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Using the definition of equation 9, we define a new shaping operator as:
![$\displaystyle \mathbf{S}'=\mathbf{L}(\mathbf{S}[\mathbf{d}'_n],\mathbf{S}[\mathbf{d}'_{n-1}]),$](img49.png) |
(12) |
where
is a new version of the commonly defined
shown in equation 6 and
denotes a linear combination operator. This new shaping operation apply a biased combination between the current model and the previous model, thus is thought to be faster.
Substituting
in equation 6 with
in equation 12, and combined with equation 10, we get a faster version of shaping regularization:
![$\displaystyle \mathbf{d}_{n+1} = \mathbf{L}(\mathbf{S}[\mathbf{d}'_n],\mathbf{S}[\mathbf{d}'_{n-1}]).$](img52.png) |
(13) |
The linear combination operator
can be defined as
![$\displaystyle \mathbf{L}(\mathbf{a},\mathbf{b})=\alpha\mathbf{a}+\beta\mathbf{b},$](img54.png) |
(14) |
where
.
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Next: Comparison with the traditional
Up: Theory
Previous: Connection with projection onto
2015-11-24