Some Properties of Generalized Fused Lasso and Its Applications to High Dimensional Data

Identifying homogeneous subgroups of variables can be challenging in high dimensional data analysis with highly correlated predictors. The generalized fused lasso has been proposed to simultaneously select correlated variables and identify them as predictive clusters. In this article, we study several properties of generalized fused lasso. First, we present a geometric interpretation of the generalized fused lasso along with a discussion of its persistency. Second, we analytically show its grouping property. Third, we introduce a modified version of the generalized fused lasso and perform comprehensive simulation studies to compare our version of the generalized fused lasso with other existing methods, showing that the generalized fused lasso outperforms other variable selection methods in terms of prediction error and parsimony. We describe two applications of our method in soil science and near infrared spectroscopy studies. These examples having vastly different data types demonstrate the flexibility of the methodology particularly for high-dimensional data.