Mappings
These mappings are similar but not identical.
library(ggplot2)input=-5:5df=data.frame(input,logistic(input),Gompertz(input))ggplot(df,aes(input,logistic(input)))+geom_line()+geom_line(aes(input,Gompertz(input)),colour='red')Thesigmoid() function returns the sigmoid value of theinput(s), by default this is done using thestandard logisticfunction.
library(sigmoid)sigmoid(3)## [1] 0.9525741Inputs can also be tensors, such as vectors, matrices, or arrays.
sigmoid(-5:5)## [1] 0.006692851 0.017986210 0.047425873 0.119202922 0.268941421 0.500000000## [7] 0.731058579 0.880797078 0.952574127 0.982013790 0.993307149sigmoid(matrix(-3:5,nrow=3) )# etc.## [,1] [,2] [,3]## [1,] 0.04742587 0.5000000 0.9525741## [2,] 0.11920292 0.7310586 0.9820138## [3,] 0.26894142 0.8807971 0.9933071Thesigmoid() function is a wrapper, which by defaultuses thelogistic() function, it can also use othermethods.
sigmoid(-5:5,method='Gompertz' )## [1] 3.507389e-65 1.942338e-24 1.892179e-09 6.179790e-04 6.598804e-02## [6] 3.678794e-01 6.922006e-01 8.734230e-01 9.514320e-01 9.818511e-01## [11] 9.932847e-01These functions can also be accessed directly.
Gompertz(-1:-5)## [1] 6.598804e-02 6.179790e-04 1.892179e-09 1.942338e-24 3.507389e-65Rectified Linear Unit (ReLU)
sigmoid(-5:5,method='ReLU')## [1] 0 0 0 0 0 0 1 2 3 4 5Leaky Rectified Linear Unit
sigmoid(-5:5,method="leakyReLU")## [1] -0.05 -0.04 -0.03 -0.02 -0.01 0.00 1.00 2.00 3.00 4.00 5.00These mappings are similar but not identical.
library(ggplot2)input=-5:5df=data.frame(input,logistic(input),Gompertz(input))ggplot(df,aes(input,logistic(input)))+geom_line()+geom_line(aes(input,Gompertz(input)),colour='red')The wrapper can also apply the inverse of the method, returning theoriginal values.
sigmoid(sigmoid(-5:5),inverse=TRUE )## [1] -5 -4 -3 -2 -1 0 1 2 3 4 5Which also works for other methods.
sigmoid(sigmoid(-5:5,method='Gompertz'),method='Gompertz',inverse=TRUE )## [1] -5 -4 -3 -2 -1 0 1 2 3 4 5In addition to this, the SoftMax algorithm can be pre applied.
sigmoid(-3:5 )sigmoid(-3:5,SoftMax =TRUE )## [1] 0.04742587 0.11920292 0.26894142 0.50000000 0.73105858 0.88079708 0.95257413## [8] 0.98201379 0.99330715## [1] 0.01006486 0.03102509 0.09159656 0.24101050 0.50000000 0.75898950 0.90840344## [8] 0.96897491 0.98993514Several parameters can be specified (for details seehelp(logistic), etc.). This can for instance be used topreserve greater entropy.
x=seq(1,5,by=0.05)qplot(sigmoid(x))qplot(sigmoid(x,k=sd(x),x0=mean(x) ) )