Efficient Construction of Neighborhood Graphs by the Multiple Sorting Method

Details Efficient Construction of Neighborhood Graphs by the Multiple Sorting Method Efficient Construction of Neighborhood Graphs by the Multiple Sorting Method

2009-04-21

arxiv.org/abs/0904.3151v1

Computer Science

Data Structures and Algorithms

Scientific paper

Neighborhood graphs are gaining popularity as a concise data representation in machine learning. However, naive graph construction by pairwise distance calculation takes $O(n^2)$ runtime for $n$ data points and this is prohibitively slow for millions of data points. For strings of equal length, the multiple sorting method (Uno, 2008) can construct an $\epsilon$-neighbor graph in $O(n+m)$ time, where $m$ is the number of $\epsilon$-neighbor pairs in the data. To introduce this remarkably efficient algorithm to continuous domains such as images, signals and texts, we employ a random projection method to convert vectors to strings. Theoretical results are presented to elucidate the trade-off between approximation quality and computation time. Empirical results show the efficiency of our method in comparison to fast nearest neighbor alternatives.

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