Detailed explanation of all transfer function (activation function) formulas of MATLAB neural network

Original article , Reprint please indicate from 《 Old cake explains neural networks 》:bp.bbbdata.com

About 《 Old cake explains neural networks 》：

This website structurally explains the knowledge of Neural Networks , Principle and code .

repeat matlab Algorithm of neural network toolbox , It is a good assistant for learning neural networks . 

---

Catalog

One 、 Pass function name

Two 、 Transfer function image

3、 ... and 、 The transfer function expression is

---

In this paper, matlab Detailed explanation of transfer function formula and image in neural network toolbox .

One 、 Pass function name

matlab The transfer functions of the neural network toolbox are as follows ：

function	The name of the function	Explain in English
tansig	symmetry S Shape function	Symmetric sigmoid transfer function.
logsig	logarithm S Shape function	Logarithmic sigmoid transfer function.
elliotsig	Elliot S Shape function	Elliot sigmoid transfer function.
hardlim	Positive hard limit function	Positive hard limit transfer function.
hardlims	Symmetric hard limit function	Symmetric hard limit transfer function.
poslin	Positive linear function	Positive linear transfer function.
purelin	Linear function	Linear transfer function.
satlin	Positive linear saturation function	Positive saturating linear transfer function.
satlins	Symmetric linear saturation function	Symmetric saturating linear transfer function.
netinv	Inverse function	Inverse transfer function.
tribas	Trigonometric basis function	Triangular basis transfer function.
radbas	Radial basis function	Radial basis transfer function.
radbasn	Normalized radial basis function	Radial basis normalized transfer function.
compet	Competition function	Competitive transfer function.
softmax	Soft maximization function	Soft max transfer function.

Two 、 Transfer function image

Their images are drawn as follows ：

( It doesn't contain radbasn,softmax,compet)

3、 ... and 、 The transfer function expression is

Their expression is ：

(1) tansig  symmetry S Shape function

 (2)elliotsig   (Elliot  S Shape function )

 (3) logsig   logarithm S Shape function

 (4)compet   Competition function

Set the largest of the vectors to 1, The rest are in 0. 
Example ,compet([0.2 0.5 0.8 ]) = [0 0 1]

(5)  hardlim  Positive hard limit function

(6) hardlims   Symmetric hard limit function

 (7) poslin   Positive linear function

 (8) purelin  Linear function

 (9) satlin  Positive linear saturation function

(10) satlins  Symmetric linear saturation function

 (11) netinv  Inverse function

(12) tribas  Trigonometric basis function  

(13) radbas   Radial basis function

(14) radbasn     Normalized radial basis function

In order to reduce the exp Calculation produces numerical problems , But for xi Do the following ：

 (15) softmax  Soft maximization function

---

Related articles

​《BP Neural network gradient derivation 》

​​​​​​《BP The mathematical expression extracted by neural network 》

《 One BP Complete modeling process 》