Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Analysis and extension of spectral methods for nonlinear dimensionality reduction
ICML '05 Proceedings of the 22nd international conference on Machine learning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Face Recognition via Sparse Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Exact Matrix Completion via Convex Optimization
Foundations of Computational Mathematics
Unsupervised learning of image manifolds by semidefinite programming
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Fast manifold learning based on riemannian normal coordinates
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Hi-index | 0.00 |
We consider the dimensionality reduction task under the scenario that data vectors lie on (or near by) multiple independent linear subspaces. We propose a robust dimensionality reduction algorithm, named as Low-Rank Embedding(LRE). In LRE, the affinity weights are calculated via low-rank representation and the embedding is yielded by spectral method. Owing to the affinity weight induced from low-rank model, LRE can reveal the subtle multiple subspace structure robustly. In the virtual of spectral method, LRE transforms the subtle multiple subspaces structure into multiple clusters in the low dimensional Euclidean space in which most of the ordinary algorithms can perform well. To demonstrate the advantage of the proposed LRE, we conducted comparative experiments on toy data sets and benchmark data sets. Experimental results confirmed that LRE is superior to other algorithms.