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