Efficient Construction of Neighborhood Graphs by the Multiple Sorting Method
| dc.creator | Uno, Takeaki | |
| dc.creator | Sugiyama, Masashi | |
| dc.creator | Tsuda, Koji | |
| dc.date | 2009-04-21 | |
| dc.date.accessioned | 2026-07-07T13:06:46Z | |
| dc.date.available | 2026-07-07T13:06:46Z | |
| dc.description | 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 $ε$-neighbor graph in $O(n+m)$ time, where $m$ is the number of $ε$-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. | |
| dc.identifier | https://arxiv.org/abs/0904.3151 | |
| dc.identifier | http://arxiv.org/abs/0904.3151 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227887 | |
| dc.subject | Data Structures and Algorithms | |
| dc.subject | Machine Learning | |
| dc.title | Efficient Construction of Neighborhood Graphs by the Multiple Sorting Method | |
| dc.type | text |