Spatial transformations in the parietal cortex using basis functions *Journal of Cognitive Neuroscience*, Vol. 9, No. 2. (1 March 1997), pp. 222-237, doi:10.1162/jocn.1997.9.2.222 by Alexandre Pouget, Terrence J. Sejnowski

@article{pouget-and-sejnowski-1997, abstract = {Sensorimotor transformations are nonlinear mappings of sensory inputs to motor responses. We explore here the possibility that the responses of single neurons in the parietal cortex serve as basis functions for these transformations. Basis function decomposition is a general method for approximating nonlinear functions that is computationally efficient and well suited for adaptive modification. In particular, the responses of single parietal neurons can be approximated by the product of a Gaussian function of retinal location and a sigmoid function of eye position, called a gain field. A large set of such functions forms a basis set that can be used to perform an arbitrary motor response through a direct projection. We compare this hypothesis with other approaches that are commonly used to model population codes, such as computational maps and vectorial representations. Neither of these alternatives can fully account for the responses of parietal neurons, and they are computationally less efficient for nonlinear transformations. Basis functions also have the advantage of not depending on any coordinate system or reference frame. As a consequence, the position of an object can be represented in multiple reference frames simultaneously, a property consistent with the behavior of hemineglect patients with lesions in the parietal cortex.}, address = {Cambridge, MA, USA}, author = {Pouget, Alexandre and Sejnowski, Terrence J.}, day = {1}, doi = {10.1162/jocn.1997.9.2.222}, journal = {Journal of Cognitive Neuroscience}, keywords = {biology, math, model, motor, multi-modality}, month = mar, number = {2}, pages = {222--237}, posted-at = {2012-04-11 13:37:19}, priority = {2}, publisher = {MIT Press}, title = {Spatial transformations in the parietal cortex using basis functions}, url = {http://dx.doi.org/10.1162/jocn.1997.9.2.222}, volume = {9}, year = {1997} }

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In order to work with spatial information from different sensory modalities and use it for motor control, coordinate transformation must happen at some point during information processing. Pouget and Sejnowski state that in many instances such transformations are non-linear. They argue that functions describing receptive fields and neural activation can be thought of and used as basis functions for the approximation of non-linear functions such as those occurring in sensory-motor coordinate transformation. ⇒