Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization
Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization
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DOI：
10.1109/tpami.2013.226
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发表时间：
2014-04-01
影响因子：
23.6
通讯作者：
Vavasis, Stephen A.
中科院分区：
文献类型：
--
作者：
Gillis, Nicolas;Vavasis, Stephen A.
本文研究了在可分性假设下的非负矩阵分解问题(即存在一个由包含所有列的输入非负数据矩阵的列的一个小子集所跨越的锥体)，它等价于线性混合模型和纯像素假设下的超谱分解问题。我们提出了一类快速递归算法，并证明了它们在输入数据矩阵的任何微小扰动下都是健壮的。这一族推广了现有的几种高光谱分解算法，从而首次为它们更好的实际性能提供了理论上的证明。
In this paper, we study the nonnegative matrix factorization problem under the separability assumption ( that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns), which is equivalent to the hyperspectral unmixing problem under the linear mixing model and the pure-pixel assumption. We present a family of fast recursive algorithms and prove they are robust under any small perturbations of the input data matrix. This family generalizes several existing hyperspectral unmixing algorithms and hence provides for the first time a theoretical justification of their better practical performance.