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The generalized OSH is the solution of minimizing 1 2 w · w + C ∑ i = 1 N ξ i (13).
It follows that maximizing L x) is equivalent to minimizing (1) which we call the score.
Minimizing the trace-norm of Z = WH T is equivalent to minimizing 1 2 (| W | F 2 + | H | F 2 ).
The mean vector, bases, and the corresponding projections can be estimated by maximizing the data likelihood which is an optimization problem equivalent to minimizing (1).
According to learning theory [ 26], minimizing 1 n w T (X T P X ) w corresponds to empirical risk minimization, whereas minimizing the objective in Eq. (10) corresponds to structural risk minimization that improves the generalizability of the resultant model.
Maximizing the margin is therefore equivalent to minimizing: (1) subject to the constraints: (2) As a constrained optimization problem, the above formulation can be reduced to minimization of a Lagrange function, consisting of the sum of the objective function and the m constraints multiplied by their respective Lagrange multipliers, (that satisfy ).
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The LR method focuses on minimizing (R^2).
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