Foundations of Computational Mathematics

, Volume 10, Issue 1, pp 67–91

Mathematics of the Neural Response

  • S. Smale
  • L. Rosasco
  • J. Bouvrie
  • A. Caponnetto
  • T. Poggio

DOI: 10.1007/s10208-009-9049-1

Cite this article as:
Smale, S., Rosasco, L., Bouvrie, J. et al. Found Comput Math (2010) 10: 67. doi:10.1007/s10208-009-9049-1


We propose a natural image representation, the neural response, motivated by the neuroscience of the visual cortex. The inner product defined by the neural response leads to a similarity measure between functions which we call the derived kernel. Based on a hierarchical architecture, we give a recursive definition of the neural response and associated derived kernel. The derived kernel can be used in a variety of application domains such as classification of images, strings of text and genomics data.


Unsupervised learning Computer vision Kernels 

Mathematics Subject Classification (2000)

68Q32 68T45 68T10 

Copyright information

© SFoCM 2009

Authors and Affiliations

  • S. Smale
    • 1
  • L. Rosasco
    • 2
  • J. Bouvrie
    • 3
  • A. Caponnetto
    • 4
  • T. Poggio
    • 5
  1. 1.Toyota Technological Institute at Chicago and University of CaliforniaBerkeleyUSA
  2. 2.CBCL, McGovern Institute, MIT & DISIUniversità di GenovaCambridgeUSA
  3. 3.CBCL, Brain and Cognitive SciencesMassachusetts Institute of TechnologyCambridgeUSA
  4. 4.Department of MathematicsCity University of Hong KongHong KongChina
  5. 5.CBCL, McGovern Institute, CSAIL, BCSMassachusetts Institute of TechnologyCambridgeUSA