[EN] 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.