1
Neural networks [1.2] : Feedforward neural network - activation function
DATE: 2013/11/15::
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Sigmoid function
DATE: 2014/08/16::
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The Sigmoid Curve
DATE: 2012/11/11::
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Organizational Learning Tool: The Sigmoid Curve
DATE: 2013/10/15::
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Normalised Tunable Sigmoid Function Demo in Unity3D
DATE: 2013/06/26::
6
Intro to Neural Networks
DATE: 2013/06/10::
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Julia Programming : The Sigmoid Function Programming Exercise
DATE: 2014/03/02::
8
Mathematical Biology. 19: Sigmoidal Functions, Multisite Systems
DATE: 2014/02/25::
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Derivative of the sigmoid activation function, 9/2/2015
DATE: 2015/02/10::
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Normalised Tunable Sigmoid Function 2.0
DATE: 2013/11/24::
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The Gompertz Sigmoid Function and Its Derivative
DATE: 2009/07/16::
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Sigmoid function displacement time servo control
DATE: 2009/05/30::
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The Gompertz Sigmoid Function and Its Derivative
DATE: 2010/04/13::
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Contrast Enhancement of Color Images using Tunable Sigmoid Function.wmv
DATE: 2011/03/16::
15
Impact of Bias on the Sigmoid Activation function
DATE: 2014/10/19::
16
EC50 and IC50 Determination in Excel
DATE: 2013/07/10::
17
Retro Sigmoid Vestibular Nerve Section for Meniere's Disease
DATE: 2009/07/02::
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DATE: 2013/05/08::
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Curve Fitting in Excel
DATE: 2013/06/26::
20
Polypectomy of Colon Sigmoid Polyp
DATE: 2012/10/04::
21
Neural network tutorial: The back-propagation algorithm (Part 1)
DATE: 2012/01/07::
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Mod-08 Lec-26 Multilayer Feedforward Neural networks with Sigmoidal activation functions;
DATE: 2013/12/02::
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Plot 5 of 6 - Continuous A* - Obstacle Created Using the Product of Sigmoid Functions
DATE: 2008/11/12::
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Spiral Weaving Time
DATE: 2013/08/24::
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Introduction to Neural Networks for C#(Class 4/16, Part 2/5) - activation function
DATE: 2009/02/07::
26
Neural Network Part 2
DATE: 2010/10/14::
27
Developing neural network in MATLAB method2 nntool] [fitting tool]
DATE: 2013/07/23::
28
Logistic regression
DATE: 2011/11/12::
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Plot 6 of 6 - Continuous A* - Simple Maze
DATE: 2008/11/12::
30
Colon Resection
DATE: 2010/12/13::
31
Sigmoidal Meaning
DATE: 2015/05/11::
32
Logistic function
DATE: 2014/08/13::
33
Ignite Columbus 2 - Joshua Scott - Jump!
DATE: 2009/03/05::
34
Developing neural network in MATLAB method1 command window] [fitting tool]
DATE: 2013/07/23::
35
A Neural Network Learning his name
DATE: 2014/04/29::
36
CSCI4477-R11-classify-housing-SVM
DATE: 2013/02/22::
37
Neural Network Tutorial - Ch. 7.1 More transfer functions (Part 1)
DATE: 2012/01/30::
38
Forex ANN Neural Network Close Price Prediction
DATE: 2014/04/26::
39
5.1 Loss Functions | 5 Support Vector Machines | Pattern Recognition Class 2012
DATE: 2012/11/22::
40
Equivalence of two activation functions in hidden layer: example
DATE: 2014/01/04::
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5.3 Nonlinear SVM | 5 Support Vector Machines | Pattern Recognition Class 2012
DATE: 2012/11/22::
42
Curve Fitting with Microsoft Excel
DATE: 2013/05/07::
43
"Deep Transform: Cocktail Party Source Separation via Complex Convolution in a Deep Neural Network"
DATE: 2015/05/08::
44
Neural Networks Classification with Sharky Neural Network (SNN) - shape "c|n"
DATE: 2009/08/22::
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1.6 Sigmoid Emax model - Hill factor
DATE: 2012/03/12::
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Two Spirals Problem - classification with Sharky Neural Network (SNN)
DATE: 2009/08/23::
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decision feedback equalizer
DATE: 2012/02/09::
48
Mega-R4. Neural Nets
DATE: 2014/01/10::
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5.3.2 Draw and label a graph showing a sigmoid (S-shaped) population growth curve
DATE: 2013/04/05::
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DATE: 2015/03/20::
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RESULTS [51 .. 101]
Plot of the error function

A sigmoid function is a mathematical function having an "S" shape (sigmoid curve). Often, sigmoid function refers to the special case of the logistic function shown in the first figure and defined by the formula

$S(t) = \frac{1}{1 + e^{-t}}.$

Other examples of similar shapes include the Gompertz curve (used in modeling systems that saturate at large values of t) and the ogee curve (used in the spillway of some dams). 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, such as the integrals of the logistic distribution, the normal distribution, and Student's t probability density functions.

## Definition

A sigmoid function is a bounded differentiable real function that is defined for all real input values and has a positive derivative at each point.[1]

## Properties

In general, a sigmoid function is real-valued and differentiable, having either a non-negative or non-positive first derivative[citation needed] which is bell shaped. There are also a pair of horizontal asymptotes as $t \rightarrow \pm \infty$. The differential equation $\tfrac{d}{dt} S(t) = c_1 S(t) \left( c_2 - S(t) \right)$, with the inclusion of a boundary condition providing a third degree of freedom, $c_3$, provides a class of functions of this type.

## Examples

Some sigmoid functions compared. In the drawing all functions are normalized in such a way that their slope at the origin is 1.

Many natural processes, such as those of complex system learning curves, exhibit a progression from small beginnings that accelerates and approaches a climax over time. When a detailed description is lacking, a sigmoid function is often used[2] .

Besides the logistic function, sigmoid functions include the ordinary arctangent, the hyperbolic tangent, the Gudermannian function, and the error function, but also the generalised logistic function and algebraic functions like $f(x)=\tfrac{x}{\sqrt{1+x^2}}$.

The integral of any smooth, positive, "bump-shaped" function will be sigmoidal, thus the cumulative distribution functions for many common probability distributions are sigmoidal. The most famous such example is the error function, which is related to the cumulative distribution function (CDF) of a normal distribution.