Abstract
Let \(\mathbb{U}\) be a set of elements and d a distance function defined among them. Let NN k (u) be the k elements in \(\mathbb{U}-\{u\}\) having the smallest distance to u. The k-nearest neighbor graph (k nng) is a weighted directed graph \(G(\mathbb{U},E)\) such that E = {(u,v), v ∈ NN k (u)}. Several k nng construction algorithms are known, but they are not suitable to general metric spaces. We present a general methodology to construct k nngs that exploits several features of metric spaces. Experiments suggest that it yields costs of the form c 1 n 1.27 distance computations for low and medium dimensional spaces, and c 2 n 1.90 for high dimensional ones.
Supported in part by Millennium Nucleus Center for Web Research, Grant P04-067-F, Mideplan, Chile; and CONACyT, Mexico.
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Paredes, R., Chávez, E., Figueroa, K., Navarro, G. (2006). Practical Construction of k-Nearest Neighbor Graphs in Metric Spaces. In: Àlvarez, C., Serna, M. (eds) Experimental Algorithms. WEA 2006. Lecture Notes in Computer Science, vol 4007. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11764298_8
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DOI: https://doi.org/10.1007/11764298_8
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