Abstract This paper develops a novel framework for a family of correlation classifiers that are reconstructed from uncertain convex programs under data perturbation. Under this framework, correlation classifiers are exploited from the pessimistic viewpoint under possible perturbation of data, and the max-min optimization problem is formulated by simplifying the original model in terms of adaptive uncertainty regions. The proposed model can be formulated as a minimization problem under proper conditions. The proximal majorization-minimization optimization (PMMO) based on Bregman divergences is devised to solve the proposed model that may be nonconvex or nonsmooth. It is found that using PMMO to solve the proposed model can exploit the convergence rate of the solution sequence in the nonconvex case. In the case of specific functions we can use the accelerated versions of first-order methods to solve the proposed model with convexity in order to make them have fast convergence rates in terms of the objective function. Extensive experiments on some data sets are conducted to demonstrate the feasibility and validity of the proposed model.

中文翻译：

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基于数据扰动的相关分类器：新公式和算法

摘要 本文为一系列相关分类器开发了一个新框架，这些分类器是从数据扰动下的不确定凸程序重建的。在此框架下，在数据可能扰动的情况下，从悲观的角度利用相关分类器，并通过在自适应不确定区域方面简化原始模型来制定最大-最小优化问题。在适当的条件下，所提出的模型可以表述为一个最小化问题。基于 Bregman 分歧的近端优化-最小化优化 (PMMO) 旨在解决所提出的可能是非凸或非光滑的模型。发现使用PMMO求解所提出的模型可以利用非凸情况下求解序列的收敛速度。在特定函数的情况下，我们可以使用一阶方法的加速版本来解决所提出的具有凸性的模型，以使它们在目标函数方面具有快速的收敛速度。对一些数据集进行了大量实验，以证明所提出模型的可行性和有效性。