  The problem of fitting a union of subspaces to a collection of data points
drawn from multiple subspaces is considered in this paper. In the traditional
low rank representation model, the dictionary used to represent the data points
is chosen as the data points themselves and thus the dictionary is corrupted
with noise. This problem is solved in the low rank subspace clustering model
which decomposes the corrupted data matrix as the sum of a clean and
self-expressive dictionary plus a matrix of noise and gross errors. Also, the
clustering results of the low rank representation model can be enhanced by
using a graph of data similarity. This model is called Laplacian regularized
low rank representation model with a graph regularization term added to the
objective function. Inspired from the above two ideas, in this paper a
Laplacian regularized low rank subspace clustering model is proposed. This
model uses a clean dictionary to represent the data points and a graph
regularization term is also incorporated in the objective function.
Experimental results show that, compared with the traditional low rank
representation model, low rank subspace clustering model and several other
state-of-the-art subspace clustering model, the model proposed in this paper
can get better subspace clustering results with lower clustering error.
