Skip to main content

Spectral Composition of Semantic Spaces

  • Conference paper
Quantum Interaction (QI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7052))

Included in the following conference series:

  • 764 Accesses

Abstract

Spectral theory in mathematics is key to the success of as diverse application domains as quantum mechanics and latent semantic indexing, both relying on eigenvalue decomposition for the localization of their respective entities in observation space. This points at some implicit “energy” inherent in semantics and in need of quantification. We show how the structure of atomic emission spectra, and meaning in concept space, go back to the same compositional principle, plus propose a tentative solution for the computation of term, document and collection “energy” content.

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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. LeCun, Y., Chopra, S., Hadsell, R.: A tutorial on energy-based learning. In: Predicting Structured Data, pp. 1–59. MIT Press, Cambridge (2006)

    Google Scholar 

  2. Pettersen, B., Hawley, S.: A spectroscopic survey of red dwarf flare stars. Astronomy and Astrophysics 217, 187–200 (1989)

    Google Scholar 

  3. Landauer, T., Dumais, S.: A solution to Plato’s problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge. Psychological Review 104(2), 211–240 (1997)

    Article  Google Scholar 

  4. Gärdenfors, P.: Conceptual spaces: The geometry of thought. The MIT Press, Cambridge (2000)

    Google Scholar 

  5. Salton, G., Wong, A., Yang, C.: A vector space model for information retrieval. Journal of the American Society for Information Science 18(11), 613–620 (1975)

    MATH  Google Scholar 

  6. Deerwester, S., Dumais, S., Furnas, G., Landauer, T., Harshman, R.: Indexing by latent semantic analysis. Journal of the American Society for Information Science 41(6), 391–407 (1990)

    Article  Google Scholar 

  7. Lund, K., Burgess, C.: Producing high-dimensional semantic spaces from lexical co-occurrence. Behavior Research Methods Instruments and Computers 28, 203–208 (1996)

    Article  Google Scholar 

  8. Bruza, P., Woods, J.: Quantum collapse in semantic space: interpreting natural language argumentation. In: Proceedings of QI 2008, 2nd International Symposium on Quantum Interaction. College Publications, Oxford (2008)

    Google Scholar 

  9. Lyons, J.: Introduction to theoretical linguistics. Cambridge University Press, New York (1968)

    Book  Google Scholar 

  10. Harris, Z.: Distributional structure. In: Harris, Z. (ed.) Papers in Structural and Transformational Linguistics. Formal Linguistics, pp. 775–794. Humanities Press, New York (1970)

    Chapter  Google Scholar 

  11. Bruza, P., Cole, R.: Quantum logic of semantic space: An exploratory investigation of context effects in practical reasoning. In: Artemov, S., Barringer, H., d’ Avila Garcez, A.S., Lamb, L., Woods, J. (eds.) We Will Show Them: Essays in Honour of Dov Gabbay. College Publications (2005)

    Google Scholar 

  12. Aerts, D., Czachor, M.: Quantum aspects of semantic analysis and symbolic artificial intelligence. Journal of Physics A: Mathematical and General 37, L123–L132 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kanerva, P., Kristofersson, J., Holst, A.: Random indexing of text samples for latent semantic analysis. In: Proceedings of CogSci 2000, 22nd Annual Conference of the Cognitive Science Society, Philadelphia, PA, USA, vol. 1036 (2000)

    Google Scholar 

  14. Blei, D., Ng, A., Jordan, M.: Latent Dirichlet allocation. The Journal of Machine Learning Research 3, 993–1022 (2003)

    MATH  Google Scholar 

  15. Dhillon, I., Modha, D.: Concept decompositions for large sparse text data using clustering. Machine Learning 42(1), 143–175 (2001)

    Article  MATH  Google Scholar 

  16. Kitto, K., Bruza, P., Sitbon, L.: Generalising unitary time evolution. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds.) QI 2009. LNCS, vol. 5494, pp. 17–28. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  17. Beaver, D.: Presupposition and assertion in dynamic semantics. CSLI publications, Stanford (2001)

    Google Scholar 

  18. van Eijck, J., Visser, A.: Dynamic semantics. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (2010)

    Google Scholar 

  19. Frege, G.: Sense and reference. The Philosophical Review 57(3), 209–230 (1948)

    Article  Google Scholar 

  20. Baker, A.: Computational approaches to the study of language change. Language and Linguistics Compass 2(3), 289–307 (2008)

    MathSciNet  Google Scholar 

  21. Salton, G.: Dynamic information and library processing (1975)

    Google Scholar 

  22. Beeferman, D., Berger, A., Lafferty, J.: A model of lexical attraction and repulsion. In: Proceedings of ACL 1997, 35th Annual Meeting of the Association for Computational Linguistics, Madrid, Spain, pp. 373–380. ACL, Morristown (1997)

    Chapter  Google Scholar 

  23. Shi, S., Wen, J., Yu, Q., Song, R., Ma, W.: Gravitation-based model for information retrieval. In: Proceedings of SIGIR 2005, 28th International Conference on Research and Development in Information Retrieval, Salvador, Brazil, pp. 488–495. ACM, New York (2005)

    Google Scholar 

  24. Dorrer, C., Londero, P., Anderson, M., Wallentowitz, S., Walmsley, I.: Computing with interference: all-optical single-query 50-element database search. In: Proceedings of QELS 2001, Quantum Electronics and Laser Science Conference, pp. 149–150 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wittek, P., Darányi, S. (2011). Spectral Composition of Semantic Spaces. In: Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds) Quantum Interaction. QI 2011. Lecture Notes in Computer Science, vol 7052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24971-6_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24971-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24970-9

  • Online ISBN: 978-3-642-24971-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics