Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit
This addresses the efficiency and robustness trade-off in subspace clustering for applications like image analysis, though it is incremental as it builds on existing regularization methods.
The paper tackles the problem of subspace clustering by proposing a method based on orthogonal matching pursuit, which achieves a subspace-preserving affinity under broad conditions while being computationally efficient, with experiments showing it achieves the best trade-off between accuracy and efficiency in applications like handwritten digit and face clustering.
Subspace clustering methods based on $\ell_1$, $\ell_2$ or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact both theory and practice. For instance, $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad conditions (e.g., arbitrary subspaces and corrupted data). However, it requires solving a large scale convex optimization problem. On the other hand, $\ell_2$ and nuclear norm regularization provide efficient closed form solutions, but require very strong assumptions to guarantee a subspace-preserving affinity, e.g., independent subspaces and uncorrupted data. In this paper we study a subspace clustering method based on orthogonal matching pursuit. We show that the method is both computationally efficient and guaranteed to give a subspace-preserving affinity under broad conditions. Experiments on synthetic data verify our theoretical analysis, and applications in handwritten digit and face clustering show that our approach achieves the best trade off between accuracy and efficiency.