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Sigmoid
Sigmoid
Published: 2015/02/23
Channel: Udacity
Why We Use Sigmoid Function in Neural Networks
Why We Use Sigmoid Function in Neural Networks
Published: 2017/03/09
Channel: Mohammad Ramadan
Which Activation Function Should I Use?
Which Activation Function Should I Use?
Published: 2017/05/27
Channel: Siraj Raval
The Sigmoid Curve
The Sigmoid Curve
Published: 2012/11/11
Channel: Pete Dalgleish
Neural networks [1.2] : Feedforward neural network - activation function
Neural networks [1.2] : Feedforward neural network - activation function
Published: 2013/11/16
Channel: Hugo Larochelle
Simple Logistic Regression
Simple Logistic Regression
Published: 2012/11/20
Channel: Steve Grambow
Activation Functions in Neural Networks (Sigmoid, ReLU, tanh, softmax)
Activation Functions in Neural Networks (Sigmoid, ReLU, tanh, softmax)
Published: 2017/02/23
Channel: The SemiColon
Neural Networks (1): Basics
Neural Networks (1): Basics
Published: 2015/01/26
Channel: Alexander Ihler
Sigmoid function
Sigmoid function
Published: 2014/08/16
Channel: Audiopedia
Julia Programming : The Sigmoid Function Programming Exercise
Julia Programming : The Sigmoid Function Programming Exercise
Published: 2014/03/03
Channel: Dragonfly Statistics
Logistic function application | First order differential equations | Khan Academy
Logistic function application | First order differential equations | Khan Academy
Published: 2014/07/25
Channel: Khan Academy
Logistic regression example sigmoid function in python
Logistic regression example sigmoid function in python
Published: 2017/06/06
Channel: The New Edge
Neural network tutorial: The back-propagation algorithm (Part 1)
Neural network tutorial: The back-propagation algorithm (Part 1)
Published: 2012/01/07
Channel: Ryan Harris
Neural Network Calculation (Part 2): Activation Functions & Basic Calculation
Neural Network Calculation (Part 2): Activation Functions & Basic Calculation
Published: 2010/10/15
Channel: Jeff Heaton
5.3.2 Draw and label a graph showing a sigmoid (S-shaped) population growth curve
5.3.2 Draw and label a graph showing a sigmoid (S-shaped) population growth curve
Published: 2013/04/05
Channel: Stephanie Castle
Derivative of the sigmoid activation function, 9/2/2015
Derivative of the sigmoid activation function, 9/2/2015
Published: 2015/02/10
Channel: Lutfi Al-Sharif The University of Jordan
Sigmoid Function
Sigmoid Function
Published: 2016/07/18
Channel: Various Artists - Topic
Organizational Learning Tool: The Sigmoid Curve
Organizational Learning Tool: The Sigmoid Curve
Published: 2013/10/15
Channel: Sigmoid Curve Consulting Group - Experts in Change Leadership
Derivatives of Exponential Functions
Derivatives of Exponential Functions
Published: 2008/11/29
Channel: patrickJMT
Deep Learning with Tensorflow - Activation Functions
Deep Learning with Tensorflow - Activation Functions
Published: 2017/01/04
Channel: Cognitive Class
Mathematical device used in Deep Learning V - Sigmoid function
Mathematical device used in Deep Learning V - Sigmoid function
Published: 2015/10/23
Channel: Vasu Srinivasan
Horrible Explanation About Neural Network - Basic 1 - Sigmoid Function
Horrible Explanation About Neural Network - Basic 1 - Sigmoid Function
Published: 2017/01/25
Channel: Jae duk Seo
Impact of Bias on the Sigmoid Activation function
Impact of Bias on the Sigmoid Activation function
Published: 2014/10/19
Channel: N RS
Mathematical Biology. 19: Sigmoidal Functions, Multisite Systems
Mathematical Biology. 19: Sigmoidal Functions, Multisite Systems
Published: 2014/02/25
Channel: UCI Open
Activation Fuctions - Sigmoid,Softmax,ReLU,identity,tanh
Activation Fuctions - Sigmoid,Softmax,ReLU,identity,tanh
Published: 2017/06/24
Channel: Quick KT
Using the Flexible Spline function (FlexSpline) in Excel
Using the Flexible Spline function (FlexSpline) in Excel
Published: 2013/11/14
Channel: SRS1Software
Activation Functions (C1W3L06)
Activation Functions (C1W3L06)
Published: 2017/08/25
Channel: Deeplearning.ai
Neural networks [2.5] : Training neural networks - activation function derivative
Neural networks [2.5] : Training neural networks - activation function derivative
Published: 2013/11/16
Channel: Hugo Larochelle
Intro to Neural Networks
Intro to Neural Networks
Published: 2013/06/11
Channel: Michael Zibulevsky
Derivative of tanh and sigmoid functions
Derivative of tanh and sigmoid functions
Published: 2017/11/11
Channel: Ahmed Fathi
Mod-08 Lec-26 Multilayer Feedforward Neural networks with Sigmoidal activation functions;
Mod-08 Lec-26 Multilayer Feedforward Neural networks with Sigmoidal activation functions;
Published: 2013/12/02
Channel: nptelhrd
Lecture 6.4 — Logistic Regression | Cost Function — [ Machine Learning | Andrew Ng]
Lecture 6.4 — Logistic Regression | Cost Function — [ Machine Learning | Andrew Ng]
Published: 2017/01/01
Channel: Video Tutorials - All in One
Sigmoid Curve model of Change
Sigmoid Curve model of Change
Published: 2015/11/18
Channel: Mary-Anne Murphy
Lecture 13.3 — Learning sigmoid belief nets  [Neural Networks for Machine Learning]
Lecture 13.3 — Learning sigmoid belief nets [Neural Networks for Machine Learning]
Published: 2016/02/05
Channel: Colin McDonnell
Sigmoid
Sigmoid
Published: 2017/07/24
Channel: Jaideep Nath S Anand
Sigmoid function displacement time servo control
Sigmoid function displacement time servo control
Published: 2009/05/31
Channel: Devraj Joshi
Sigmoid Function (Throw3r Remix)
Sigmoid Function (Throw3r Remix)
Published: 2016/07/18
Channel: Various Artists - Topic
Sigmoid Function and Gradient in Backpropagation
Sigmoid Function and Gradient in Backpropagation
Published: 2016/07/10
Channel: dr3rubens
The sigmoid growth curve
The sigmoid growth curve
Published: 2011/05/18
Channel: IBbiologyBlog
Fitting S-Curves with a Boltzmann Equation
Fitting S-Curves with a Boltzmann Equation
Published: 2016/02/02
Channel: Dr. Gerard Verschuuren
SANKEY DIAGRAM TABLEAU
SANKEY DIAGRAM TABLEAU
Published: 2017/05/13
Channel: SuperDataScience
The Cost Function and The need for the sigmoid
The Cost Function and The need for the sigmoid
Published: 2017/10/10
Channel: Ahmed Fathi
Equivalence of two activation functions in hidden layer: example
Equivalence of two activation functions in hidden layer: example
Published: 2014/01/05
Channel: Anish Turlapaty
Calculus - 3.9 Notes Example 8: Derivative of Logistic Functions
Calculus - 3.9 Notes Example 8: Derivative of Logistic Functions
Published: 2013/11/15
Channel: Scott Haselwood
Million Reasons - Sigmoid Cover
Million Reasons - Sigmoid Cover
Published: 2016/11/25
Channel: Sigmoid Official
The Gompertz Sigmoid Function and Its Derivative
The Gompertz Sigmoid Function and Its Derivative
Published: 2009/07/17
Channel: wolframmathematica
The Gompertz Sigmoid Function and Its Derivative
The Gompertz Sigmoid Function and Its Derivative
Published: 2010/04/14
Channel: wolframmathematica
Activation Functions
Activation Functions
Published: 2017/06/16
Channel: Data Skeptic
The Sigmoid Curve (Positive Psychology)
The Sigmoid Curve (Positive Psychology)
Published: 2012/10/04
Channel: MrLiveanew
Sigmoid Display - Guppies
Sigmoid Display - Guppies
Published: 2014/09/14
Channel: AndtheIvy
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WIKIPEDIA ARTICLE

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Plot of the error function

A 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

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.

Definition[edit]

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

Properties[edit]

In general, a sigmoid function is real-valued, monotonic, and differentiable having a non-negative first derivative which is bell shaped. A sigmoid function is constrained by a pair of horizontal asymptotes as .

Examples[edit]

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

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

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 specific mathematical model is lacking, a sigmoid function is often used.[2]

See also[edit]

References[edit]

  1. ^ Han, Jun; Morag, Claudio (1995). "The influence of the sigmoid function parameters on the speed of backpropagation learning". In Mira, José; Sandoval, Francisco. From Natural to Artificial Neural Computation. pp. 195–201. 
  2. ^ Gibbs, M.N. (Nov 2000). "Variational Gaussian process classifiers". IEEE Transactions on Neural Networks. 11 (6): 1458–1464. doi:10.1109/72.883477. 
  • Mitchell, Tom M. (1997). Machine Learning. WCB–McGraw–Hill. ISBN 0-07-042807-7. . In particular see "Chapter 4: Artificial Neural Networks" (in particular pp. 96–97) where Mitchell uses the word "logistic function" and the "sigmoid function" synonymously – this function he also calls the "squashing function" – and the sigmoid (aka logistic) function is used to compress the outputs of the "neurons" in multi-layer neural nets.
  • Humphrys, Mark. "Continuous output, the sigmoid function".  Properties of the sigmoid, including how it can shift along axes and how its domain may be transformed.

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