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Building k-connected neighborhood graphs for isometric data embedding

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1 Author(s)
Li Yang ; Dept. of Comput. Sci., Western Michigan Univ., Kalamazoo, MI, USA

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 undersampled or nonuniformly distributed.

Published in:

IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:28 ,  Issue: 5 )