for?