Skip to main content

Organizing Similarity Spaces Using Metric Hulls

  • Conference paper
  • First Online:
Similarity Search and Applications (SISAP 2021)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 13058))

Included in the following conference series:

Abstract

A novel concept of a metric hull has recently been introduced to encompass a set of objects by a few selected border objects. Following one of the metric-hull computation methods that generate a hierarchy of metric hulls, we introduce a metric index structure for unstructured and complex data, a Metric Hull Tree (MH-tree). We propose a construction of MH-tree by a bulk-loading procedure and outline an insert operation. With respect to the design of the tree, we provide an implementation of an approximate kNN search operation. Finally, we utilized the Profimedia dataset to evaluate various building and ranking strategies of MH-tree and compared the results with M-tree.

The publication of this paper and the follow-up research was supported by the ERDF “CyberSecurity, CyberCrime and Critical Information Infrastructures Center of Excellence” (No. CZ.02.1.01/0.0/0.0/16_019/0000822).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Or even distance spaces where no implicit coordinate system is defined.

References

  1. Amato, G., Gennaro, C., Savino, P.: MI-File: using inverted files for scalable approximate similarity search. Multimedia Tools Appl. 71(3), 1333–1362 (2012). https://doi.org/10.1007/s11042-012-1271-1

    Article  Google Scholar 

  2. Antol, M., Janosova, M., Dohnal, V.: Metric hull as similarity-aware operator for representing unstructured data. Pattern Recognit. Lett. 1–8 (2021). https://doi.org/10.1016/j.patrec.2021.05.011

  3. Batko, M.: Distributed and scalable similarity searching in metric spaces. In: Lindner, W., Mesiti, M., Türker, C., Tzitzikas, Y., Vakali, A.I. (eds.) EDBT 2004. LNCS, vol. 3268, pp. 44–53. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30192-9_5

    Chapter  Google Scholar 

  4. Batko, M., Dohnal, V., Zezula, P.: M-grid: similarity searching in grid. In: P2PIR 2006: International Workshop on Information Retrieval in Peer-to-Peer Networks (2006). https://doi.org/10.1145/1183579.1183583

  5. Böhm, C., Berchtold, S., Keim, D.A.: Searching in high-dimensional spaces: index structures for improving the performance of multimedia databases. ACM Comput. Surv. 33(3), 322–373 (2001). https://doi.org/10.1145/502807.502809

    Article  Google Scholar 

  6. Brin, S.: Near neighbor search in large metric spaces. In: Proceedings of the International Conference on Very Large Data Bases (1995)

    Google Scholar 

  7. Ciaccia, P., Patella, M., Zezula, P.: M-tree: an efficient access method for similarity search in metric spaces. In: Proceedings of the 23rd International Conference on Very Large Data Bases (VLDB), pp. 426–435. Morgan Kaufmann (1997)

    Google Scholar 

  8. Hetland, M.L.: Comparison-based indexing from first principles. arXiv preprint arXiv:1908.06318 (2019)

  9. Jánošová, M.: Representing sets of unstructured data. Master thesis, Masaryk University, Faculty of Informatics (2020). https://is.muni.cz/th/vqton/

  10. Krizhevsky, A., Sutskever, I., Hinton, G.E.: ImageNet classification with deep convolutional neural networks. Commun. ACM (2017). https://doi.org/10.1145/3065386

    Article  Google Scholar 

  11. Laverde, N.A., Cazzolato, M.T., Traina, A.J., Traina, C.: Semantic similarity group by operators for metric data. In: Beecks, C., Borutta, F., Kröger, P., Seidl, T. (eds.) Similarity Search and Applications. LNCS, vol. 10609, pp. 247–261. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68474-1_17

    Chapter  Google Scholar 

  12. Mic, V., Novak, D., Zezula, P.: Binary sketches for secondary filtering. ACM Trans. Inf. Syst. 37(1), 1:1–1:28 (2019). https://doi.org/10.1145/3231936

