  We propose an effective subspace selection scheme as a post-processing step
to improve results obtained by sparse subspace clustering (SSC). Our method
starts by the computation of stable subspaces using a novel random sampling
scheme. Thus constructed preliminary subspaces are used to identify the
initially incorrectly clustered data points and then to reassign them to more
suitable clusters based on their goodness-of-fit to the preliminary model. To
improve the robustness of the algorithm, we use a dominant nearest subspace
classification scheme that controls the level of sensitivity against
reassignment. We demonstrate that our algorithm is convergent and superior to
the direct application of a generic alternative such as principal component
analysis. On several popular datasets for motion segmentation and face
clustering pervasively used in the sparse subspace clustering literature the
proposed method is shown to reduce greatly the incidence of clustering errors
while introducing negligible disturbance to the data points already correctly
clustered.
