Sigmoid

Sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve. A common example of a sigmoid function is the logistic function.

Definition

In general, a sigmoid function is real-valued and differentiable, having either a non-negative or non-positive first derivative which is bell shaped. There are also many other differential equations which have sigmoid solution.

Examples

There are many known sigmoid functions such as the Logistic function, Hyperbolic tangent, Arctangent, Error function, Generalised logistic function, Smoothstep, Gudermannian function, Algebraic sigmoid function, and Hill equation.

Uses

Sigmoid functions are often used in Artificial neural networks to introduce nonlinearity in the model. They are also used in Machine learning algorithms to map predictions to probabilities.

See also

• Logistic regression
• Logistic function
• Activation function
• Softmax function
• Rectifier (neural networks)