100 lines
3.7 KiB
VB.net
100 lines
3.7 KiB
VB.net
#Region "Microsoft.VisualBasic::149889335b38136e0d3eccf502b78876, Microsoft.VisualBasic.Core\Extensions\Math\Information\Entropy.vb"
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' Author:
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'
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' asuka (amethyst.asuka@gcmodeller.org)
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' xie (genetics@smrucc.org)
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' xieguigang (xie.guigang@live.com)
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'
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' Copyright (c) 2018 GPL3 Licensed
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'
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'
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' GNU GENERAL PUBLIC LICENSE (GPL3)
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'
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'
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' This program is free software: you can redistribute it and/or modify
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' it under the terms of the GNU General Public License as published by
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' the Free Software Foundation, either version 3 of the License, or
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' (at your option) any later version.
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'
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' This program is distributed in the hope that it will be useful,
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' but WITHOUT ANY WARRANTY; without even the implied warranty of
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' MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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' GNU General Public License for more details.
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'
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' You should have received a copy of the GNU General Public License
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' along with this program. If not, see <http://www.gnu.org/licenses/>.
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' /********************************************************************************/
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' Summaries:
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' Module Entropy
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'
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' Function: ShannonEnt, ShannonEntropy
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'
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'
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' /********************************************************************************/
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#End Region
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Imports System.Runtime.CompilerServices
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Imports stdNum = System.Math
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Namespace Math.Information
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''' <summary>
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''' 信息熵越大表示所含信息量越多
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''' </summary>
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Public Module Entropy
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''' <summary>
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''' 计算出目标序列的香农信息熵
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''' </summary>
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''' <typeparam name="T"></typeparam>
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''' <param name="collection"></param>
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''' <returns></returns>
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''' <remarks>
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''' ###### 计算公式
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'''
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''' ```
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''' H(x) = E[ I(xi) ]
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''' = E[ log(2, 1/p(xi)) ]
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''' = -∑ p(xi)log(2, p(xi)) (i=1, 2, ..., n)
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''' ```
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'''
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''' 其中，``x``表示随机变量，与之相对应的是所有可能输出的集合，定义为符号集，随机变量的输出用``x``表示。
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''' ``P(x)``表示输出概率函数。变量的不确定性越大，熵也就越大，把它搞清楚所需要的信息量也就越大.
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''' </remarks>
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<Extension>
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Public Function ShannonEnt(Of T)(collection As IEnumerable(Of T)) As Double
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Dim distincts = (From x As T In collection Group x By x Into Count).ToArray
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Dim numEntries% = Aggregate g In distincts Into Sum(g.Count)
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Dim probs = From item In distincts Select item.Count / numEntries
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Dim entropy# = ShannonEntropy(probs)
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Return entropy
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End Function
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''' <summary>
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''' 直接从一个概率向量之中计算出香农信息熵
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''' </summary>
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''' <param name="probs">Sum of this probability vector must equals to 1</param>
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''' <returns></returns>
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'''
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<Extension>
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Public Function ShannonEntropy(probs As IEnumerable(Of Double)) As Double
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Dim entropy# = Aggregate prob As Double
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In probs
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Where prob > 0 ' 因为是求和，所以prob等于零的时候，乘上ln应该也是零的，因为零对求和无影响，所以在这里直接使用where跳过零了
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Let ln = stdNum.Log(prob, newBase:=2)
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Into Sum(prob * ln)
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' 和的负数，注意在这里最后的结果还需要乘以-1
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' 有一个负号
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Return -entropy
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End Function
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End Module
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End Namespace
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