An Iteratively Re-weighted Method for Problems with Sparsity-Inducing Norms
This provides a practical optimization method for sparsity problems in machine learning, but it appears incremental as it builds on existing re-weighted approaches.
The paper tackles optimization problems with sparsity-inducing norms in machine learning tasks like feature selection and subspace clustering by proposing an Iteratively Re-Weighted method (IRW) with convergence guarantees. Experimental results on real data show it significantly outperforms alternative methods in a robust feature selection model.
This work aims at solving the problems with intractable sparsity-inducing norms that are often encountered in various machine learning tasks, such as multi-task learning, subspace clustering, feature selection, robust principal component analysis, and so on. Specifically, an Iteratively Re-Weighted method (IRW) with solid convergence guarantee is provided. We investigate its convergence speed via numerous experiments on real data. Furthermore, in order to validate the practicality of IRW, we use it to solve a concrete robust feature selection model with complicated objective function. The experimental results show that the model coupled with proposed optimization method outperforms alternative methods significantly.