  A l1-norm penalized orthogonal forward regression (l1-POFR) algorithm is
proposed based on the concept of leaveone- out mean square error (LOOMSE).
Firstly, a new l1-norm penalized cost function is defined in the constructed
orthogonal space, and each orthogonal basis is associated with an individually
tunable regularization parameter. Secondly, due to orthogonal computation, the
LOOMSE can be analytically computed without actually splitting the data set,
and moreover a closed form of the optimal regularization parameter in terms of
minimal LOOMSE is derived. Thirdly, a lower bound for regularization parameters
is proposed, which can be used for robust LOOMSE estimation by adaptively
detecting and removing regressors to an inactive set so that the computational
cost of the algorithm is significantly reduced. Illustrative examples are
included to demonstrate the effectiveness of this new l1-POFR approach.
