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Moreover, its generalization risk bound is tighter than that of LapRLS in terms of the Rademacher complexity.
This is a version of the well-known Hajek-Le Cam minimax risk bound (see, e.g., Ibragimov and Has'minskii (1981), Theorem 2.12.1).
More importantly, we have demonstrated that the proposed multi-view approach generally has a tighter generalization risk bound than its single-view one in terms of the Rademacher complexity analysis.
The characters of the RMultiV-MHKS are: (1) distributing more weight to the favorable views which can reflect the property of the problem; (2) owning a tighter generalization risk bound than its corresponding single-view learning machine in terms of the Rademacher complexity; (3) having a statistically superior classification performance to the original MultiV-MHKS.
Therefore, according to the structural risk minimization inductive principle, the training of an SVM is to minimize the guaranteed risk bound, min w,b,e ϕ (w,b,e) = 1 2 W T W + 1 2 C ∑ i = 1 1 e i 2, subject to the constraints yi[< w, xi > + b] ≥ 1 - ei, i = 1,... , l
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