A Multibody Factorization Method for Independently Moving Objects
International Journal of Computer Vision
Mixtures of probabilistic principal component analyzers
Neural Computation
Journal of Optimization Theory and Applications
From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Global Optimization
Lambertian Reflectance and Linear Subspaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Evaluation and Selection of Models for Motion Segmentation
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Acquiring Linear Subspaces for Face Recognition under Variable Lighting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized Principal Component Analysis (GPCA)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Statistical Estimation and Segmentation of Multiple Subspaces
CVPRW '06 Proceedings of the 2006 Conference on Computer Vision and Pattern Recognition Workshop
An Algorithm for Finding Intrinsic Dimensionality of Data
IEEE Transactions on Computers
Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA
International Journal of Computer Vision
Spectral Curvature Clustering (SCC)
International Journal of Computer Vision
Foundations of a Multi-way Spectral Clustering Framework for Hybrid Linear Modeling
Foundations of Computational Mathematics
Motion Segmentation in the Presence of Outlying, Incomplete, or Corrupted Trajectories
IEEE Transactions on Pattern Analysis and Machine Intelligence
Clustering appearances of objects under varying illumination conditions
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Segmentation of Multivariate Mixed Data via Lossy Data Coding and Compression
IEEE Transactions on Pattern Analysis and Machine Intelligence
Greedy feature selection for subspace clustering
The Journal of Machine Learning Research
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We present a simple and fast geometric method for modeling data by a union of affine subspaces. The method begins by forming a collection of local best-fit affine subspaces, i.e., subspaces approximating the data in local neighborhoods. The correct sizes of the local neighborhoods are determined automatically by the Jones' β 2 numbers (we prove under certain geometric conditions that our method finds the optimal local neighborhoods). The collection of subspaces is further processed by a greedy selection procedure or a spectral method to generate the final model. We discuss applications to tracking-based motion segmentation and clustering of faces under different illuminating conditions. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the suggested algorithms on these problems and also on synthetic hybrid linear data as well as the MNIST handwritten digits data; and we demonstrate how to use our algorithms for fast determination of the number of affine subspaces.