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
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Recognition
Image distance functions for manifold learning
Image and Vision Computing
Letters: ISOLLE: LLE with geodesic distance
Neurocomputing
Using graph algebra to optimize neighborhood for isometric mapping
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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 nonlinear dimensionality reduction for visualization and classification
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Locally centralizing samples for nearest neighbors
PRICAI'10 Proceedings of the 11th Pacific Rim international conference on Trends in artificial intelligence
Neighborhood selection and eigenvalues for embedding data complex in low dimension
ACIIDS'12 Proceedings of the 4th Asian conference on Intelligent Information and Database Systems - Volume Part I
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Current isometric embedding approaches are topologically unstable when confronted with noisy data, as where the neighborhood is critically distorted. Based on the cognitive law, a relative transformation (RT), which improves the distinction between data points and diminishes the impact of noise on isometric embedding approaches, is proposed. As the constructed space from large scale data by RT is high-dimensional, local relative transformation (LRT) is further proposed. Subsequently, a new isometric embedding approach is developed by using LRT to construct a better neighborhood graph with fewer short-circuit edges, while the embedding is still performed in the original space. This approach has significantly increased performance and reduced running time. The proposed approach was validated by experiments on challenging benchmark data sets.