  Algebraic Subspace Clustering (ASC) is a simple and elegant method based on
polynomial fitting and differentiation for clustering noiseless data drawn from
an arbitrary union of subspaces. In practice, however, ASC is limited to
equi-dimensional subspaces because the estimation of the subspace dimension via
algebraic methods is sensitive to noise. This paper proposes a new ASC
algorithm that can handle noisy data drawn from subspaces of arbitrary
dimensions. The key ideas are (1) to construct, at each point, a decreasing
sequence of subspaces containing the subspace passing through that point; (2)
to use the distances from any other point to each subspace in the sequence to
construct a subspace clustering affinity, which is superior to alternative
affinities both in theory and in practice. Experiments on the Hopkins 155
dataset demonstrate the superiority of the proposed method with respect to
sparse and low rank subspace clustering methods.
