SIAM Review
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
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
Unsupervised learning of image manifolds by semidefinite programming
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Unsupervised Learning of Image Manifolds by Semidefinite Programming
International Journal of Computer Vision
A duality view of spectral methods for dimensionality reduction
ICML '06 Proceedings of the 23rd international conference on Machine learning
Regression on manifolds using kernel dimension reduction
Proceedings of the 24th international conference on Machine learning
A sensorimotor approach to sound localization
Neural Computation
MLDM '07 Proceedings of the 5th international conference on Machine Learning and Data Mining in Pattern Recognition
Manifold Learning: The Price of Normalization
The Journal of Machine Learning Research
An introduction to nonlinear dimensionality reduction by maximum variance unfolding
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Manifold-based learning and synthesis
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Dimensionality Estimation, Manifold Learning and Function Approximation using Tensor Voting
The Journal of Machine Learning Research
Embedding new data points for manifold learning via coordinate propagation
PAKDD'07 Proceedings of the 11th Pacific-Asia conference on Advances in knowledge discovery and data mining
Multilevel manifold learning with application to spectral clustering
CIKM '10 Proceedings of the 19th ACM international conference on Information and knowledge management
Manifold topological multi-resolution analysis method
Pattern Recognition
Front end analysis of speech recognition: a review
International Journal of Speech Technology
Ensemble-Based discriminant manifold learning for face recognition
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part I
Riemannian manifold learning for nonlinear dimensionality reduction
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Image Dimensionality Reduction Based on the Intrinsic Dimension and Parallel Genetic Algorithm
International Journal of Cognitive Informatics and Natural Intelligence
Dimensionality reduction by low-rank embedding
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Supervised Distance Preserving Projections
Neural Processing Letters
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Many unsupervised algorithms for nonlinear dimensionality reduction, such as locally linear embedding (LLE) and Laplacian eigenmaps, are derived from the spectral decompositions of sparse matrices. While these algorithms aim to preserve certain proximity relations on average, their embeddings are not explicitly designed to preserve local features such as distances or angles. In this paper, we show how to construct a low dimensional embedding that maximally preserves angles between nearby data points. The embedding is derived from the bottom eigenvectors of LLE and/or Laplacian eigenmaps by solving an additional (but small) problem in semidefinite programming, whose size is independent of the number of data points. The solution obtained by semidefinite programming also yields an estimate of the data's intrinsic dimensionality. Experimental results on several data sets demonstrate the merits of our approach.