  13. Moriyama, A., Rodrigues, L.S., Scabora, L.C., Cazzolato, M.T., Traina, A.J.M., Traina, C.: VD-Tree: how to build an efficient and fit metric access method using voronoi diagrams. In: Proceedings of the 36th Annual ACM Symposium on Applied Computing (SAC), pp. 327–335. ACM, New York (2021)

    Google Scholar 

  14. Novak, D., Batko, M., Zezula, P.: Large-scale image retrieval using neural net descriptors. In: Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 1039–1040. ACM (2015)

    Google Scholar 

  15. Paredes, R.U., Navarro, G.: EGNAT: a fully dynamic metric access method for secondary memory. In: 2nd International Workshop on Similarity Search and Applications, SISAP 2009 (2009). https://doi.org/10.1109/SISAP.2009.20

  16. Pola, I.R.V., Traina, C., Traina, A.J.M.: The NOBH-tree: improving in-memory metric access methods by using metric hyperplanes with non-overlapping nodes. Data Knowl. Eng. (2014). https://doi.org/10.1016/j.datak.2014.09.001

    Article  Google Scholar 

  17. Procházka, D.: Indexing structure based on metric hulls. Bachelor thesis, Masaryk University, Faculty of Informatics (2021). https://is.muni.cz/th/jk21s/

  18. Samet, H.: Foundations of Multidimensional and Metric Data Structures. The Morgan Kaufmann Series in Data Management Systems. Morgan Kaufmann (2006)

    Google Scholar 

  19. Skopal, T., Pokorný, J., Snasel, V.: PM-tree: Pivoting Metric Tree for Similarity Search in Multimedia Databases. ADBIS, Computer and Automation Research Institute Hungarian Academy of Science (2004)

    Google Scholar 

  20. Skopal, T., Pokorný, J., Snášel, V.: Nearest neighbours search using the PM-tree. In: Zhou, L., Ooi, B.C., Meng, X. (eds.) DASFAA 2005. LNCS, vol. 3453, pp. 803–815. Springer, Heidelberg (2005). https://doi.org/10.1007/11408079_73

    Chapter  Google Scholar 

  21. Smith, J.R.: MPEG7 standard for multimedia databases. SIGMOD Record (2001). https://doi.org/10.1145/376284.375814

  22. Traina, C., Traina, A., Faloutsos, C., Seeger, B.: Fast indexing and visualization of metric data sets using Slim-trees. IEEE Trans. Knowl. Data Eng. (2002). https://doi.org/10.1109/69.991715

    Article  Google Scholar 

  23. Uhlmann, J.K.: Satisfying general proximity/similarity queries with metric trees. Inf. Process. Lett. 40(4), 175–179 (1991)

    Article  Google Scholar 

  24. Vilar, J.M.: Reducing the overhead of the AESA metric-space nearest neighbour searching algorithm. Inf. Process. Lett. 56(5), 265–271 (1995)

    Article  MathSciNet  Google Scholar 

  25. Zhou, X., Wang, G., Yu, J.X., Yu, G.: M+-tree: a new dynamical multidimensional index for metric spaces. In: Proceedings of the 14th Australasian Database Conference, pp. 161–168 (2003)

    Google Scholar 

  26. Zhou, X., Wang, G., Zhou, X., Yu, G.: BM\(^{+}\)-tree: a hyperplane-based index method for high-dimensional metric spaces. In: Zhou, L., Ooi, B.C., Meng, X. (eds.) DASFAA 2005. LNCS, vol. 3453, pp. 398–409. Springer, Heidelberg (2005). https://doi.org/10.1007/11408079_36

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vlastislav Dohnal .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Jánošová, M., Procházka, D., Dohnal, V. (2021). Organizing Similarity Spaces Using Metric Hulls. In: Reyes, N., et al. Similarity Search and Applications. SISAP 2021. Lecture Notes in Computer Science(), vol 13058. Springer, Cham. https://doi.org/10.1007/978-3-030-89657-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-89657-7_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-89656-0

  • Online ISBN: 978-3-030-89657-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics