  State-of-the-art subspace clustering methods are based on self-expressive
model, which represents each data point as a linear combination of other data
points. By enforcing such representation to be sparse, sparse subspace
clustering is guaranteed to produce a subspace-preserving data affinity where
two points are connected only if they are from the same subspace. On the other
hand, however, data points from the same subspace may not be well-connected,
leading to the issue of over-segmentation. We introduce dropout to address the
issue of over-segmentation, which is based on randomly dropping out data points
in self-expressive model. In particular, we show that dropout is equivalent to
adding a squared $\ell_2$ norm regularization on the representation
coefficients, therefore induces denser solutions. Then, we reformulate the
optimization problem as a consensus problem over a set of small-scale
subproblems. This leads to a scalable and flexible sparse subspace clustering
approach, termed Stochastic Sparse Subspace Clustering, which can effectively
handle large scale datasets. Extensive experiments on synthetic data and real
world datasets validate the efficiency and effectiveness of our proposal.
