The sigmoid()
function returns the sigmoid value of the
input(s), by default this is done using the standard logistic
function.
library(sigmoid)
sigmoid(3)
## [1] 0.9525741
Inputs 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 0.993307149
sigmoid( 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 0.9933071
The sigmoid()
function is a wrapper, which by default
uses the logistic()
function, it can also use other
methods.
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-01
These functions can also be accessed directly.
Gompertz(-1:-5)
## [1] 6.598804e-02 6.179790e-04 1.892179e-09 1.942338e-24 3.507389e-65
Rectified Linear Unit (ReLU)
sigmoid( -5:5, method='ReLU')
## [1] 0 0 0 0 0 0 1 2 3 4 5
Leaky 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 5.00
These mappings are similar but not identical.
library(ggplot2)
= -5:5
input
= data.frame(input, logistic(input), Gompertz(input))
df
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 the original values.
sigmoid( sigmoid(-5:5), inverse=TRUE )
## [1] -5 -4 -3 -2 -1 0 1 2 3 4 5
Which 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 5
In 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 0.98993514
Several parameters can be specified (for details see
help(logistic)
, etc.). This can for instance be used to
preserve greater entropy.
= seq(1,5, by=0.05)
x qplot(sigmoid(x))
qplot( sigmoid(x, k=sd(x), x0=mean(x) ) )