# How can I measure separability between different number of instance of one feature vector?

How can I measure separability between different number of instance of one feature vector? For example the main vector is V=[1 1 2 3 4 5 7 8 10 100 1000 99 999 54] and three sub-vector with different sample lengths are t1=[1 1 2 3 99 1000] or t2=[1 10 1000] or t3=[2 3 4 10 100 99 999 54].

Which one is more separable and more informative? I mean I am looking for a sub-vector with minimum length and maximum separability power.

If I put it in GMM, the sub-vector with less samples has better probability which is not fairly approach.

train=[1 2 1 2 1 2 100 101 102 99 100 101 1000 1001 999 1003];
No_of_Iterations=10;
No_of_Clusters=3;
[mm,vv,ww]=gaussmix(train,[],No_of_Iterations,No_of_Clusters);
test1=[1 1 1 2 2 2 100 100 100 101 1000 1000 1000];
test2=[1 1 2 2 100 99 1000 999];
test3=[1 100 1000];
[lp,rp,kh,kp]=gaussmixp(test1,mm,vv,ww);
sum(lp)
[lp,rp,kh,kp]=gaussmixp(test2,mm,vv,ww);
sum(lp)
[lp,rp,kh,kp]=gaussmixp(test3,mm,vv,ww);
sum(lp)


The results are as follow :

ans =

-8.0912e+05

ans =

-8.1782e+05

ans =

-5.0381e+05


I will really appreciate, if you could help me.