In this paper, we study the embedded feature selection problem in linear
Support Vector Machines (SVMs), in which a cardinality constraint is employed,
leading to a fully explainable selection model. The problem is NP-hard due to
the presence of the cardinality constraint, even though the original linear SVM
amounts to a problem solvable in polynomial time. To handle the hard problem,
we first introduce two mixed-integer formulations for which novel SDP
relaxations are proposed. Exploiting the sparsity pattern of the relaxations,
we decompose the problems and obtain equivalent relaxations in a much smaller
cone, making the conic approaches scalable. To make the best usage of the
decomposed relaxations, we propose heuristics using the information of its
optimal solution. Moreover, an exact procedure is proposed by solving a
sequence of mixed-integer decomposed SDPs. Numerical results on classical
benchmarking datasets are reported, showing the efficiency and effectiveness of
our approach.

我们研究了线性支持向量机（SVM）中的嵌入式特征选择问题，其中采用了基数约束，从而形成了一个完全可解释的选择模型。我们提出了两种混合整数模型，并针对其提出了新的 SDP 松弛策略。通过利用松弛策略的稀疏性模式，我们将问题进行分解，并在一个较小的锥体中获得了等效的松弛策略，使锥形方法具有可伸缩性。为了最大程度地利用分解的松弛策略，我们提出了使用其最优解信息的启发式方法。此外，通过解决一系列混合整数分解的 SDP 问题，我们提出了一种精确的过程。我们报告了在经典基准数据集上的数值实验结果，展示了我们方法的效率和效果。

通过硬基数约束的线性支持向量机特征选择：一种可扩展的 SDP 分解方法

Feature selection in linear SVMs via hard cardinality constraint: a  scalable SDP decomposition approach

While social media offer great communication opportunities, they also
increase the vulnerability of young people to threatening situations online.
Recent studies report that cyberbullying constitutes a growing problem among
youngsters. Successful prevention depends on the adequate detection of
potentially harmful messages and the information overload on the Web requires
intelligent systems to identify potential risks automatically. The focus of
this paper is on automatic cyberbullying detection in social media text by
modelling posts written by bullies, victims, and bystanders of online bullying.
We describe the collection and fine-grained annotation of a training corpus for
English and Dutch and perform a series of binary classification experiments to
determine the feasibility of automatic cyberbullying detection. We make use of
linear support vector machines exploiting a rich feature set and investigate
which information sources contribute the most for this particular task.
Experiments on a holdout test set reveal promising results for the detection of
cyberbullying-related posts. After optimisation of the hyperparameters, the
classifier yields an F1-score of 64% and 61% for English and Dutch
respectively, and considerably outperforms baseline systems based on keywords
and word unigrams.

本研究旨在探讨使用线性支持向量机通过模拟欺凌者、受害者和旁观者的帖子，实现自动检测社交媒体文本中的网络欺凌，并收集并德细注释英语和荷兰语的训练语料库。我们利用丰富的特征集进行一系列二元分类实验，研究哪些信息源对于这一特定任务最有贡献，同时对参数进行优化，分类器在英语和荷兰语分别获得了 64% 和 61% 的 F1 分数，显著优于基于关键字和词单元的基准系统。