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Building k-Connected Neighborhood Graphs for Isometric Data Embedding
May 2006 (vol. 28 no. 5)
pp. 827-831
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.

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Index Terms:
Data embedding, graph connectivity, manifold learning, network flow.
Citation:
Li Yang, "Building k-Connected Neighborhood Graphs for Isometric Data Embedding," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 5, pp. 827-831, May 2006, doi:10.1109/TPAMI.2006.89
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