Journal of Mathematical Imaging and Vision

, Volume 52, Issue 3, pp 459–468 | Cite as

Explicit Embeddings for Nearest Neighbor Search with Mercer Kernels

  • Anthony Bourrier
  • Florent Perronnin
  • Rémi Gribonval
  • Patrick Pérez
  • Hervé Jégou
Article

Abstract

Many approximate nearest neighbor search algorithms operate under memory constraints, by computing short signatures for database vectors while roughly keeping the neighborhoods for the distance of interest. Encoding procedures designed for the Euclidean distance have attracted much attention in the last decade. In the case where the distance of interest is based on a Mercer kernel, we propose a simple, yet effective two-step encoding scheme: first, compute an explicit embedding to map the initial space into a Euclidean space; second, apply an encoding step designed to work with the Euclidean distance. Comparing this simple baseline with existing methods relying on implicit encoding, we demonstrate better search recall for similar code sizes with the chi-square kernel in databases comprised of visual descriptors, outperforming concurrent state-of-the-art techniques by a large margin.

Keywords

Explicit embeddings Nearest Neighbor search Mercer kernels 

References

  1. 1.
    Boiman, O., Shechman, E., Irani, M.: In defense of nearest neighbor based image classification. In: Proceedings of the Computer Vision and Pattern Recognition (CVPR) (2008)Google Scholar
  2. 2.
    Braun, M.: Accurate error bounds for the eigenvalues of the kernel matrix. J. Mach. Learn. Res. 7, 2303–2328 (2006)MATHMathSciNetGoogle Scholar
  3. 3.
    Charikar, M.: Similarity estimation techniques from rounding algorithms. In: Proceedings of the ACM Symposium on Theory of Computing, STOC (2002)Google Scholar
  4. 4.
    Datar, M., Immorlica, N., Indyk, P., Mirrokni, V.: Locality-sensitive hashing scheme based on p-stable distributions. In: Proceedings of the Symposium on Computational Geometry, pp. 253–262 (2004)Google Scholar
  5. 5.
    Deng, J., Dong, W., Socher, R., Li, L.J., Li, K., Fei-Fei, L.: ImageNet: a large-scale hierarchical image database. In: Proceedings of the Computer Vision and Pattern Recognition CVPR (2009)Google Scholar
  6. 6.
    Gong, Y., Lazebnik, S.: Iterative quantization: A procrustean approach to learning binary codes. In: Proceedings of the Computer Vision and Pattern Recognition CVPR (2011)Google Scholar
  7. 7.
    Gorisse, D., Cord, M., Precioso, F.: Locality-sensitive hashing for chi2 distance. IEEE Trans. Pattern Anal. Mach. Intell. 34(2), 402–409 (2012)Google Scholar
  8. 8.
    Grauman, K., Darrell, T.: The pyramid match kernel: Discriminative classification with sets of image features. In: Proceedings of the International Conference on Computer Vision ICCV (2005)Google Scholar
  9. 9.
    He, J., Liu, W., Chang, S.F.: Scalable similarity search with optimized kernel hashing. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’10, pp. 1129–1138. ACM, New York (2010)Google Scholar
  10. 10.
    Jégou, H., Douze, M., Schmid, C.: Product quantization for nearest neighbor search. Trans. PAMI 33(1), 117–128 (2011)Google Scholar
  11. 11.
    Jégou, H., Douze, M., Schmid, C., Pérez, P.: Aggregating local descriptors into a compact image representation. In: Proceedings of the Computer Vision Pattern Recognition CVPR (2010)Google Scholar
  12. 12.
    Jégou, H., Tavenard, R., Douze, M., Amsaleg, L.: Searching in one billion vectors: re-rank with source coding. In: International Conference on Acoustics, Speech and Signal Processing ICASSP. Prague Czech Republic (2011)Google Scholar
  13. 13.
    Joly, A., Buisson, O.: Random maximum margin hashing. In: Proceedings of the Computer Vision and Pattern Recognition CVPR (2011)Google Scholar
  14. 14.
    Knig, H.: Eigenvalues of compact operators with applications to integral operators. Linear Algebra Appl. 84, 111–122 (1986)Google Scholar
  15. 15.
    Kulis, B., Grauman, K.: Kernelized locality-sensitive hashing for scalable image search. In: Proceedings of the International Conference on Computer Vision ICCV (2009)Google Scholar
  16. 16.
    Lowe, D.: Distinctive image features from scale-invariant keypoints. IJCV 60(2), 91–110 (2004)CrossRefGoogle Scholar
  17. 17.
    Maji, S., Berg, A.: Max-margin additive models for detection. In: Proceedings of the International Conference on Computer Vision ICCV (2009)Google Scholar
  18. 18.
    Mikolajczyk, K., Tuytelaars, T., Schmid, C., Zisserman, A., Matas, J., Schaffalitzky, F., Kadir, T., Gool, L.V.: A comparison of affine region detectors. IJCV 65(1/2), 43–72 (2005)CrossRefGoogle Scholar
  19. 19.
    Muja, M., Lowe, D.G.: Fast approximate nearest neighbors with automatic algorithm configuration. In: VISAPP International Conference on Computer Vision Theory and Applications (2009)Google Scholar
  20. 20.
    Perronnin, F., Sánchez, J., Liu, Y.: Large-scale image categorization with explicit data embedding. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition CVPR (2010)Google Scholar
  21. 21.
    Raginsky, M., Lazebnik, S.: Locality-sensitive binary codes from shift-invariant kernels. In: Proceedings of the Advances in Neural Information Processing Systems NIPS (2010)Google Scholar
  22. 22.
    Schölkopf, B., Smola, A.: Learning with Kernels: Support Vector Machines, Regularization, Optimization and Beyond. MIT Press, Cambridge, MA (2002)Google Scholar
  23. 23.
    Schölkopf, B., Smola, A., Müller, K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput., 10(5), 1299–1319 (1998)Google Scholar
  24. 24.
    Shawe-Taylor, J., Williams, C., Cristianini, N., Kandola, J.: On the eigenspectrum of the gram matrix and the generalization error of kernel pca. IEEE Trans. Inform. Theory 51(7), 2510–2522 (2005)Google Scholar
  25. 25.
    Sivic, J., Zisserman, A.: Video Google: A text retrieval approach to object matching in videos. In: Proceedings of the International Conference on Computer Vision ICCV (2003)Google Scholar
  26. 26.
    Torralba, A., Fergus, R., Weiss, Y.: Small codes and large databases for recognition. In: Proceedings of the Computer Vision and Pattern Recognition CVPR (2008)Google Scholar
  27. 27.
    Vedaldi, A., Zisserman, A.: Efficient additive kernels via explicit feature maps. In: Proceedings of the Computer Vision and Pattern Recognition CVPR (2010)Google Scholar
  28. 28.
    Vedaldi, A., Zisserman, A.: Efficient additive kernels via explicit feature maps. Trans. PAMI 34(3), 480–492 (2012)Google Scholar
  29. 29.
    Weiss, Y., Torralba, A., Fergus, R.: Spectral hashing. In: Proceedings of the Neural Information Processing Systems NIPS (2008)Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Anthony Bourrier
    • 1
  • Florent Perronnin
    • 2
  • Rémi Gribonval
    • 3
  • Patrick Pérez
    • 4
  • Hervé Jégou
    • 3
  1. 1.Gipsa-LabSaint-Martin-d’HèresFrance
  2. 2.Xerox Research Center EuropeMeylanFrance
  3. 3.INRIA Rennes-Bretagne AtlantiqueRennesFrance
  4. 4.TechnicolorCesson-SévignéFrance

Personalised recommendations