NOKMeans: Non-Orthogonal K-means Hashing

  • Xiping Fu
  • Brendan McCane
  • Steven Mills
  • Michael Albert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9003)

Abstract

Finding nearest neighbor points in a large scale high dimensional data set is of wide interest in computer vision. One popular and efficient approach is to encode each data point as a binary code in Hamming space using separating hyperplanes. One condition which is often implicitly assumed is that the separating hyperplanes should be mutually orthogonal. With the aim of increasing the representation capability of the hyperplanes when used for indexing, we relax the orthogonality assumption without forsaking the alternate view of using cluster centers to represent the indexing partitions. This is achieved by viewing the data points in a space determined by their distances to the hyperplanes. We show that the proposed method is superior to existing state-of-the-art techniques on several large computer vision datasets.

References

  1. 1.
    Brown, M., Lowe, D.: Recognising panoramas. In: ICCV, pp. 1218–1225 (2003)Google Scholar
  2. 2.
    Frome, A., Singer, Y., Sha, F., Malik, J.: Learning globally-consistent local distance functions for shape-based image retrieval and classification. In: ICCV, pp. 1–8 (2007)Google Scholar
  3. 3.
    Torralba, A., Fergus, R., Weiss, Y.: Small codes and large image databases for recognition. In: CVPR pp. 1–8 (2008)Google Scholar
  4. 4.
    Weber, R., Schek, H., Blott, S.: A quantitative analysis and performance study for similarity-search methods in high-dimensional spaces. In: Proceedings of the 24th VLDB Conference, pp. 194–205 (1998)Google Scholar
  5. 5.
    Indyk, P., Motwani, R.: Approximate nearest neighbors: towards removing the curse of dimensionality. In: Proceedings of the 30th Annual ACM Symposium on Theory of Computing, pp. 604–613 (1998)Google Scholar
  6. 6.
    Charikar, M.S.: Similarity estimation techniques from rounding algorithms. In: Proceedings of the Thiry-Fourth Annual ACM Symposium on Theory of Computing, pp. 380–388 (2002)Google Scholar
  7. 7.
    Shen, F., Shen, C., Shi, Q., Hengel, A.V.D., Tang, Z.: Inductive hashing on manifolds. In: CVPR, pp. 1562–1569 (2013)Google Scholar
  8. 8.
    Datar, M., Immorlica, N., Indyk, P., Mirrokni, V.S.: Locality-sensitive hashing scheme based on p-stable distributions. In: Symposium on Computational Geometry, pp. 252–262 (2004)Google Scholar
  9. 9.
    Raginsky, M., Lazebnik, S.: Locality-sensitive binary codes from shift-invariant kernels. In: NIPS (2009)Google Scholar
  10. 10.
    Yu, F.X., Sanjiv, K., Gong, Y., Chang, S.F.: Circulant binary embedding. In: ICML (2014)Google Scholar
  11. 11.
    Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: NIPS (2001)Google Scholar
  12. 12.
    Weiss, Y., Antonio, T., Robert, F.: Spectral hashing. In: NIPS, pp. 1753–1760 (2008)Google Scholar
  13. 13.
    Jin, Z.M., Hu, Y., Lin, Y., Zhang, D.B., Lin, S.D., Cai, D., Li, X.: Complementary projection hashing. In: ICCV, pp. 257–264 (2013)Google Scholar
  14. 14.
    Kim, S., Kang, Y., Choi, S.: Sequential spectral learning to hash with multiple representations. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part V. LNCS, vol. 7576, pp. 538–551. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  15. 15.
    Xu, H., Wang, J., Li, Z., Zeng, G., Li, S., Yu, N.: Complementary hashing for approximate nearest neighbor search. In: ICCV, pp. 1631–1638 (2011)Google Scholar
  16. 16.
    Wang, J., Kumar, S., Chang, S.F.: Sequential projection learning for hashing with compact codes. In: ICML, pp. 1127–1134 (2010)Google Scholar
  17. 17.
