Airbus A320 SOP 07Descent

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Therefore, the SRM is going to be useful in order to separate the dependence on mapped vectors from estimation matrices. In the following sub-sections, several SRMs are explicitly shown for different kind of estimation matrices. Kernel Principal Component Analysis - KPCA In this problem, the objective function, to be maximized, represents the projection variance: σ 2 (w ) = where m= 1 NV NV 1 NV −1 ∑ {(φ n − m) T w n =1 } 2 = wT Φ C Φ TC NV - 1 w = w TC w (11) NV ∑i =1 φ n is the mean mapped vector, and C is the covariance matrix.

Then it is simple to obtain: [ ] Φ C = ( φ 1 − m ) & ( φ NV − m ) ∈ MM×NV , (12) and this can be directly written as ΦC = Φ BC , with: (B C ) i j = δ i j − 1 NV ∈ MNV×NV , (13) where δi j is the Kronecker delta. The rank of BC is NV-1 because its column vectors have zero mean. It is well-known that the maximization of (11) is obtained by solving the FCP of C for non-zeros eigenvalues. Then, we can write the solution directly by using expression (8): ~ WC = 1 NV -1 ~ ~ Φ B C VC Λ C−1/2 . (14) ~ As in (8), (14) shows that the set of vectors WC lies in the span of the training vectors Φ, but in this case this is due to the presence of the SRM BC.

And Statistics 2001, pp. 98-104, 2001. , “Fisher Discriminant Analysis with Kernels”, Neural Networks for Signal Processing IX, pp. 41-48, 1999. , “A Mathematical Programming Approach to the Kernel Fisher Analysis”, Neural Networks for Signal Processing IX, pp. 4148, 1999. , “Comparative Study Between Different Eigenspace-based Approaches for Face Recognition”, Lecture Notes in Artificial Intelligence 2275 (AFSS 2002), pp. 178-184, Springer, 2002. , Advances on Kernel Methods – Support Vector Learning, pp.

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