Play Video
1
Sigmoid function
Sigmoid function
::2014/08/16::
Play Video
2
The Sigmoid Curve
The Sigmoid Curve
::2012/11/11::
Play Video
3
Intro to Neural Networks
Intro to Neural Networks
::2013/06/10::
Play Video
4
Julia Programming : The Sigmoid Function Programming Exercise
Julia Programming : The Sigmoid Function Programming Exercise
::2014/03/02::
Play Video
5
Normalised Tunable Sigmoid Function Demo in Unity3D
Normalised Tunable Sigmoid Function Demo in Unity3D
::2013/06/26::
Play Video
6
The Gompertz Sigmoid Function and Its Derivative
The Gompertz Sigmoid Function and Its Derivative
::2009/07/16::
Play Video
7
Sigmoid function displacement time servo control
Sigmoid function displacement time servo control
::2009/05/30::
Play Video
8
Normalised Tunable Sigmoid Function 2.0
Normalised Tunable Sigmoid Function 2.0
::2013/11/24::
Play Video
9
Contrast Enhancement of Color Images using Tunable Sigmoid Function.wmv
Contrast Enhancement of Color Images using Tunable Sigmoid Function.wmv
::2011/03/16::
Play Video
10
The Gompertz Sigmoid Function and Its Derivative
The Gompertz Sigmoid Function and Its Derivative
::2010/04/13::
Play Video
11
Derivative of the sigmoid activation function, 9/2/2015
Derivative of the sigmoid activation function, 9/2/2015
::2015/02/10::
Play Video
12
Mathematical Biology. 19: Sigmoidal Functions, Multisite Systems
Mathematical Biology. 19: Sigmoidal Functions, Multisite Systems
::2014/02/25::
Play Video
13
Impact of Bias on the Sigmoid Activation function
Impact of Bias on the Sigmoid Activation function
::2014/10/19::
Play Video
14
免費統計教學範例39 Sigmoidal Function Fit S曲線回歸
免費統計教學範例39 Sigmoidal Function Fit S曲線回歸
::2013/05/08::
Play Video
15
Neural networks [1.2] : Feedforward neural network - activation function
Neural networks [1.2] : Feedforward neural network - activation function
::2013/11/15::
Play Video
16
Curve Fitting in Excel
Curve Fitting in Excel
::2013/06/26::
Play Video
17
Organizational Learning Tool: The Sigmoid Curve
Organizational Learning Tool: The Sigmoid Curve
::2013/10/15::
Play Video
18
Mod-08 Lec-26 Multilayer Feedforward Neural networks with Sigmoidal activation functions;
Mod-08 Lec-26 Multilayer Feedforward Neural networks with Sigmoidal activation functions;
::2013/12/02::
Play Video
19
Retro Sigmoid Vestibular Nerve Section for Meniere
Retro Sigmoid Vestibular Nerve Section for Meniere's Disease
::2009/07/02::
Play Video
20
Neural network tutorial: The back-propagation algorithm (Part 1)
Neural network tutorial: The back-propagation algorithm (Part 1)
::2012/01/07::
Play Video
21
EC50 and IC50 Determination in Excel
EC50 and IC50 Determination in Excel
::2013/07/10::
Play Video
22
Logistic function
Logistic function
::2014/08/13::
Play Video
23
Polypectomy of Colon Sigmoid Polyp
Polypectomy of Colon Sigmoid Polyp
::2012/10/04::
Play Video
24
Plot 5 of 6 - Continuous A* - Obstacle Created Using the Product of Sigmoid Functions
Plot 5 of 6 - Continuous A* - Obstacle Created Using the Product of Sigmoid Functions
::2008/11/12::
Play Video
25
Neural Network Part 2
Neural Network Part 2
::2010/10/14::
Play Video
26
Developing neural network in MATLAB method2 nntool] [fitting tool]
Developing neural network in MATLAB method2 nntool] [fitting tool]
::2013/07/23::
Play Video
27
Logistic regression
Logistic regression
::2011/11/12::
Play Video
28
Spiral Weaving Time
Spiral Weaving Time
::2013/08/24::
Play Video
29
Neural Network Tutorial - Ch. 7.1 More transfer functions (Part 1)
Neural Network Tutorial - Ch. 7.1 More transfer functions (Part 1)
::2012/01/30::
Play Video
30
Developing neural network in MATLAB method1 command window] [fitting tool]
Developing neural network in MATLAB method1 command window] [fitting tool]
::2013/07/23::
Play Video
31
Plot 6 of 6 - Continuous A* - Simple Maze
Plot 6 of 6 - Continuous A* - Simple Maze
::2008/11/12::
Play Video
32
Colon Resection
Colon Resection
::2010/12/13::
Play Video
33
5.1 Loss Functions | 5 Support Vector Machines | Pattern Recognition Class 2012
5.1 Loss Functions | 5 Support Vector Machines | Pattern Recognition Class 2012
::2012/11/22::
Play Video
34
Equivalence of two activation functions in hidden layer: example
Equivalence of two activation functions in hidden layer: example
::2014/01/04::
Play Video
35
A Neural Network Learning his name
A Neural Network Learning his name
::2014/04/29::
Play Video
36
CSCI4477-R11-classify-housing-SVM
CSCI4477-R11-classify-housing-SVM
::2013/02/22::
Play Video
37
VLSI 2014 EFFICIENT VLSI IMPLEMENTATION OF NEURAL NETWORKS WITH HYPERBOLIC TANGENT ACTIVATION..
VLSI 2014 EFFICIENT VLSI IMPLEMENTATION OF NEURAL NETWORKS WITH HYPERBOLIC TANGENT ACTIVATION..
::2014/10/31::
Play Video
38
Forex ANN Neural Network Close Price Prediction
Forex ANN Neural Network Close Price Prediction
::2014/04/26::
Play Video
39
Ignite Columbus 2 - Joshua Scott - Jump!
Ignite Columbus 2 - Joshua Scott - Jump!
::2009/03/05::
Play Video
40
Mega-R4. Neural Nets
Mega-R4. Neural Nets
::2014/01/10::
Play Video
41
decision feedback equalizer
decision feedback equalizer
::2012/02/09::
Play Video
42
Two Spirals Problem - classification with Sharky Neural Network (SNN)
Two Spirals Problem - classification with Sharky Neural Network (SNN)
::2009/08/23::
Play Video
43
Neural Networks Classification with Sharky Neural Network (SNN) - shape "c|n"
Neural Networks Classification with Sharky Neural Network (SNN) - shape "c|n"
::2009/08/22::
Play Video
44
SELECTING THE OPTIMUM LOCATION OF THE CLUSTER HEAD IN THE WSNs AND CLUSTERING VİA NSGA-II AND MOPSO
SELECTING THE OPTIMUM LOCATION OF THE CLUSTER HEAD IN THE WSNs AND CLUSTERING VİA NSGA-II AND MOPSO
::2013/12/24::
Play Video
45
1.6 Sigmoid Emax model - Hill factor
1.6 Sigmoid Emax model - Hill factor
::2012/03/12::
Play Video
46
Neural Network Consensus Forming
Neural Network Consensus Forming
::2011/03/02::
Play Video
47
Introduction to Neural Networks for C#(Class 4/16, Part 2/5) - activation function
Introduction to Neural Networks for C#(Class 4/16, Part 2/5) - activation function
::2009/02/07::
Play Video
48
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
::2013/04/05::
Play Video
49
Inferior Mesenteric Artery: Easy Anatomy Mnemonic Tutorial- Branches: colic, sigmoid, rectal
Inferior Mesenteric Artery: Easy Anatomy Mnemonic Tutorial- Branches: colic, sigmoid, rectal
::2013/07/29::
Play Video
50
Diverticulitis Meditoons™
Diverticulitis Meditoons™
::2012/12/02::
NEXT >>
RESULTS [51 .. 101]
From Wikipedia, the free encyclopedia
Jump to: navigation, search
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[edit]

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[edit]

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[edit]

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.

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.
Wikipedia content is licensed under the GFDL License
Powered by YouTube
MASHPEDIA
LEGAL
  • Mashpedia © 2015