Foundations of Computational Mathematics

, Volume 10, Issue 1, pp 67-91

First online:

Mathematics of the Neural Response

  • S. SmaleAffiliated withToyota Technological Institute at Chicago and University of California
  • , L. RosascoAffiliated withCBCL, McGovern Institute, MIT & DISI, Università di Genova
  • , J. BouvrieAffiliated withCBCL, Brain and Cognitive Sciences, Massachusetts Institute of Technology Email author 
  • , A. CaponnettoAffiliated withDepartment of Mathematics, City University of Hong Kong
  • , T. PoggioAffiliated withCBCL, McGovern Institute, CSAIL, BCS, Massachusetts Institute of Technology

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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