Metric Embedding into the Hamming Space with the n-Simplex Projection
Abstract
Transformations of data objects into the Hamming space are often exploited to speed-up the similarity search in metric spaces. Techniques applicable in generic metric spaces require expensive learning, e.g., selection of pivoting objects. However, when searching in common Euclidean space, the best performance is usually achieved by transformations specifically designed for this space. We propose a novel transformation technique that provides a good trade-off between the applicability and the quality of the space approximation. It uses the n-Simplex projection to transform metric objects into a low-dimensional Euclidean space, and then transform this space to the Hamming space. We compare our approach theoretically and experimentally with several techniques of the metric embedding into the Hamming space. We focus on the applicability, learning cost, and the quality of search space approximation.
Keywords
Sketch Metric search Metric embedding n-point propertyNotes
Acknowledgements
The work was partially supported by VISECH ARCO-CNR, CUP B56J17001330004, and AI4EU project, funded by the EC (H2020 - Contract n. 825619). This research was supported by ERDF “CyberSecurity, CyberCrime and Critical Information Infrastructures Center of Excellence” (No. CZ.02.1.01/0.0/0.0/ 16_019/0000822).
References
- 1.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
- 2.Beecks, C., Uysal, M.S., Seidl, T.: Signature quadratic form distance. In: Proceedings of the ACM-CIVR 2010, pp. 438–445. ACM (2010)Google Scholar
- 3.Blumenthal, L.M.: Theory and Applications of Distance Geometry. Clarendon Press, Oxford (1953)zbMATHGoogle Scholar
- 4.Cao, Y., et al.: Binary hashing for approximate nearest neighbor search on big data: a survey. IEEE Access 6, 2039–2054 (2018)CrossRefGoogle Scholar
- 5.Charikar, M.S.: Similarity estimation techniques from rounding algorithms. In: Proceedings of ACM-STOC 2002. ACM (2002)Google Scholar
- 6.Chávez, E., Figueroa, K., Navarro, G.: Effective proximity retrieval by ordering permutations. IEEE Trans. Pattern Anal. Mach. Intell. 30(9), 1647–1658 (2008)CrossRefGoogle Scholar
- 7.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
- 8.Connor, R., Vadicamo, L., Cardillo, F.A., Rabitti, F.: Supermetric search. Inf. Syst. 80, 108–123 (2018)CrossRefGoogle Scholar
- 9.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, Heidelberg (2017). https://doi.org/10.1007/978-3-319-68474-1_7CrossRefGoogle Scholar
- 10.Donahue, J., et al.: DeCAF: a deep convolutional activation feature for generic visual recognition. In: Proceedings of ICML 2014, vol. 32, pp. 647–655 (2014)Google Scholar
- 11.Douze, M., Jégou, H., Perronnin, F.: Polysemous codes. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9906, pp. 785–801. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46475-6_48CrossRefGoogle Scholar
- 12.Gong, Y., Lazebnik, S., Gordo, A., Perronnin, F.: Iterative quantization: a procrustean approach to learning binary codes for large-scale image retrieval. IEEE Trans. Pattern Anal. Mach. Intell. 35(12), 2916–2929 (2013)CrossRefGoogle Scholar
- 13.Gordo, A., Perronnin, F., Gong, Y., Lazebnik, S.: Asymmetric distances for binary embeddings. IEEE Trans. Pattern Anal. Mach. Intell. 36(1), 33–47 (2014)CrossRefGoogle Scholar
- 14.Indyk, P., Motwani, R.: Approximate nearest neighbors: towards removing the curse of dimensionality. In: Proceedings of ACM STOC, pp. 604–613 (1998)Google Scholar
- 15.Jégou, H., Douze, M., Schmid, C., Pérez, P.: Aggregating local descriptors into a compact image representation. In: Proceedings of CVPR 2010, pp. 3304–3311. IEEE (2010)Google Scholar
- 16.Kruskal, J.B.: Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29(1), 1–27 (1964)MathSciNetCrossRefGoogle Scholar
- 17.Mic, V., Novak, D., Vadicamo, L., Zezula, P.: Selecting sketches for similarity search. In: Proceedings of ADBIS, pp. 127–141 (2018)CrossRefGoogle Scholar
- 18.Mic, V., Novak, D., Zezula, P.: Designing sketches for similarity filtering. In: Proceedings of IEEE ICDM Workshops, pp. 655–662 (2016)Google Scholar
- 19.Mic, V., Novak, D., Zezula, P.: Binary sketches for secondary filtering. ACM Trans. Inf. Syst. 37(1), 1:1–1:28 (2018)CrossRefGoogle Scholar
- 20.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
- 21.Zezula, P., Amato, G., Dohnal, V., Batko, M.: Similarity Search: The Metric Space Approach, vol. 32. Springer, New York (2006). https://doi.org/10.1007/0-387-29151-2CrossRefzbMATHGoogle Scholar