# Sigmoid Function

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A Sigmoid Function is a numeric function that is a special case of logistic function.

**AKA:**Sigmoid, Sigmoid Curve.**Context:**- It can be mathematically defined as [math]\displaystyle{ S(x) = \frac{1}{1 + e^{-x}} }[/math].
- It is characterized by S-shaped curved, i.e. a sigmoid curve.

**Example(s)****Counter-Example(s):****See:**Perceptron Algorithm.

## References

### 2018

- (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Sigmoid_function Retrieved:2018-1-14.
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**sigmoid function**is a mathematical function having a characteristic "S"-shaped curve or**sigmoid curve**. Often,*sigmoid function*refers to the special case of the logistic function shown in the first figure and defined by the formula : [math]\displaystyle{ S(x) = \frac{1}{1 + e^{-x}} = \frac{e^x}{e^x + 1}. }[/math] Other examples of similar shapes include the Gompertz curve (used in modeling systems that saturate at large values of x) and the ogee curve (used in the spillway of some dams). Sigmoid functions have domain of all real numbers, with return value monotonically increasing most often from 0 to 1 or alternatively from −1 to 1, depending on convention.A wide variety of sigmoid functions have been used as the activation function of artificial neurons, including the logistic and hyperbolic tangent functions. Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic distribution, the normal distribution, and Student's

*t*probability density functions.

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