# find the optimal correspondence matrix

I have two sets of points and I find with different methods, different correspondence matrices which shows which point in one set correspond to other point in the other set. How could I find the optimal correspondence matrix in order to minimize the distance between two sets of points from having both these matrices in hand?!!

For instance, if there is seven points in one set and four points in the other set, then the correspondence matrix that relates points in x-y space, might look like this

BTW, each of the correspondence matrices have just zero and one entries which shows which point corresponds to other point. Thanks in advance

• First, please show how a correspondence matrix of yours looks like. Second, what are these plots and how to understand them? Oct 3, 2014 at 19:49
• @ttnphns the plots are a set of points in x-y plane. Oct 3, 2014 at 20:01
• What do you mean by an "optimal" correspondence matrix? One which minimizes sum of squared distances between the correspondent points? Oct 3, 2014 at 20:08
• @user31264 the matrix that minimizes the distance between the points with the correspondence in the other set. Oct 3, 2014 at 20:11
• If you have n rectangular similarity matrices (between the same two sets of items in all n cases) you may use Multidimensional Unfolding (MDU) technique in individual scaling (INDSCAL) regime to embed the points of both sets in a low dimensional Euclidean space. Oct 4, 2014 at 8:49