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Learning sparse classifiers with Difference of Convex functions Algorithms

机译：学习稀疏分类器具有凸函数算法的差异

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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尺寸的理想条件。本文调查了二进制分类的两种互补迹象：在示例的数量的特征和稀疏性中的稀疏性。考虑了几种不同的损失和校长：铰链损耗和斜坡损失，（L）2，（L）1，近似（L）0，并加盖（L）1正则化。我们提出了两个新的客观功能，进一步促进稀疏性，对应于近似（L）0的斜坡损失版本并限制（L）1正则化。我们导出凸函数算法（DCA）的差异来解决这些新颖的非凸起目标函数。我们还提出了一种有效的DCA，用于优化最近研究的封闭（L）1规则器，铰链损耗。所提出的算法被证明可以将有限数量的迭代收敛到局部最小值。使用模拟数据和来自UCI机器学习存储库的多个数据集，我们经验研究了不同分类器所需的特征和示例的分数和示例。

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