Mathematics of the neural response - University of Chicago.pdfVIP

November 17, 2008 CBCL Paper November 17, 2008 Mathematics of the neural response ‡ † † Steve Smale , Lorenzo Rosasco , Jake Bouvrie , Andrea Caponnetto , Tomaso Poggio† ‡ Toyota Technological Institute at Chicago and University of California, Berkeley Department of Mathematics, City University of Hong Kong DISI, Universit`a di Genova † CBCL, McGovern Institute, Artificial Intelligence Lab, BCS, MIT Abstract 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. 1 Introduction The goal of this paper is to define a distance function on a space of images which reflects how humans see the images. The distance between two images corresponds to how similar they appear to an observer. Most learning algorithms critically depend on a suitably defined similarity measure, though the theory of learning so far provides no general rule to choose such a similarity measure [19, 4, 11, 5]. In practice, problem specific metrics are often used [16]. In this paper we propose a natural image representation, the neural response, motivate