Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Distance-Preserving Projection of High-Dimensional Data for Nonlinear Dimensionality Reduction
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Building k Edge-Disjoint Spanning Trees of Minimum Total Length for Isometric Data Embedding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Building k-edge-connected neighborhood graph for distance-based data projection
Pattern Recognition Letters
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
Comments on " ANew Algorithm for Generating Prime Implicants"
IEEE Transactions on Computers
Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets
IEEE Transactions on Neural Networks
Improving geodesic distance estimation based on locally linear assumption
Pattern Recognition Letters
Local relative transformation with application to isometric embedding
Pattern Recognition Letters
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
Dynamic Neighborhood Selection for Nonlinear Dimensionality Reduction
MDAI '09 Proceedings of the 6th International Conference on Modeling Decisions for Artificial Intelligence
Linear discriminant projection embedding based on patches alignment
Image and Vision Computing
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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Isometric data embedding using geodesic distance requires the construction of a connected neighborhood graph so that the geodesic distance between every pair of data points can be estimated. This paper proposes an approach for constructing k-connected neighborhood graphs. The approach works by applying a greedy algorithm to add each edge, in a nondecreasing order of edge length, to a neighborhood graph if end vertices of the edge are not yet k-connected on the graph. The k-connectedness between vertices is tested using a network flow technique by assigning every vertex a unit flow capacity. This approach is applicable to a wide range of data. Experiments show that it gives better estimation of geodesic distances than other approaches, especially when the data are under-sampled or nonuniformly distributed.