Sigmoid function

A sigmoid function is a mathematical function that produces a sigmoid curve — a curve having an "S" shape. Often, sigmoid function refers to the special case of the logistic function shown at right and defined by the formula:

Related Topics:
Mathematical - Function - Logistic function

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: P(t) = rac{1}{1 + e^{-t}}

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In general, a sigmoid function is real-valued and differentiable, having a non-negative or non-positive first derivative, one local minimum, and one local maximum.

Related Topics:
Real - Differentiable - Negative - Positive - Derivative - Local minimum - Local maximum

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Besides the logistic function, sigmoid functions include the ordinary arc-tangent, the hyperbolic tangent, and the error function. The integral of any smooth, positive, "bump-shaped" function will be sigmoidal, thus the cumulative distribution functions for many common probability distributions are sigmoidal.

Related Topics:
Arc-tangent - Hyperbolic tangent - Error function - Integral - Cumulative distribution function - Probability distribution

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