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Learning sparse classifiers with Difference of Convex functions Algorithms

机译：具有凸函数差异的稀疏分类器算法

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Sparsity of a classifier is a desirable condition for high dimensional data and large sample sizes. This paper investigates the two complementary notions of sparsity for binary classification: sparsity in the number of features and sparsity in the number of examples. Several different losses and regularizers are considered: the hinge loss and ramp loss, and (l)2, (l)1, approximate (l)0, and capped (l)1 regularization. We propose two new objective functions that further promote sparsity, corresponding to the ramp loss versions of approximate (l)0 and capped (l)1 regularization. We derive difference of convex functions algorithms (DCA) for solving these novel nonconvex objective functions. We also propose an efficient DCA for optimizing the recently studied capped (l)1 regularizer under hinge loss. The proposed algorithms are shown to converge in a finite number of iterations to a local minimum. Using simulated data and several datasets from the UCI machine learning repository, we empirically investigate the fraction of features and examples required by the different classifiers.
机译：分类器的稀疏性是高维数据和大样本量的理想条件。本文研究了用于二进制分类的稀疏性的两个互补概念：特征数量上的稀疏性和示例数量上的稀疏性。考虑了几种不同的损耗和调节器：铰链损耗和斜坡损耗，以及（l）2，（l）1，近似（l）0和上限（l）1正则化。我们提出了两个进一步促进稀疏性的新目标函数，分别对应于近似（l）0和有上限（l）1正则化的斜坡损失版本。我们导出凸函数算法（DCA）的差异，以解决这些新颖的非凸目标函数。我们还提出了一种有效的DCA，用于优化铰链损耗下最近研究的带帽（l）1正则化器。所提出的算法显示在有限数量的迭代中收敛到局部最小值。使用来自UCI机器学习存储库的模拟数据和几个数据集，我们根据经验研究了不同分类器所需的功能和示例的比例。

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