Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 2 - Volume 02
Incremental Nonlinear Dimensionality Reduction by Manifold Learning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Building k-Connected Neighborhood Graphs for Isometric Data Embedding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Selection of the optimal parameter value for the Isomap algorithm
Pattern Recognition Letters
Building Connected Neighborhood Graphs for Locally Linear Embedding
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 04
Pattern Recognition
Robust locally linear embedding
Pattern Recognition
Using graph algebra to optimize neighborhood for isometric mapping
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Rapid and brief communication: Incremental locally linear embedding
Pattern Recognition
Clustering-based nonlinear dimensionality reduction on manifold
PRICAI'06 Proceedings of the 9th Pacific Rim international conference on Artificial intelligence
Performing locally linear embedding with adaptable neighborhood size on manifold
PRICAI'06 Proceedings of the 9th Pacific Rim international conference on Artificial intelligence
Supervised locally linear embedding
ICANN/ICONIP'03 Proceedings of the 2003 joint international conference on Artificial neural networks and neural information processing
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Locally linear embedding heavily depends on whether the neighborhood graph represents the underlying geometry structure of the data manifolds. Inspired from the cognitive relativity, this paper proposes a relative transformation that can be applied to build the relative space from the original space of data. In relative space, the noise and outliers will become further away from the normal points, while the near points will become relative closer. Accordingly we determine the neighborhood in the relative space for Hessian locally linear embedding, while the embedding is still performed in the original space. The conducted experiments on both synthetic and real data sets validate the approach.