k-Edge Connected Neighborhood Graph for Geodesic Distance Estimation and Nonlinear Data Projection
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 1 - Volume 01
Face Recognition Based on Discriminative Manifold Learning
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 4 - Volume 04
Building k Edge-Disjoint Spanning Trees of Minimum Total Length for Isometric Data Embedding
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
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Using graph algebra to optimize neighborhood for isometric mapping
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Performing locally linear embedding with adaptable neighborhood size on manifold
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IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Adaptive Neighborhood Select Based on Local Linearity for Nonlinear Dimensionality Reduction
ISICA '09 Proceedings of the 4th International Symposium on Advances in Computation and Intelligence
Nonlinear dimension reduction using ISOMap based on class information
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
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Locally centralizing samples for nearest neighbors
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Neurocomputing
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To deal with the highly twisted and folded manifold, this paper propose a geodesic distance-based approach to build the neighborhood graph for isometric embedding. This approach assumes that the neighborhood of a point located at the highly twisted place of the manifold may not be linear so that its neighbors should be determined by geodesic distance. This approach firstly determines the neighborhood for each point using Euclidean distance and then applies the locally estimated geodesic distances to optimize the neighborhood. It increases only linear time complexity. Furthermore the optimized neighborhood can speed up the subsequent embedding process. The proposed approach is simple, general and easy to deal with a wider range of data. The conducted experiments on both synthetic and real data sets validate the approach.