given a set of fix vectors and a set of vectors where all can be expressed as a convex combination of the vectors in :
where is the j'th coefficient of vector i.
Now the mission is: given a vector , find the vector which has the smallest distance to using the squared euclid distance (and of course != ).
Suppose that the vectors in are stored in their convex combination form and that the combination is not calculated yet.
An easy but expensive way to solve the problem is:
1) calculate the convex combinations for all vectors in
2) find by comparing the distance of to all vactors in and picking the one with the smallest distance.
Is there an alternative way to efficiently calculate this (from a practical + implementation point of view) ? Probably by respecting the fact that the vectors in do not change and that the vectors in are expressed as convex combination.
(We assume that all vectors are in .)