The Logistic Fuction

an inflection point perspective

Interactive Sigmoid Function Plots

The sigmoid function of the form

\[f(x) = \frac{1}{1 + be^{-ax}}\]

is plotted below with varying parameters a and b.

Notice how b shifts the point of inflection p along the x-axis and a changes the width of the sigmoid function.

Here is the plot of the function with varying a parameter:

Here is the plot of the function with varying b parameter:

Both of these together produce the effect of translating the point of inflection and controlling the width of the sigmoid function which produce a better classification. However the logistic function is of a sligtly different form and is given by:

\[f(x) = \frac{1}{1 + e^{-wx+c}}\]

where we control b in the fuction above through C and a through W. Notice how they are the same

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