dA {plsdof} | R Documentation |
This function computes the derivative of the function
v\mapsto \frac{w}{\|w\|_A}
with respect to y.
dA(w,A, dw)
w |
vector of length n.
|
A |
square matrix that defines the norm |
dw |
derivative of w with respect to y. As y is a vector of length n, the derivative is a matrix of size nxn. |
The first derivative of the normalization operator is
\frac{\partial}{\partial y}\left(w\mapsto \frac{w}{\|w\|_A}\right)=\frac{1}{\|w\|}\left(I_n - \frac{w w^ \top A}{w^\top w}\right) \frac{\partial w}{\partial y}
the Jacobian matrix of the normalization function. This is a matrix of size nxn.
Nicole Kraemer
Kraemer, N., Braun, M.L. (2007) "Kernelizing PLS, Degrees of Freedom, and Efficient Model Selection", Proceedings of the 24th International Conference on Machine Learning, Omni Press, 441 - 448
w<-rnorm(15) dw<-diag(15) A<-diag(1:15) d.object<-dA(w,A,dw)