Distance measure for probability distribution function of mixture type

摘要

In accordance with our invention, for two mixture-type probability distribution functions (PDF's), G, H, 1 $G\left(x\right)=\sum _{i=1}^N{\mathrm{mu}}_i{g}_i\left(x\right),H\left(x\right)=\sum _{k=1}^K{\mathrm{gamma}}_k{h}_k\left(x\right),$ where G is a mixture of N component PDF's gi (x), H is a mixture of K component PDF's hk (x), mui and gammak are corresponding weights that satisfy 2 $\sum _{i=1}^N{\mathrm{mu}}_i=1\mathrm{and}\sum _{k=1}^K{\mathrm{gamma}}_k=1;$ we define their distance, DM(G, H), as 3 $D_M\left(G,H\right)=$