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Commonly used initialization methods for MLDA-TTP are: pseudo-identity matrices (truncated identity matrices) and random matrices. Commonly used initialization methods for MLDA-TVP are: all ones and random vectors. 3 Multilinear Discriminant Analysis 33 based on projections obtained from the n-mode vectors of the input tensor samples [30, 45]. 7 Relationships Between the LDA, MLDA-TTP, and MLDA-TVP To study the relationships between the LDA, MLDA-TTP, and MLDA-TVP, it is beneficial to investigate what are the relationships between VVP, TTP, and TVP first.

Regarding the comparison between LDA and MLDA, there is an interesting observation from this experiment. 3.

U(N) can be written as y = X, U ; it is then straightforward to show Proposition 2. y = X, U = vec(X ), vec(U) = [vec(U)]T vec(X ). Thus, an EMP is equivalent to a linear projection of vec(X ), the vectorized representation of X, on a vector vec(U ). Since U = u(1) ◦ u(2) ◦ · · · ◦ u(N) , Proposition 2 indicates that the EMP is in effect a linear projection with constraint on the projection vector such that it is the vectorized representation of a rank-one tensor. Compared with a projection vector of size I × 1 in VVP specified by I parameters (I = N n=1 In N for an Nth-order tensor), an EMP in TVP can be specified by n=1 In parameters.

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(0, 1, 2, 4) Interpolation by G -splines

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