tanh Function

zhichengMLE

于 2017-10-30 23:15:11 发布

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分类专栏：机器学习-数学基础机器学习数学基础文章标签：函数 tanh math matrix

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本文对比了两种常用的神经网络激活函数：tanh函数与Sigmoid函数。详细介绍了它们的数学公式及导数，并通过图表直观展示了两者的特性。此外，还提供了tanh函数在Octave中的实现示例。

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tanh Function

1. Introduction

To limit all data within the range of -1 to 1. Comparing to Sigmoid Function which output range is [0,1]

2. Formula

The formula and derivative of tanh is:

f (z) f' (z) = t a n h (z) = e z - e - z e z + e - z = 1 - (f (z)) 2

$\begin{align*} f(z) &= tanh(z) = \frac{e^z - e^{-z}}{e^z+e^{-z}} \\ f'(z) &= 1 - (f(z))^2 \end{align*}$
where as the sigmoid function is pretty close

f (z) f' (z) = s i g m o i d (z) = 1 1 + e - z = 1 - f (z)

$\begin{align*} f(z) &= sigmoid(z) = \frac{1}{1+e^{-z}} \\ f'(z) &= 1 - f(z) \end{align*}$

See the figure of tanh and sigmoid below.
tanh

tanh Function

sigmoid

sigmoid Function

3. Implementation

3.1 Octave

 x = linspace(-10, 10 ,10000);
 y = zeros( size(x, 1), size(x, 2));

 for i = 1:length(x)
   y(i) = 1/(1+e^(-x(i)));
 endfor

 figure();
 plot( x,y);
 grid on;
 xlabel("x");
 ylabel("y=1/(1+e^-x)");
 title("Sigmoid Function");