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Mathematics of the neural response

By Steve Smale, Lorenzo Rosasco, Jake Bouvrie and Andrea Caponnetto


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 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 choos

Year: 2013
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