Pruned Bi-directed K-nearest Neighbor Graph for Proximity Search

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9939)

Abstract

In this paper, we address the problems with fast proximity searches for high-dimensional data by using a graph as an index. Graph-based methods that use the k-nearest neighbor graph (KNNG) as an index perform better than tree-based and hash-based methods in terms of search precision and query time. To further improve the performance of the KNNG, the number of edges should be increased. However, increasing the number takes up more memory, while the rate of performance improvement gradually falls off. Here, we propose a pruned bi-directed KNNG (PBKNNG) in order to improve performance without increasing the number of edges. Different directed edges for existing edges between a pair of nodes are added to the KNNG, and excess edges are selectively pruned from each node. We show that the PBKNNG outperforms the KNNG for SIFT and GIST image descriptors. However, the drawback of the KNNG is that its construction cost is fatally expensive. As an alternative, we show that a graph can be derived from an approximate neighborhood graph, which costs much less to construct than a KNNG, in the same way as the PBKNNG and that it also outperforms a KNNG.

References

  1. 1.
    Gionis, A., Indyk, P., Motwani, R.: Similarity search in high dimensions via hashing. In: Proceedings of 25th International Conference on Very Large Data Bases, pp. 518–528 (1999)Google Scholar
  2. 2.
    Datar, M., Immorlica, N., Indyk, P., Mirrokni, V.: Locality-sensitive hashing scheme based on p-stable distributions. In: Proceedings of the 20th Annual Symposium on Computational Geometry, pp. 253–262. ACM (2004)Google Scholar
  3. 3.
    Weiss, Y., Torralba, A., Fergus, R.: Spectral hashing. In: Advances in Neural Information Processing Systems, pp. 1753–1760 (2009)Google Scholar
  4. 4.
    Gong, Y., Lazebnik, S.: Iterative quantization: a procrustean approach to learning binary codes. In: 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 817–824. IEEE (2011)Google Scholar
  5. 5.
    Jegou, H., Douze, M., Schmid, C.: Product quantization for nearest neighbor search. IEEE Trans. Pattern Anal. Mach. Intell. 33(1), 117–128 (2011)CrossRefGoogle Scholar
  6. 6.
    Bentley, J.: Multidimensional binary search trees used for associative searching. Commun. ACM 18, 509–517 (1975)CrossRefMATHGoogle Scholar
  7. 7.
    White, D., Jain, R.: Similarity indexing with the SS-tree. In: Proceedings of 12th International Conference on Data Engineering, pp. 516–523 (1996)Google Scholar
  8. 8.
    Yianilos, P.: Data structures and algorithms for nearest neighbor search in general metric spaces. In: Proceedings of the 4th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 311–321 (1993)Google Scholar
  9. 9.
    Ciaccia, P., Patella, M., Zezula, P.: M-tree: An efficient access method for similarity search in metric spaces. In: Proceedings of International Conference on Very Large Data Bases, pp. 426–435 (1997)Google Scholar
  10. 10.
    Arya, S., Mount, D., Netanyahu, N., Silverman, R., Wu, A.: An optimal algorithm for approximate nearest neighbor searching fixed dimensions. J. ACM 45(6), 891–923 (1998)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Houle, M.E., Sakuma, J.: Fast approximate similarity search in extremely high-dimensional data sets. In: 21st International Conference on Data Engineering (ICDE 2005), pp. 619–630. IEEE (2005)Google Scholar
  12. 12.
    Muja, M., Lowe, D.G.: Scalable nearest neighbor algorithms for high dimensional data. IEEE Trans. Pattern Anal. Mach. Intell. 36(11), 2227–2240 (2014)CrossRefGoogle Scholar
  13. 13.
    Silpa-Anan, C., Hartley, R.: Optimised KD-trees for fast image descriptor matching. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2008, pp. 1–8. IEEE (2008)Google Scholar
  14. 14.
    Nister, D., Stewenius, H.: Scalable recognition with a vocabulary tree. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 2161–2168. IEEE (2006)Google Scholar
  15. 15.
    Arya, S., Mount, D.M.: Approximate nearest neighbor queries in fixed dimensions. In: Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1993, Philadelphia, PA, USA, pp. 271–280. Society for Industrial and Applied Mathematics (1993)Google Scholar
  16. 16.
    Sebastian, T., Kimia, B.: Metric-based shape retrieval in large databases. In: Proceedings of 16th International Conference on Pattern Recognition, vol. 3. 291–296 (2002)Google Scholar
  17. 17.
    Wang, J., Li, S.: Query-driven iterated neighborhood graph search for large scale indexing. In: Proceedings of the 20th ACM International Conference on Multimedia, MM 2012, pp. 179–188. ACM, New York (2012)Google Scholar
  18. 18.
    Hajebi, K., Abbasi-Yadkori, Y., Shahbazi, H., Zhang, H.: Fast approximate nearest-neighbor search with k-nearest neighbor graph. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, pp. 1312–1317 (2011)Google Scholar
  19. 19.
    Dong, W., Moses, C., Li, K.: Efficient k-nearest neighbor graph construction for generic similarity measures. In: Proceedings of the 20th International Conference on World Wide Web, WWW 2011, pp. 577–586. ACM, New York (2011)Google Scholar
  20. 20.
    Iwasaki, M.: Proximity search in metric spaces using approximate k nearest neighbor graph (in Japanese). IPSJ Trans. Database 3(1), 18–28 (2010)Google Scholar
  21. 21.
    Iwasaki, M.: Proximity search using approximate k nearest neighbor graph with a tree structured index (in Japanese). IPSJ J. 52(2), 817–828 (2011)Google Scholar
  22. 22.
    Navarro, G.: Searching in metric spaces by spatial approximation. VLDB J. 11(1), 28–46 (2002)CrossRefGoogle Scholar
  23. 23.
    Lowe, D.G.: Object recognition from local scale-invariant features. In: The Proceedings of the Seventh IEEE International Conference on Computer Vision, vol. 2, pp. 1150–1157. IEEE (1999)Google Scholar
  24. 24.
    Oliva, A., Torralba, A.: Modeling the shape of the scene: a holistic representation of the spatial envelope. Int. J. Comput. Vis. 42(3), 145–175 (2001)CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Yahoo Japan CorporationTokyoJapan

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