To determine the optimum length of these devices, we maximize the projection of the propagated field in the multimode section onto the desired field profile.
This can be written: More precisely, if k - 1 successive orthogonalizations are performed relatively to the k - 1 vectors q1 · · · qk-1which form an orthonormal basis, one obtains for step k: Then, maximizing the projection norm of x on the subspace spanned by is done by choosing the vector maximizing with.
Maximal projection vs projection of signal on curved surface.
At step k, the subspace of dimension k - 1 previously determined and spanned by fj (1)··· fj (k- 1 is extended by the vector fj (k), which maximizes the projection norm of x on all possible subspaces of dimension k spanned by fj(1)··· fj (k-1 f k-1 f
The canonical discriminant functions are calculated by maximizing a fraction, the projection of a linear function of the variance covariance matrix of between groups to that of the variance covariance matrix within the groups, i.e. maximizing the separation of the groups.
We chose to maximize visualization of projections (terminal boutons) of FR using BDA (10 000 MW) in the present study to allow appropriate comparison with our group of animals in which the same tracer was injected in PMv (Dancause, Barbay, Frost, Plautz, et al. 2006).
For motion capture applications, we define in order to maximize the overlap between the projection of the articulated chain into the images and the human body.
According to Yeung and Ruzzo [57], "PCs are uncorrelated and ordered, such that the kth PC has kth largest variance among all PCs; and the kth PC can be interpreted as the direction that maximizes the variation of the projection of the data points such that it is orthogonal to the first (k-1) PCs".
The vector vco is chosen as to maximize the projection v co H h ext while satisfying the constraints on the traces of K 1 ( 2 ) and Kr.
PCA chooses a dimensionality reduction by linear projection that maximizes the scattering of all projected samples.
