Many classification problems focus on maximizing the performance only on the samples with the highest relevance instead of all samples. As an example, we can mention ranking problems, accuracy at the top or search engines where only the top few queries matter. In our previous work, we derived a general framework including several classes of these linear classification problems. In this paper, we extend the framework to nonlinear classifiers. Utilizing a similarity to SVM, we dualize the problems, add kernels and propose a componentwise dual ascent method.

翻译：许多分类问题仅关注最大化最高相关性样本上的性能，而非所有样本。例如，排序问题、顶部准确率或搜索引擎中仅需考量少数最相关查询。在先前工作中，我们构建了一个包含多类此类线性分类问题的通用框架。本文将框架扩展至非线性分类器。利用与支持向量机的相似性，我们对问题进行对偶化处理、引入核函数，并提出一种分量对偶上升方法。