SPLX-Perm: A Novel Permutation-Based Representation for Approximate Metric Search
Abstract
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.
Keywords
Approximate metric search Permutation-based indexing Metric embedding n-point property n-Simplex projectionNotes
Acknowledgements
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.
References
- 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). https://doi.org/10.1007/978-3-319-46759-7_15CrossRefGoogle Scholar
- 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). https://doi.org/10.1007/978-3-319-46759-7_7CrossRefGoogle Scholar
- 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). https://doi.org/10.1007/978-3-319-11988-5_4CrossRefGoogle Scholar
- 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.Babenko, A., Lempitsky, V.: The inverted multi-index. IEEE Trans. Pattern Anal. Mach. Intell. 37(6), 1247–1260 (2015)CrossRefGoogle Scholar
- 6.Blumenthal, L.M.: Theory and Applications of Distance Geometry. Clarendon Press, Oxford (1953)zbMATHGoogle Scholar
- 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.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.Connor, R., Vadicamo, L., Cardillo, F.A., Rabitti, F.: Supermetric search. Inf. Syst. 80, 108–123 (2018)CrossRefGoogle Scholar
- 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). https://doi.org/10.1007/978-3-319-68474-1_7CrossRefGoogle Scholar
- 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.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.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.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). https://doi.org/10.1007/978-3-662-49214-7_2CrossRefGoogle Scholar
- 15.Zezula, P., Amato, G., Dohnal, V., Batko, M.: Similarity Search: The Metric Space Approach, vol. 32. Springer, Boston (2006). https://doi.org/10.1007/0-387-29151-2CrossRefzbMATHGoogle Scholar
- 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