  This letter presents a new spectral-clustering-based approach to the subspace
clustering problem. Underpinning the proposed method is a convex program for
optimal direction search, which for each data point d finds an optimal
direction in the span of the data that has minimum projection on the other data
points and non-vanishing projection on d. The obtained directions are
subsequently leveraged to identify a neighborhood set for each data point. An
alternating direction method of multipliers framework is provided to
efficiently solve for the optimal directions. The proposed method is shown to
notably outperform the existing subspace clustering methods, particularly for
unwieldy scenarios involving high levels of noise and close subspaces, and
yields the state-of-the-art results for the problem of face clustering using
subspace segmentation.
