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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.
Data embedding, graph connectivity, manifold learning, network flow.

L. Yang, "Building k-Connected Neighborhood Graphs for Isometric Data Embedding," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 28, no. , pp. 827-831, 2006.
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