用稀疏奇异向量选特征，癌症检测准确率接近完美。
Optimizing Sparse Generalized Singular Vectors for Feature Selection in Proximal Support Vector Machines with Application to Breast and Ovarian Cancer Detection
- 通过 $\ ext{l}_1$ 与 $\ ext{l}_q$ 正则化求解广义奇异值问题，生成稀疏解。
- 在乳腺癌和卵巢癌数据集上，仅用少数特征即实现近完美的平衡准确率。
- 适合高维生物数据中的特征选择与癌症分类任务。
本文提出计算广义奇异值问题（GSVP）稀疏解的方法。通过 $\ell_1$-范数和 $\ell_q$-惩罚（$0<q<1$）对 GSVP 进行正则化，得到 $\ell_1$-GSVP 与 $\ell_q$-GSVP 框架。采用固定步长的近端梯度下降法求解，利用解的内在稀疏性进行特征选择，并结合非平行支持向量机（SVM）进行二分类。将 SVM 融入 $\ell_1$-GSVP 与 $\ell_q$-GSVP 框架，形成 $\ell_1$-GSVPSVM 与 $\ell_q$-GSVPSVM 变体。应用于癌症检测任务，在乳腺癌与卵巢癌数据集上，仅使用少量特征即实现近完美的平衡准确率。
原文摘要 · Abstract (English)
This paper presents approaches to compute sparse solutions of Generalized Singular Value Problem (GSVP). The GSVP is regularized by $\ell_1$-norm and $\ell_q$-penalty for $0<q<1$, resulting in the $\ell_1$-GSVP and $\ell_q$-GSVP formulations. The solutions of these problems are determined by applying the proximal gradient descent algorithm with a fixed step size. The inherent sparsity levels within the computed solutions are exploited for feature selection, and subsequently, binary classification with non-parallel Support Vector Machines (SVM). For our feature selection task, SVM is integrated into the $\ell_1$-GSVP and $\ell_q$-GSVP frameworks to derive the $\ell_1$-GSVPSVM and $\ell_q$-GSVPSVM variants. Machine learning applications to cancer detection are considered. We remarkably report near-to-perfect balanced accuracy across breast and ovarian cancer datasets using a few selected features.
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