This paper introduces the Group Linear Algorithm with Sparse Principal decomposition, an algorithm for supervised variable selection and clustering. Our approach extends the Sparse Group Lasso regularization to calculate clusters as part of the model fit. Therefore, unlike Sparse Group Lasso, our idea does not require prior specification of clusters between variables. To determine the clusters, we solve a particular case of sparse Singular Value Decomposition, with a regularization term that follows naturally from the Group Lasso penalty. Moreover, this paper proposes a unified implementation to deal with, but not limited to, linear regression, logistic regression, and proportional hazards models with right-censoring. Our methodology is evaluated using both biological and simulated data, and details of the implementation in R and hyperparameter search are discussed.

本文介绍了具有稀疏主分解的组线性算法，这是一种用于监督变量选择和聚类的算法。我们的方法扩展了稀疏组套索正则化来计算集群作为模型拟合的一部分。因此，与稀疏组套索不同，我们的想法不需要事先指定变量之间的集群。为了确定聚类，我们解决了稀疏奇异值分解的特殊情况，其正则化项自然来自 Group Lasso 惩罚。此外，本文提出了一个统一的实现来处理但不限于线性回归、逻辑回归和具有右删失的比例风险模型。我们的方法是使用生物学和模拟数据进行评估的，