Abstract
An approximate algorithm to efficiently solve the k-Closest- Pairs problem in high-dimensional spaces is presented. The method is based on dimensionality reduction of the space ℝd through the Hilbert space filling curve and performs at most d+1 scans of the data set. After each scan, those points whose contribution to the solution has already been analyzed, are eliminated from the data set. The pruning is lossless, in fact the remaining points along with the approximate solution found can be used for the computation of the exact solution. Although we are able to guarantee an O(d 1+ 1/t ) approximation to the solution, where t = 1,…,∞ denotes the used L t metric, experimental results give the exact k-Closest-Pairs for all the data sets considered and show that the pruning of the search space is effective.
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Angiulli, F., Pizzuti, C. (2002). Approximate k-Closest-Pairs with Space Filling Curves. In: Kambayashi, Y., Winiwarter, W., Arikawa, M. (eds) Data Warehousing and Knowledge Discovery. DaWaK 2002. Lecture Notes in Computer Science, vol 2454. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46145-0_13
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DOI: https://doi.org/10.1007/3-540-46145-0_13
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