  Subspace segmentation assumes that data comes from the union of different
subspaces and the purpose of segmentation is to partition the data into the
corresponding subspace. Low-rank representation (LRR) is a classic
spectral-type method for solving subspace segmentation problems, that is, one
first obtains an affinity matrix by solving a LRR model and then performs
spectral clustering for segmentation. This paper proposes a group norm
regularized factorization model (GNRFM) inspired by the LRR model for subspace
segmentation and then designs an Accelerated Augmented Lagrangian Method (AALM)
algorithm to solve this model. Specifically, we adopt group norm regularization
to make the columns of the factor matrix sparse, thereby achieving a purpose of
low rank, which means no Singular Value Decompositions (SVD) are required and
the computational complexity of each step is greatly reduced. We obtain
affinity matrices by using different LRR models and then performing cluster
testing on different sets of synthetic noisy data and real data, respectively.
Compared with traditional models and algorithms, the proposed method is faster
and more robust to noise, so the final clustering results are better. Moreover,
the numerical results show that our algorithm converges fast and only requires
approximately ten iterations.
