Hausdorff regression

Linear regression minimizing the Hausdorff between the line segment and the given set of points.

The main advantages of the Hausdorff regression are that one should not specify the direction of the errors (vertical, horizontal, orthogonal ... with the ordinary least squares) and that it is less sensitive with respect to the square of the distance.

This is the original idea. Any contribution is welcome! Let me know if you are interested.