Least-Squares Opposite

Question

Is there an opposite formulation of least-squares projection where the distance between each point–say, $(x_{i}, y_{i})$– and the subspace that it's projected onto (e.g. a line through the origin) is maximized? In researching the subject, it seems that the singular value decomposition (SVD) of a matrix is somehow involved, but I couldn't find a clear-cut answer.