Multiscale geometric and spectral analysis of plane arrangements

Modeling data by multiple low-dimensional planes is an important problem in many applications such as computer vision and pattern recognition. In the most general setting where only coordinates of the data are given, the problem asks to determine the optimal model parameters (i.e., number of planes and their dimensions), estimate the model planes, and cluster the data accordingly. Though many algorithms have been proposed, most of them need to assume prior knowledge of the model parameters and thus address only the last two components of the problem. In this paper we propose an efficient algorithm based on multiscale SVD analysis and spectral methods to tackle the problem in full generality. We also demonstrate its state-of-the-art performance on both synthetic and real data.