Building connected neighborhood graphs for isometric data embedding
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
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
Building k-Connected Neighborhood Graphs for Isometric Data Embedding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Data embedding techniques and applications
Proceedings of the 2nd international workshop on Computer vision meets databases
A spectral approach to shape-based retrieval of articulated 3D models
Computer-Aided Design
Using graph algebra to optimize neighborhood for isometric mapping
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Shape-based retrieval of articulated 3d models using spectral embedding
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
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Nonlinear data projection based on geodesic distances requires the construction of a neighborhood graph that spans all data points so that the geodesic distance between any pair of data points could be estimated by the graph distance between the pair. This paper proposes an approach for constructing a k-edge connected neighborhood graph. The approach works by repeatedly extracting minimum spanning trees from the complete Euclidean graph of all data points. The constructed neighborhood graph has the following properties: (1) it is k-connected; (2) each point connects to its k nearest neighbors; (3) if the graph is cut into two partitions, the cut edges contain k shortest edges between the two partitions. Experiments show that the presented approach works well for clustered data and outperforms the nearest neighbor approaches used in Isomap for evenly distributed data.