人工神经网络框架AForge学习(二):Sigmoid激活函数

Code

namespace AForge.Neuro

{

using System;

/// <summary>

/// Sigmoid activation function

/// 西格玛激活函数

/// </summary>

///

/// <remarks>The class represents sigmoid activation function with

/// the next expression:<br />

/// 这个类表示西格玛激活函数按照下面的公示描述：

/// <code>

/// 1

/// f(x) = ------------------

/// 1 + exp(-alpha * x)

///

/// alpha * exp(-alpha * x )

/// f'(x) = ---------------------------- = alpha * f(x) * (1 - f(x))

/// (1 + exp(-alpha * x))^2

/// </code>

/// Output range of the function: <b>[0, 1]</b><br /><br />

/// 输出范围在[0,1]区间

/// Functions graph:<br />

/// <img src="sigmoid.bmp" width="242" height="172" />

/// </remarks>

public class SigmoidFunction : IActivationFunction

{

// sigmoid's alpha value

// 阀值、偏置、活性值?

private double alpha = 2;

/// <summary>

/// Sigmoid's alpha value

/// </summary>

///

/// <remarks>The value determines steepness of the function. Default value: <b>2</b>.

/// </remarks>

public double Alpha

{

get { return alpha; }

set { alpha = value; }

}

/// <summary>

/// Initializes a new instance of the <see cref="SigmoidFunction"/> class

/// 初始化

/// </summary>

public SigmoidFunction( ) { }

/// <summary>

/// Initializes a new instance of the <see cref="SigmoidFunction"/> class

/// </summary>

///

/// <param name="alpha">Sigmoid's alpha value 指定修正值</param>

public SigmoidFunction( double alpha )

{

this.alpha = alpha;

}

/// <summary>

/// Calculates function value

/// 计算函数值

/// </summary>

///

/// <param name="x">Function input value</param>

///

/// <returns>Function output value, <i>f(x)</i></returns>

///

/// <remarks>The method calculates function value at point <b>x</b>.</remarks>

///

public double Function( double x )

{

return ( 1 / ( 1 + Math.Exp( -alpha * x ) ) );

}

/// <summary>

/// Calculates function derivative

/// 计算导数

/// </summary>

///

/// <param name="x">Function input value</param>

///

/// <returns>Function derivative, <i>f'(x)</i> 返回导数值</returns>

///

/// <remarks> The method calculates function derivative at point <b>x</b>.</remarks>

///

public double Derivative( double x )

{

double y = Function( x );

return ( alpha * y * ( 1 - y ) );

}

/// <summary>

/// Calculates function derivative

/// 计算导数

/// </summary>

///

/// <param name="y">Function output value - the value, which was obtained

/// with the help of <see cref="Function"/> method

/// 由Function计算出来的y

/// </param>

///

/// <returns>Function derivative, <i>f'(x)</i></returns>

///

/// <remarks>The method calculates the same derivative value as the

/// <see cref="Derivative"/> method, but it takes not the input <b>x</b> value

/// itself, but the function value, which was calculated previously with

/// the help of <see cref="Function"/> method. <i>(Some applications require as

/// function value, as derivative value, so they can seve the amount of

/// calculations using this method to calculate derivative)</i>

/// 这个方法和Derivative一样计算导数，但它不以输入值x为参数，而是以原先由Funcion计算

/// 出的y为参数.

/// </remarks>

///

public double Derivative2( double y )

{

return ( alpha * y * ( 1 - y ) );

}

}

}