  Subspace clustering refers to the problem of clustering high-dimensional data
into a union of low-dimensional subspaces. Current subspace clustering
approaches are usually based on a two-stage framework. In the first stage, an
affinity matrix is generated from data. In the second one, spectral clustering
is applied on the affinity matrix. However, the affinity matrix produced by
two-stage methods cannot fully reveal the similarity between data points from
the same subspace (intra-subspace similarity), resulting in inaccurate
clustering. Besides, most approaches fail to solve large-scale clustering
problems due to poor efficiency. In this paper, we first propose a new scalable
sparse method called Iterative Maximum Correlation (IMC) to learn the affinity
matrix from data. Then we develop Piecewise Correlation Estimation (PCE) to
densify the intra-subspace similarity produced by IMC. Finally we extend our
work into a Sparse-Dense Subspace Clustering (SDSC) framework with a dense
stage to optimize the affinity matrix for two-stage methods. We show that IMC
is efficient when clustering large-scale data, and PCE ensures better
performance for IMC. We show the universality of our SDSC framework as well.
Experiments on several data sets demonstrate the effectiveness of our
approaches. Moreover, we are the first one to apply densification on affinity
matrix before spectral clustering, and SDSC constitutes the first attempt to
build a universal three-stage subspace clustering framework.
