Mathematics of the Neural Response

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. Communicated by Felipe Cucker. S. Smale Toyota Technological Institute at Chicago and University of California, Berkeley, CA, USA e-mail: [email protected] L. Rosasco CBCL, McGovern Institute, MIT & DISI, Università di Genova, Cambridge, MA, USA e-mail: [email protected] J. Bouvrie ( ) CBCL, Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA e-mail: [email protected] A. Caponnetto Department of Mathematics, City University of Hong Kong, Hong Kong, China e-mail: [email protected] T. Poggio CBCL, McGovern Institute, CSAIL, BCS, Massachusetts Institute of Technology, Cambridge, MA, USA e-mail: [email protected]