Equations · Machine learning
Sigmoid (logistic) function
An S-shaped curve that squeezes any number into the range between 0 and 1.
σ(x) = 1 / (1 + e^(−x))
Aethel says
sigma of x equals 1 over the quantity 1 plus e to the power of negative x
What it says
Large positive inputs give values close to 1, large negative inputs give values close to 0, and an input of 0 gives exactly one half.
Its output can be read as a probability, which is why it ends binary classifiers and logistic regression.
Symbol by symbol
| Symbol | Say it | Means |
|---|---|---|
| σ(x) | sigma of x | the sigmoid function of x |
| e^(−x) | e to the power of negative x | the exponential of minus x |
More onσSigma
Where you meet it
Logistic regression, neural networks and population models.
Questions
How do you say Sigmoid (logistic) function out loud?
σ(x) = 1 / (1 + e^(−x)) is read: “sigma of x equals 1 over the quantity 1 plus e to the power of negative x.” That is exactly what Aethel says when it meets the formula in a book.
What does σ(x) mean in Sigmoid (logistic) function?
σ(x) (said “sigma of x”) is the sigmoid function of x.
What does e^(−x) mean in Sigmoid (logistic) function?
e^(−x) (said “e to the power of negative x”) is the exponential of minus x.
Can I listen to the equations in my own textbook like this?
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