Online low-rank representation learning for joint multi-subspace recovery and clustering

Benefiting from global rank constraints, the lowrank representation (LRR) method has been shown to be an effective solution to subspace learning. However, the global mechanism also means that the LRR model is not suitable for handling large-scale data or dynamic data. For large-scale data, the LRR method suffers from high time complexity, and for dynamic data, it has to recompute a complex rank minimization for the entire data set whenever new samples are dynamically added, making it prohibitively expensive. Existing attempts to online LRR either take a stochastic approach or build the representation purely based on a small sample set and treat new input as out-of-sample data. The former often requires multiple runs for good performance and thus takes longer time to run, and the latter formulates online LRR as an out-ofsample classification problem and is less robust to noise. In this paper, a novel online low-rank representation subspace learning method is proposed for both large-scale and dynamic data. The proposed algorithm is composed of two stages: static learning and dynamic updating. In the first stage, the subspace structure is learned from a small number of data samples. In the second stage, the intrinsic principal components of the entire data set are computed incrementally by utilizing the learned subspace structure, and the low-rank representation matrix can also be incrementally solved by an efficient online singular value decomposition (SVD) algorithm. The time complexity is reduced dramatically for large-scale data, and repeated computation is avoided for dynamic problems. We further perform theoretical analysis comparing the proposed online algorithm with the batch LRR method. Finally, experimental results on typical tasks of subspace recovery and subspace clustering show that the proposed algorithm performs comparably or better than batch methods including the batch LRR, and significantly outperforms state-of-the-art online methods

Holistic 3D Reconstruction of Urban Structures from Low-Rank Textures

We introduce a new approach to reconstructing accurate camera geometry and 3D models for urban structures in a holistic fashion, i.e., without relying on extraction or matching of traditional local features such as points and edges. Instead, we use semi-global or global features based on transform invariant low-rank textures, which are ubiquitous in urban scenes. Modern high-dimensional optimization techniques enable us to accurately and robustly recover precise and consistent camera calibration and scene geometry from single or multiple images of the scene. We demonstrate how to construct 3D models of large-scale buildings from sequences of multiple large-baseline uncalibrated images that conventional SFM systems do not apply. 1