LargeScale Sparse Subspace Clustering Using Landmarks. Subspace clustering methods based on expressing each data point as a linear combination of all other points in a dataset are popular unsupervised learning techniques. However, existing methods incur high computational complexity on largescale datasets as they require solving an expensive optimization problem and performing spectral clustering on large affinity matrices. This paper presents an efficient approach to subspace clustering by selecting a small subset of the input data called landmarks. The resulting subspace clustering method in the reduced domain runs in linear time with respect to the size of the original data. Numerical experiments on synthetic and real data demonstrate the effectiveness of our method.

Nonnegative SelfRepresentation with a Fixed Rank Constraint for Subspace Clustering Abstract   A number of approaches to graphbased subspace clustering, which assumes that the clustered data points were drawn from an unknown union of multiple subspaces, have been proposed in recent years. Despite their successes in computer vision and data mining, most neglect to simultaneously consider global and local information, which may improve clustering performance. On the other hand, the number of connected components reflected by the learned affinity matrix is commonly inconsistent with the true number of clusters. To this end, we propose an adaptive affinity matrix learning method, nonnegative selfrepresentation with a fixed rank constraint (NSFRC), in which the nonnegative selfrepresentation and an adaptive distance regularization jointly uncover the intrinsic structure of data. In particular, a fixed rank constraint as a prior is imposed on the Laplacian matrix associated with the data representation coefficients to urge the true number of clusters to exactly equal the number of connected components in the learned affinity matrix. Also, we derive an efficient iterative algorithm based on an augmented Lagrangian multiplier to optimize NSFRC. Extensive experiments conducted on realworld benchmark datasets demonstrate the superior performance of the proposed method over some stateoftheart approaches.