We prove a few representer theorems for a localised version of the
regularised and multiview support vector machine learning problem introduced by
H.Q.~Minh, L.~Bazzani, and V.~Murino, \textit{Journal of Machine Learning
Research}, \textbf{17}(2016) 1--72, that involves operator valued positive
semidefinite kernels and their reproducing kernel Hilbert spaces. The results
concern general cases when convex or nonconvex loss functions and finite or
infinite dimensional input spaces are considered. We show that the general
framework allows infinite dimensional input spaces and nonconvex loss functions
for some special cases, in particular in case the loss functions are G\^ateaux
differentiable. Detailed calculations are provided for the exponential least
squares loss functions that leads to partially nonlinear problems.

本论文证明了一些 representer 定理，用于处理一般情况下的支持向量机学习问题，该问题涉及到算子值半正定核和它们的再生核希尔伯特空间。在有限和无限维输入空间和凸或非凸损失函数情况下，我们证明了这个普遍框架允许无限维输入空间和某些特殊案例下的非凸损失函数等。对于导致部分非线性问题的指数最小二乘损失函数进行了详细计算。