  Subspace clustering refers to the problem of clustering high-dimensional data
that lie in a union of low-dimensional subspaces. State-of-the-art subspace
clustering methods are based on the idea of expressing each data point as a
linear combination of other data points while regularizing the matrix of
coefficients with L1, L2 or nuclear norms for a sparse solution. L1
regularization is guaranteed to give a subspace-preserving affinity (i.e.,
there are no connections between points from different subspaces) under broad
theoretical conditions, but the clusters may not be fully connected. L2 and
nuclear norm regularization often improve connectivity, but give a
subspace-preserving affinity only for independent subspaces. Mixed L1, L2 and
nuclear norm regularization could offer a balance between the
subspace-preserving and connectedness properties, but this comes at the cost of
increased computational complexity. This paper focuses on using L1 norm and
alleviating the corresponding connectivity problem by a simple yet efficient
diffusion process on subspace affinity graphs. Without adding any tuning
parameter , our method can achieve state-of-the-art clustering performance on
Hopkins 155 and Extended Yale B data sets.
