Abstract
Spectral clustering based subspace clustering methods
have emerged recently. When the inputs are 2-dimensional
(2D) data, most existing clustering methods convert such
data to vectors as preprocessing, which severely damages
spatial information of the data. In this paper, we propose
a novel subspace clustering method for 2D data with enhanced capability of retaining spatial information for clustering. It seeks two projection matrices and simultaneously
constructs a linear representation of the projected data,
such that the sought projections help construct the most
expressive representation with the most variational information. We regularize our method based on covariance
matrices directly obtained from 2D data, which have much
smaller size and are more computationally amiable. Moreover, to exploit nonlinear structures of the data, a nonlinear
version is proposed, which constructs an adaptive manifold
according to updated projections. The learning processes
of projections, representation, and manifold thus mutually
enhance each other, leading to a powerful data representation. Efficient optimization procedures are proposed, which
generate non-increasing objective value sequence with theoretical convergence guarantee. Extensive experimental results confirm the effectiveness of proposed method.