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
Building k Edge-Disjoint Spanning Trees of Minimum Total Length for Isometric Data Embedding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Rapid and brief communication: Incremental locally linear embedding
Pattern Recognition
Supervised locally linear embedding
ICANN/ICONIP'03 Proceedings of the 2003 joint international conference on Artificial neural networks and neural information processing
Fusion of locally linear embedding and principal component analysis for face recognition (FLLEPCA)
ICAPR'05 Proceedings of the Third international conference on Pattern Recognition and Image Analysis - Volume Part II
Self-organized locally linear embedding for nonlinear dimensionality reduction
ICNC'05 Proceedings of the First international conference on Advances in Natural Computation - Volume Part I
Supervised nonlinear dimensionality reduction for visualization and classification
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Local relative transformation with application to isometric embedding
Pattern Recognition Letters
Locally linear embedding: a survey
Artificial Intelligence Review
Improved locally linear embedding by cognitive geometry
LSMS'07 Proceedings of the 2007 international conference on Life System Modeling and Simulation
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Locally linear embedding approach (LLE) is one of most efficient nonlinear dimensionality reduction approaches with good representational capacity for a broader range of manifolds and high computational efficiency. However, LLE and its variants are based on the assumption that the whole data manifold is evenly distributed so that they fail to nicely deal with most real problems that are unevenly distributed. This paper first proposes an approach to judge whether the manifold is even or not, and then logically divides the unevenly distributed manifold into many evenly distributed sub-manifolds, where the neighourhood size for each sub-manifold is automatically determined based on its structure. It is proved, by visualization and classification experiments on benchmark data sets, that our approach is competitive.