Learning high-dimensional nonlinear mapping via compressed sensing

This paper proposes an efficient framework for learning a high-dimensional nonlinear mapping using compressed sensing techniques. Given a training data set of the input and output pairs of the mapping to be learned, our framework reduces both the dimensionalities of the input and output spaces by efficient computation of random projection, and then learns a nonlinear mapping between the low-dimensional input and output data. The high-dimensional nonlinear mapping consists of (i) dimensionality reduction by the random projection of the input data, (ii) low-dimensional nonlinear mapping, and (iii) reconstruction of the high-dimensional output data on the basis of a sparse model. The processes (i) and (ii) construct a single hidden layer feedforward neural network, which can efficiently be learned by the extreme learning machine.