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
Sammon's Nonlinear Mapping Using Geodesic Distances
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 2 - Volume 02
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
Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets
IEEE Transactions on Neural Networks
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
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Neighborhood graph construction is usually the first step in algorithms for isometric data embedding and manifold learning that cope with the problem of projecting high dimensional data to a low space. This paper begins by explaining the algorithmic fundamentals of techniques for isometric data embedding and derives a general classification of these techniques. We will see that the nearest neighbor approaches commonly used to construct neighborhood graphs do not guarantee connectedness of the constructed neighborhood graphs and, consequently, may cause an algorithm fail to project data to a single low dimensional coordinate system. In this paper, we review three existing methods to construct k-edge-connected neighborhood graphs and propose a new method to construct k-connected neighborhood graphs. These methods are applicable to a wide range of data including data distributed among clusters. Their features are discussed and compared through experiments.