Skip to main content
SpringerLink
Log in

An application of formal concept analysis to semantic neural decoding

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

This paper proposes a novel application of Formal Concept Analysis (FCA) to neural decoding: the semantic relationships between the neural representations of large sets of stimuli are explored using concept lattices. In particular, the effects of neural code sparsity are modelled using the lattices. An exact Bayesian approach is employed to construct the formal context needed by FCA. This method is explained using an example of neurophysiological data from the high-level visual cortical area STSa. Prominent features of the resulting concept lattices are discussed, including indications for hierarchical face representation and a product-of-experts code in real neurons. The robustness of these features is illustrated by studying the effects of scaling the attributes.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Georgopoulos, A.P., Schwartz, A.B., Kettner, R.E.: Neuronal population coding of movement direction. Science 233(4771), 1416–1419 (1986)

    Article  Google Scholar 

  2. Földiák, P.: The ‘ideal homunculus’: statistical inference from neural population responses. In: Eeckmann, F., Bower, J. (eds.) Computation and Neural Systems, pp. 55–60. Kluwer, Norwell (1993)

    Google Scholar 

  3. Oram, M.W., Földiák, P., Perrett, D.I., Sengpiel, F.: The ‘ideal homunculus’: decoding neural population signals. Trends Neurosci. 21, 259–265 (1998)

    Article  Google Scholar 

  4. Quiroga, R.Q., Reddy, L., Koch, C., Fried, I.: Decoding visual inputs from multiple neurons in the human temporal lobe. J. Neurophysiol. 98(4), 1997–2007 (2007)

    Article  Google Scholar 

  5. Duda, O.R., Hart, P.E., Stork, D.G.: Pattern Classification. Wiley, New York (2001)

    MATH  Google Scholar 

  6. Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, New York (1991)

    Book  MATH  Google Scholar 

  7. Földiák, P.: Sparse neural representation for semantic indexing. In: XIII Conference of the European Society of Cognitive Psychology (ESCOP-2003). http://www.st-andrews.ac.uk/~pf2/escopill2.pdf (2003)

  8. Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel, Dordrecht-Boston (1982)

    Google Scholar 

  9. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer (1999)

  10. Ganter, B., Stumme, G., Wille, R. (eds.): Formal concept analysis, foundations and applications. In: Lecture Notes in Computer Science, vol. 3626. Springer (2005)

  11. Priss, U.: Formal concept analysis in information science. Annu. Rev. Inf. Sci. Technol. 40, 521–543 (2006)

    Article  Google Scholar 

  12. Földiák, P., Endres, D.: Sparse coding. Scholarpedia 3(1), 2984. http://www.scholarpedia.org/article/Sparse_coding (2008)

    Article  Google Scholar 

  13. Földiák, P.: Forming sparse representations by local anti-Hebbian learning. Biol. Cybern. 64, 165–170 (1990)

    Article  Google Scholar 

  14. Földiák, P.: Sparse coding in the primate cortex. In: Arbib, M.A. (ed.) The Handbook of Brain Theory and Neural Networks, 2nd edn., pp. 1064–1068. MIT Press (2002)

  15. Olshausen, B.A., Field, D.J., Pelah, A.: Sparse coding with an overcomplete basis set: a strategy employed by V1. Vis. Res. 37(23), 3311–3325 (1997)

    Article  Google Scholar 

  16. Olshausen, B.A.: Learning linear, sparse, factorial codes. Technical Report AIM 1580 (1996)

  17. Simoncelli, E.P., Olshausen, B.A.: Natural image statistics and neural representation. Annu. Rev. Neurosci. 24, 1193–1216 (2001)

    Article  Google Scholar 

  18. Rolls, E.T., Treves, A.: The relative advantages of sparse versus distributed encoding for neuronal networks in the brain. Netw. 1, 407–421 (1990)

    Article  Google Scholar 

  19. Dayan, P., Abbott, L.F.: Theoretical Neuroscience. MIT Press, London, Cambridge (2001)

    MATH  Google Scholar 

  20. Jones, J.P., Palmer, L.A.: An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex. J. Neurophysiol. 58(6), 1233–1258 (1987)

    Google Scholar 

  21. Ringach, D.L.: Spatial structure and symmetry of simple-cell receptive fields in macaque primary visual cortex. J. Neurophysiol. 88, 455–463 (2002)

    Google Scholar 

  22. Földiák, P., Xiao, D., Keysers, C., Edwards, R., Perrett, D.I.: Rapid serial visual presentation for the determination of neural selectivity in area STSa. Prog. Brain Res. 144, 107–116 (2004)

    Article  Google Scholar 

  23. Oram, M.W., Perrett, D.I.: Time course of neural responses discriminating different views of the face and head. J. Neurophysiol. 68(1), 70–84 (1992)

    Google Scholar 

  24. Endres, D., Földiák, P.: Exact Bayesian bin classification: a fast alternative to bayesian classification and its application to neural response analysis. J. Comput. Neurosci. 24(1), 21–35 (2008). doi:10.1007/s10827-007-0039-5

    Article  MathSciNet  Google Scholar 

  25. Endres, D.: Bayesian and information-theoretic tools for neuroscience. Ph.D. thesis, School of Psychology, University of St. Andrews, U.K. http://hdl.handle.net/10023/162 (2006)

  26. Bishop, C.M.: Pattern Recognition and Machine Learning. Springer (2007)

  27. Hinton, G.E.: Products of experts. In: Ninth International Conference on Artificial Neural Networks ICANN 99, number 470 in ICANN (1999)

  28. Kiani, R., Esteky, H., Mirpour, K., Tanaka, K.: Object category structure in response patterns of neuronal population in monkey inferior temporal cortex. J. Neurophysiol. 97(6), 4296–4309 (2007)

    Article  Google Scholar 

  29. Földiák, P.: Neural coding: non-local but explicit and conceptual. Curr. Biol. 19(19), R904–R906 (2009)

    Article  Google Scholar 

  30. Kay, K.N., Naselaris, T., Prenger, R.J., Gallant, J.L.: Identifying natural images from human brain activity. Nature 452, 352–255 (2008). doi:10.1038/nature06713

    Article  Google Scholar 

  31. Miyawaki, Y., Uchida, H., Yamashita, O., Sato, M., Morito, Y., Tanabe, H., Sadato, N., Kamitani, Y.: Visual image reconstruction from human brain activity using a combination of multiscale local image decoders. Neuron 60, 915–929 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Section for Theoretical Sensomotorics, Department of Cognitive Neurology, Hertie Institute for Clinical Brain Research and Center for Integrative Neuroscience, University Clinic Tübingen, Tübingen, Germany

    Dominik Maria Endres

  2. School of Psychology, University of St Andrews, Scotland, UK

    Peter Földiák

  3. School of Computing, Edinburgh Napier University, Edinburgh, UK

    Uta Priss

Authors
  1. Dominik Maria Endres
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Földiák
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Uta Priss
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dominik Maria Endres.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Endres, D.M., Földiák, P. & Priss, U. An application of formal concept analysis to semantic neural decoding. Ann Math Artif Intell 57, 233–248 (2009). https://doi.org/10.1007/s10472-010-9196-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-010-9196-8

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation