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Sigmoid function
Sigmoid function

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!!! Overview
[{$pagename}] is a mathematical [function] having a characteristic "S"-shaped curve or sigmoid curve.
Often, [{$pagename}] refers to the special case of the [logistic function] shown in the first figure and defined by the formula
\\
[{Image src='Sigmoid function/stock-vector-sigmoid-function-451998487.jpg' caption='Sigmoid-function' align=left width=724 height=480 style='font-size: 120%}]. \\
Other examples of similar shapes include the Gompertz curve (used in modeling systems that saturate at large values of x) and the ogee curve (used in the spillway of some dams). Sigmoid functions have domain of all real numbers, with return value monotonically increasing most often from 0 to 1 or alternatively from −1 to 1, depending on convention.
A wide variety of [{$pagename}]s have been used as the [Activation Function] of [Artificial Neurons], including the logistic and hyperbolic tangent [functions]. Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic distribution, the normal distribution, and Student's t probability density functions.
For use within [sigmoid neuron] in [Deep Learning] we also use the derivative of the [{$pagename}] which can be done in [Python] as:
%%prettify
{{{
import numpy as np
def sigmoid():
return 1 / (1 + np.exp(-x))
# derivative of sigmoid
# sigmoid(y) * (1.0 - sigmoid(y))
# the way we use this y is already sigmoided
def dsigmoid():
return y * (1.0 - y)
}}}
/%
!! More Information
There might be more information for this subject on one of the following:
[{ReferringPagesPlugin before='*' after='\n' }]
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* [#1] - [Sigmoid_function|Wikipedia:Sigmoid_function|target='_blank'] - based on information obtained 2017-11-24-
This page (revision-1) was last changed on 29-Nov-2024 16:16 by UnknownAuthorTop