A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary
A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary
复制标题
自字典非负稀疏回归的快速梯度法
DOI：
10.1109/tip.2017.2753400
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发表时间：
2016
影响因子：
10.6
通讯作者：
R. Luce
中科院分区：
文献类型：
--
作者：
Nicolas Gillis;R. Luce
非负矩阵分解（NMF）可以在可分性假设下有效地计算，该假设断言给定输入数据矩阵的所有列都属于由它们的（小）子集生成的锥。可证明的最强大的方法来识别这些圆锥基列是基于非负稀疏回归和自字典，并需要解决大规模的凸优化问题。本文研究了一类特殊的具有自字典的非负稀疏回归模型。与以前提出的模型相反，该模型产生了一个平滑的优化问题，其中稀疏性通过线性约束来实现。我们证明了由这些约束定义的多面体上的欧氏投影可以有效地计算，并提出了一种快速梯度法来求解我们的模型。我们比较我们的算法与几个国家的最先进的方法在合成数据集和现实世界的高光谱图像。
A nonnegative matrix factorization (NMF) can be computed efficiently under the separability assumption, which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably most robust methods to identify these conic basis columns are based on nonnegative sparse regression and self-dictionaries, and require the solution of large-scale convex optimization problems. In this paper, we study a particular nonnegative sparse regression model with self-dictionary. As opposed to previously proposed models, this model yields a smooth optimization problem, where the sparsity is enforced through linear constraints. We show that the Euclidean projection on the polyhedron defined by these constraints can be computed efficiently, and propose a fast gradient method to solve our model. We compare our algorithm with several state-of-the-art methods on synthetic data sets and real-world hyperspectral images.
影响因子：
64.8
作者：
Lee, DD;Seung, HS
通讯作者：
Seung, HS