    Liu, W., Wang, J., Kumar, S., Chang, S.F.: Hashing with graphs. In: ICML, pp. 1–8 (2011)Google Scholar
  18. 18.
    Weiss, Y., Fergus, R., Torralba, A.: Multidimensional spectral hashing. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part V. LNCS, vol. 7576, pp. 340–353. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  19. 19.
    Wang, J., Liu, W., Sun, A., Jiang, Y.: Learning hash codes with listwise supervision. In: ICCV, pp. 3032–3039 (2013)Google Scholar
  20. 20.
    Wang, J., Wang, J., Yu, N., Li, S.: Order preserving hashing for approximate nearest neighbor search. In: Proceedings of the 21st ACM International Conference on Multimedia, pp. 133–142 (2013)Google Scholar
  21. 21.
    Norouzi, M., Fleet, D., Salakhutdinov, R.: Hamming distance metric learning. In: NIPS, pp. 1070–1078 (2012)Google Scholar
  22. 22.
    Norouzi, M., Fleet, D.: Minimal loss hashing for compact binary codes. In: ICML, pp. 353–360 (2011)Google Scholar
  23. 23.
    Kulis, B., Darrell, T.: Learning to hash with binary reconstructive embeddings. In: NIPS, pp. 1042–1050 (2009)Google Scholar
  24. 24.
    Wang, J., Kumar, S., Chang, S.F.: Semi-supervised hashing for scalable image retrieval. In: CVPR, pp. 3424–3431 (2010)Google Scholar
  25. 25.
    Liu, W., Wang, J., Ji, R., Jiang, Y., Chang, S.F.: Supervised hashing with kernels. In: CVPR, pp. 2074–2081 (2012)Google Scholar
  26. 26.
    Gong, Y., Lazebnik, S.: Iterative quantization: a procrustean approach to learning binary codes. In: CVPR, pp. 817–824 (2011)Google Scholar
  27. 27.
    Norouzi, M., Fleet, D.: Cartesian k-means. In: CVPR, pp. 3017–3024 (2013)Google Scholar
  28. 28.
    Norouzi, M., Punjani, A., Fleet, D.: Fast search in hamming space with multi-index hashing. In: CVPR, pp. 3108–3115 (2012)Google Scholar
  29. 29.
    Jegou, H., Douze, M., Schmid, C.: Product quantization for nearest neighbor search. IEEE Trans. Pattern Anal. Mach. Intell. 33, 117–128 (2011)CrossRefGoogle Scholar
  30. 30.
    Jegou, H., Tavenard, R., Douze, M., Amsaleg, L.: Searching in one billion vectors: re-rank with source coding. In: ICASSP, pp. 861–864 (2011)Google Scholar
  31. 31.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vision 60, 91–110 (2004)CrossRefGoogle Scholar
  32. 32.
    Jegou, H., Douze, M., Schmid, C.: Improving bag-of-features for large scale image search. Int. J. Comput. Vision 14, 316–336 (2010)CrossRefGoogle Scholar
  33. 33.
    Torralba, A., Fergus, R., Freeman, W.T.: 80 million tiny images: a large database for non-parametric object and scene recognition. IEEE Trans. Pattern Anal. Mach. Intell. 30, 1958–1970 (2008)CrossRefGoogle Scholar
  34. 34.
    Jegou, H., Douze, M., Schmid, C.: Hamming embedding and weak geometric consistency for large scale image search. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part I. LNCS, vol. 5302, pp. 304–317. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  35. 35.
    Griffin, G., Holub, A., Perona, P.: Caltech-256 object category dataset. Technical report, pp. 1–20 (2007)Google Scholar
  36. 36.
    Vedaldi, A., Fulkerson, B.: VLFeat: an open and portable library of computer vision algorithms. In: Proceedings of the International Conference on Multimedia, pp. 1469–1472 (2008)Google Scholar
  37. 37.
    He, K., Wen, F., Sun, J.: K-means hashing: an affinity-preserving quantization method for learning binary compact codes. In: CVPR, pp. 2938–2945 (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Xiping Fu
    • 1
  • Brendan McCane
    • 1
  • Steven Mills
    • 1
  • Michael Albert
    • 1
  1. 1.Department of Computer ScienceUniversity of OtagoDunedinNew Zealand

Personalised recommendations