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Sigmoid - Georgia Tech - Machine Learning

Published: 2015/02/23

Channel: Udacity

The Sigmoid Curve

Published: 2012/11/11

Channel: Pete Dalgleish

Neural networks [1.2] : Feedforward neural network - activation function

Published: 2013/11/15

Channel: Hugo Larochelle

Sigmoid function

Published: 2014/08/16

Channel: Audiopedia

Julia Programming : The Sigmoid Function Programming Exercise

Published: 2014/03/02

Channel: Stats-Lab Dublin

Mathematical device used in Deep Learning V - Sigmoid function

Published: 2015/10/23

Channel: Vasu Srinivasan

Intro to Neural Networks

Published: 2013/06/10

Channel: Michael Zibulevsky

Derivative of the sigmoid activation function, 9/2/2015

Published: 2015/02/10

Channel: Lutfi Al-Sharif

Normalised Tunable Sigmoid Function Demo in Unity3D

Published: 2013/06/26

Channel: Dino Dini

Normalised Tunable Sigmoid Function 2.0

Published: 2013/11/24

Channel: Dino Dini

5.3.2 Draw and label a graph showing a sigmoid (S-shaped) population growth curve

Published: 2013/04/05

Channel: Stephanie Castle

Impact of Bias on the Sigmoid Activation function

Published: 2014/10/19

Channel: N RS

Logistic function

Published: 2014/08/13

Channel: Audiopedia

Introduction to Neural Networks for C#(Class 4/16, Part 2/5) - activation function

Published: 2009/02/07

Channel: Jeff Heaton

Mathematical Biology. 19: Sigmoidal Functions, Multisite Systems

Published: 2014/02/25

Channel: UCI Open

The Gompertz Sigmoid Function and Its Derivative

Published: 2009/07/16

Channel: wolframmathematica

The Gompertz Sigmoid Function and Its Derivative

Published: 2010/04/13

Channel: wolframmathematica

Sigmoid function displacement time servo control

Published: 2009/05/30

Channel: Devraj Joshi

Sigmoid Function and Gradient in Backpropagation

Published: 2016/07/10

Channel: dr3rubens

Contrast Enhancement of Color Images using Tunable Sigmoid Function.wmv

Published: 2011/03/16

Channel: VERILOG COURSE TEAM

딥러닝 2. How Artificial Neurons Work (한국어)

Published: 2016/04/30

Channel: J Hong

Using the Flexible Spline function (FlexSpline) in Excel

Published: 2013/11/13

Channel: SRS1Software

The sigmoid growth curve

Published: 2011/05/18

Channel: IBbiologyBlog

Mod-08 Lec-26 Multilayer Feedforward Neural networks with Sigmoidal activation functions;

Published: 2013/12/02

Channel: nptelhrd

Organizational Learning Tool: The Sigmoid Curve

Published: 2013/10/15

Channel: Sigmoid Curve Consulting Group - Experts in Change Leadership

Sigmoid Curve model of Change

Published: 2015/11/17

Channel: Mary-Anne Murphy

3. Learning Sigmoid Belief Nets

Published: 2013/11/09

Channel: Artificial Intelligence Courses

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

Published: 2010/10/15

Channel: Jeff Heaton

2. Bob Buford explains the Sigmoid Curve

Published: 2012/02/22

Channel: HalftimeOnDemand

1.6 Sigmoid Emax model - Hill factor

Published: 2012/03/12

Channel: Shankar Lanke

Neural Network Learning - Visualization - 2

Published: 2015/12/30

Channel: Christopher Gondek

Derivatives of Exponential Functions

Published: 2008/11/29

Channel: patrickJMT

The Sigmoid Curve (Positive Psychology)

