I have 2 sets of points with different number, namely $Blue=\{(x_1,y_1),(x_2,y_2),...(x_n,y_n)\}$ and $Yellow=\{(x_1,y_1),(x_2,y_2),...(x_m,y_m)\}$, how can I define some indicator to reflect the relationship (similar to correlation) of $Blue$ and $Yellow$?
Many thanks!
There is the Hausdorff distance. It can be explained as follows:
For $z\in{\mathbb R}^2$ and $r>0$ define $D_r(z)$ to be the disc of radius $r$ centered at $z$. Given an arbitrary bounded nonempty set $A \subset{\mathbb R}^2$ one may regard $$A_\epsilon:=\bigcup_{z\in A} D_\epsilon(z)$$ as a smeared out version of $A$. For two such sets $A$, $B\subset{\mathbb R}^2$ one then defines $$d_H(A,B):=\inf\bigl\{\epsilon>0\bigm| B\subset A_\epsilon\ \wedge \ A\subset B_\epsilon\bigr\}\ .$$ In your case it is about the two sets $$A:=\bigl\{(x_k,y_k)\bigm|1\leq k\leq n\bigr\},\qquad B:=\bigl\{(u_k,v_k)\bigm|1\leq k\leq m\bigr\}\ .$$