其中
Hx Marginal entropy for a discrete random variable (x)
Hy Marginal entropy for a discrete random variable (y)
Hxy Joint entropy for a discrete random variables (x and y)
得MI = Hx+Hy-Hxy
标准化MI的方法有:
marginal MI = 2*( Hx + Hy - Hxy ) / ( Hx + Hy )
joint MI = 2*( Hx + Hy - Hxy ) / ( Hxy )
min.marginal MI = ( Hx + Hy - Hxy ) / min(Hx,Hy)
max.marginal MI = ( Hx + Hy - Hxy ) /max(Hx,Hy)
min.conditional MI = ( Hx + Hy - Hxy ) / min(Hx.y,Hy.x)
max.conditional MI = ( Hx + Hy - Hxy ) / max(Hx.y,Hy.x)
这些标准化方法没有使MI值域为0,1啊? 有什么上述方法的变形可以使其到0,1,最终目的是算距离(1-NMI)?
参考包:
17页: http://cran.r-project.org/web/packages/HDMD/HDMD.pdf