Subspace Segmentation by Successive Approximations: A Method for Low-Rank and High-Rank Data with Missing Entries
This addresses subspace segmentation for incomplete data, which is incremental but provides strong specific gains.
The paper tackles the problem of reconstructing and clustering incomplete high-dimensional data from multiple subspaces, achieving greater reconstruction accuracy than current methods and significantly improving clustering performance.
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic subspace structure. Since we have a non-convex problem, we propose an iterative method to reconstruct the data and provide a sparse similarity affinity matrix. This method is robust to initialization and achieves greater reconstruction accuracy than current methods, which dramatically improves clustering performance. Extensive experiments with synthetic and real data show that our approach leads to significant improvements in the reconstruction and segmentation, outperforming current state of the art for both low and high-rank data.