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where
:<math> \rho \big ( \left \Vert \mathbf{x} - \mathbf{c}_i \right \Vert \big ) = \exp \left[ -\beta \left \Vert \mathbf{x} - \mathbf{c}_i \right \Vert ^2 \right] = \exp \left[ -\
Since the input is a [[Scalar (mathematics)|scalar]] rather than a [[Vector (geometric)|vector]], the input dimension is one. We choose the number of basis functions as N=5 and the size of the training set to be 100 exemplars generated by the chaotic time series. The weight <math> \beta </math> is taken to be a constant equal to 5. The weights <math> c_i </math> are five exemplars from the time series. The weights <math> a_i </math> are trained with projection operator training:
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