  It is a key to construct a similarity graph in graph-oriented subspace
learning and clustering. In a similarity graph, each vertex denotes a data
point and the edge weight represents the similarity between two points. There
are two popular schemes to construct a similarity graph, i.e., pairwise
distance based scheme and linear representation based scheme. Most existing
works have only involved one of the above schemes and suffered from some
limitations. Specifically, pairwise distance based methods are sensitive to the
noises and outliers compared with linear representation based methods. On the
other hand, there is the possibility that linear representation based
algorithms wrongly select inter-subspaces points to represent a point, which
will degrade the performance. In this paper, we propose an algorithm, called
Locally Linear Representation (LLR), which integrates pairwise distance with
linear representation together to address the problems. The proposed algorithm
can automatically encode each data point over a set of points that not only
could denote the objective point with less residual error, but also are close
to the point in Euclidean space. The experimental results show that our
approach is promising in subspace learning and subspace clustering.
