Given $M$ points in $\mathbb{R}^{N}$, (where $M$ is larger than $N$) I was wondering if there is an approximation algorithm to find a hyperplane which goes through the origin and also intersects as many points as possible. I believe this problem is NP-Hard, but it would be great if someone can point me to the appropriate paper for this and to the approximations for this problem.
Thank you all beforehand
EDIT: What I meant in the above is that is there a better solution than $O(M^N)$? Is there a better solution than looking at all $M$ choose $N-1$ subspaces defined by the points?