协同层次稀疏建模
Collaborative Hierarchical Sparse Modeling
摘要：
稀疏建模是一个强大的数据分析和处理框架。传统上，在这个框架中的编码是通过解决l_1正则化线性回归问题来完成的，通常称为Lasso。在这项工作中，我们首先结合了稀疏诱导属性的套索模型，在个人的功能水平，与块稀疏属性的组套索模型，稀疏组的功能进行联合编码，获得稀疏模式层次结构。这导致分层Lasso，它显示了重要的实际建模优势。然后，我们将这种方法扩展到协作的情况下，一组同时编码的信号共享相同的稀疏模式在较高的（组）水平，但不一定在较低的。然后，信号共享相同的活动组或类，但不一定是相同的活动集。这非常适合于诸如声源分离的应用。一个有效的优化过程，保证收敛到全局最优，开发这些新的模型。新的框架和优化方法的基本介绍补充实验的例子和初步的理论结果。
英文摘要：
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the sparsity-inducing property of the Lasso model, at the individual feature level, with the block-sparsity property of the group Lasso model, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured. This results in the hierarchical Lasso, which shows important practical modeling advantages. We then extend this approach to the collaborative case, where a set of simultaneously coded signals share the same sparsity pattern at the higher (group) level but not necessarily at the lower one. Signals then share the same active groups, or classes, but not necessarily the same active set. This is very well suited for applications such as source separation. An efficient optimization procedure, which guarantees convergence to the global optimum, is developed for these new models. The underlying presentation of the new framework and optimization approach is complemented with experimental examples and preliminary theoretical results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
