  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.
