  This paper studies the subspace segmentation problem. Given a set of data
points drawn from a union of subspaces, the goal is to partition them into
their underlying subspaces they were drawn from. The spectral clustering method
is used as the framework. It requires to find an affinity matrix which is close
to block diagonal, with nonzero entries corresponding to the data point pairs
from the same subspace. In this work, we argue that both sparsity and the
grouping effect are important for subspace segmentation. A sparse affinity
matrix tends to be block diagonal, with less connections between data points
from different subspaces. The grouping effect ensures that the highly corrected
data which are usually from the same subspace can be grouped together. Sparse
Subspace Clustering (SSC), by using $\ell^1$-minimization, encourages sparsity
for data selection, but it lacks of the grouping effect. On the contrary,
Low-Rank Representation (LRR), by rank minimization, and Least Squares
Regression (LSR), by $\ell^2$-regularization, exhibit strong grouping effect,
but they are short in subset selection. Thus the obtained affinity matrix is
usually very sparse by SSC, yet very dense by LRR and LSR.
  In this work, we propose the Correlation Adaptive Subspace Segmentation
(CASS) method by using trace Lasso. CASS is a data correlation dependent method
which simultaneously performs automatic data selection and groups correlated
data together. It can be regarded as a method which adaptively balances SSC and
LSR. Both theoretical and experimental results show the effectiveness of CASS.
