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Isometric data embedding requires construction of a neighborhood graph that spans all data points so that geodesic distance between any pair of data points could be estimated by distance along the shortest path between the pair on the graph. This paper presents an approach for constructing k-edge-connected neighborhood graphs. It works by finding k edge-disjoint spanning trees the sum of whose total lengths is a minimum. Experiments show that it outperforms the nearest neighbor approach for geodesic distance estimation.
Index Terms- Data embedding, dimensionality reduction, manifold learning, minimum spanning tree, neighborhood graph.

L. Yang, "Building k Edge-Disjoint Spanning Trees of Minimum Total Length for Isometric Data Embedding," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 27, no. , pp. 1680-1683, 2005.
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