Efficient Construction Of Neighborhood Graphs By The Multiple Sorting Method
Takeaki Uno, Masashi Sugiyama, Koji Tsuda . Arxiv 2009 – 9 citations
[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.