Published: 2012/10/04

Channel: MrLiveanew

You don't know what you don't know: the sigmoid curve

Published: 2010/03/11

Channel: wiscoach

Jump Your Sigmoid Curve

Published: 2014/04/24

Channel: Vic Lindal

EC50 and IC50 Determination in Excel

Published: 2013/07/10

Channel: Dr. Gerard Verschuuren

免費統計教學範例39 Sigmoidal Function Fit S曲線回歸

Published: 2013/05/08

Channel: 全傑科技

Smooth Adaptation by Sigmoid Shrinkage

Published: 2014/11/01

Channel: Mblazan

IB SL Biology Past Paper 2 Questions - Question 6 [Sigmoid Population Growth Curve]

Published: 2014/02/20

Channel: IB Blueprint

Logistic Sigmoid Market Model

Published: 2009/07/10

Channel: wolframmathematica

14 5 OPTIONAL RBMs are infinite sigmoid belief nets 17 mins

Published: 2015/07/12

Channel: Charleshche

Neural Network Learning - Visualization - 1

Published: 2015/12/30

Channel: Christopher Gondek

Neural networks [2.5] : Training neural networks - activation function derivative

Published: 2013/11/15

Channel: Hugo Larochelle

cnn 4 single node sigmoid

Published: 2015/09/01

Channel: InsiderMiner

Sigmoid Evolution

Published: 2015/09/01

Channel: Hinode XRT

Comparison of Six Sigmoid Growth Curve Models

Published: 2013/12/09

Channel: wolframmathematica

Sigmoid Curve Pattern Hard Plastic Skin Cover Case Protective for iPhone 4 from Dinodirect.com

Published: 2010/08/11

Channel: dinovideo1api1

Male sigmoid curve

Published: 2013/04/22

Channel: greatguppy1

Curve Fitting with Microsoft Excel

Published: 2013/05/07

Channel: Randy Thomas

From Wikipedia, the free encyclopedia

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A **sigmoid function** is a mathematical function having an "S" shaped curve (**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 t) and the ogee curve (used in the spillway of some dams). Sigmoid functions have finite limits at negative infinity and infinity, most often going either from 0 to 1 or 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.

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]}

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 . The differential equation , with the inclusion of a boundary condition providing a third degree of freedom, , provides a class of functions of this type.

The logistic function has this further, important property, that its derivative can be expressed by the function itself,

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 .

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.

Simpler approximations of smooth sigmoid functions, especially piecewise linear functions or piecewise constant functions, are preferred in some applications, where speed of computation is more important than precision; extreme forms are known as a **hard sigmoid**.^{[3]}^{[4]} These are particularly found in artificial intelligence, especially computer vision and artificial neural networks. The most extreme examples are the sign function or Heaviside step function, which go from −1 to 1 or 0 to 1 (which to use depends on normalization) at 0.^{[5]} For example, the Theano library provides two approximations: `ultra_fast_sigmoid`

and `hard_sigmoid`

, which is a 3-part linear approximation (output 0, line with slope 5, output 1).^{[6]}

Wikimedia Commons has media related to .Sigmoid functions |

- Cumulative distribution function
- Generalized logistic curve
- Gompertz function
- Heaviside step function
- Hyperbolic function
- Logistic distribution
- Logistic function
- Logistic regression
- Logit
- Modified hyperbolic tangent
- Softplus function
- Smoothstep function (Graphics)
- Softmax function
- Weibull distribution
- Netoid function

**^**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.**^**Gibbs, M.N. (Nov 2000). "Variational Gaussian process classifiers".*IEEE Transactions on Neural Networks*.**11**(6): 1458–1464. doi:10.1109/72.883477.**^**Quora, "What is hard sigmoid in artificial neural networks? Why is it faster than standard sigmoid? Are there any disadvantages over the standard sigmoid?", Leo Mauro's answer**^**How is Hard Sigmoid defined**^**Curves and Surfaces in Computer Vision and Graphics, Volume 1610, SPIE, 1992, "hard+sigmoid" p. 301**^**nnet – Ops for neural networks

- 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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