SPLX-Perm: A Novel Permutation-Based Representation for Approximate Metric Search

  • Lucia VadicamoEmail author
  • Richard Connor
  • Fabrizio Falchi
  • Claudio Gennaro
  • Fausto Rabitti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11807)


Many approaches for approximate metric search rely on a permutation-based representation of the original data objects. The main advantage of transforming metric objects into permutations is that the latter can be efficiently indexed and searched using data structures such as inverted-files and prefix trees. Typically, the permutation is obtained by ordering the identifiers of a set of pivots according to their distances to the object to be represented. In this paper, we present a novel approach to transform metric objects into permutations. It uses the object-pivot distances in combination with a metric transformation, called n-Simplex projection. The resulting permutation-based representation, named SPLX-Perm, is suitable only for the large class of metric space satisfying the n-point property. We tested the proposed approach on two benchmarks for similarity search. Our preliminary results are encouraging and open new perspectives for further investigations on the use of the n-Simplex projection for supporting permutation-based indexing.


Approximate metric search Permutation-based indexing Metric embedding n-point property n-Simplex projection 



This work was partially supported by VISECH ARCO-CNR, CUP B56J17001330004, the AI4EU project, funded by the EC (H2020 - Contract n. 825619), and the Short-Term-Mobility (STM) program of the CNR.


  1. 1.
    Amato, G., Falchi, F., Gennaro, C., Rabitti, F.: YFCC100M-HNfc6: a large-scale deep features benchmark for similarity search. In: Amsaleg, L., Houle, M.E., Schubert, E. (eds.) SISAP 2016. LNCS, vol. 9939, pp. 196–209. Springer, Cham (2016). Scholar
  2. 2.
    Amato, G., Falchi, F., Gennaro, C., Vadicamo, L.: Deep permutations: deep convolutional neural networks and permutation-based indexing. In: Amsaleg, L., Houle, M.E., Schubert, E. (eds.) SISAP 2016. LNCS, vol. 9939, pp. 93–106. Springer, Cham (2016). Scholar
  3. 3.
    Amato, G., Falchi, F., Rabitti, F., Vadicamo, L.: Some theoretical and experimental observations on permutation spaces and similarity search. In: Traina, A.J.M., Traina, C., Cordeiro, R.L.F. (eds.) SISAP 2014. LNCS, vol. 8821, pp. 37–49. Springer, Cham (2014). Scholar
  4. 4.
    Amato, G., Gennaro, C., Savino, P.: MI-file: using inverted files for scalable approximate similarity search. Multimed. Tools Appl. 71(3), 1333–1362 (2014)CrossRefGoogle Scholar
  5. 5.
    Babenko, A., Lempitsky, V.: The inverted multi-index. IEEE Trans. Pattern Anal. Mach. Intell. 37(6), 1247–1260 (2015)CrossRefGoogle Scholar
  6. 6.
    Blumenthal, L.M.: Theory and Applications of Distance Geometry. Clarendon Press, Oxford (1953)zbMATHGoogle Scholar
  7. 7.
    Chavez, E., Figueroa, K., Navarro, G.: Effective proximity retrieval by ordering permutations. IEEE Trans. Pattern Anal. Mach. Intell. 30(9), 1647–1658 (2008)CrossRefGoogle Scholar
  8. 8.
    Connor, R., Cardillo, F.A., Vadicamo, L., Rabitti, F.: Hilbert exclusion: improved metric search through finite isometric embeddings. ACM Trans. Inf. Syst. 35(3), 17:1–17:27 (2016)CrossRefGoogle Scholar
  9. 9.
    Connor, R., Vadicamo, L., Cardillo, F.A., Rabitti, F.: Supermetric search. Inf. Syst. 80, 108–123 (2018)CrossRefGoogle Scholar
  10. 10.
    Connor, R., Vadicamo, L., Rabitti, F.: High-dimensional simplexes for supermetric search. In: Beecks, C., Borutta, F., Kröger, P., Seidl, T. (eds.) SISAP 2017. LNCS, vol. 10609, pp. 96–109. Springer, Cham (2017). Scholar
  11. 11.
    Esuli, A.: Use of permutation prefixes for efficient and scalable approximate similarity search. Inf. Process. Manag. 48(5), 889–902 (2012)CrossRefGoogle Scholar
  12. 12.
    Fagin, R., Kumar, R., Sivakumar, D.: Comparing top k lists. In: Proceedings of SODA 2003, pp. 28–36. Society for Industrial and Applied Mathematics (2003)Google Scholar
  13. 13.
    Jégou, H., Douze, M., Schmid, C.: Product quantization for nearest neighbor search. IEEE Trans. Pattern Anal. Mach. Intell. 33(1), 117–128 (2011)CrossRefGoogle Scholar
  14. 14.
    Novak, D., Zezula, P.: PPP-codes for large-scale similarity searching. In: Hameurlain, A., Küng, J., Wagner, R., Decker, H., Lhotska, L., Link, S. (eds.) Transactions on Large-Scale Data- and Knowledge-Centered Systems XXIV. LNCS, vol. 9510, pp. 61–87. Springer, Heidelberg (2016). Scholar
  15. 15.
    Zezula, P., Amato, G., Dohnal, V., Batko, M.: Similarity Search: The Metric Space Approach, vol. 32. Springer, Boston (2006). Scholar
  16. 16.
    Zhou, B., Lapedriza, A., Xiao, J., Torralba, A., Oliva, A.: Learning deep features for scene recognition using places database. In: Proceedings of NIPS 2014, pp. 487–495. Curran Associates, Inc. (2014)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Lucia Vadicamo
    • 1
    Email author
  • Richard Connor
    • 2
  • Fabrizio Falchi
    • 1
  • Claudio Gennaro
    • 1
  • Fausto Rabitti
    • 1
  1. 1.Institute of Information Science and Technologies (ISTI)PisaItaly
  2. 2.Division of Mathematics and Computing ScienceUniversity of StirlingStirlingScotland

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