Augmented Space Linear Model

The linear model uses the space defined by the input to project the target or desired signal and find the optimal set of model parameters. When the problem is nonlinear, the adaption requires nonlinear models for good performance, but it becomes slower and more cumbersome. In this paper, we propose a linear model called Augmented Space Linear Model (ASLM), which uses the full joint space of input and desired signal as the projection space and approaches the performance of nonlinear models. This new algorithm takes advantage of the linear solution, and corrects the estimate for the current testing phase input with the error assigned to the input space neighborhood in the training phase. This algorithm can solve the nonlinear problem with the computational efficiency of linear methods, which can be regarded as a trade off between accuracy and computational complexity. Making full use of the training data, the proposed augmented space model may provide a new way to improve many modeling tasks.