论文标题
非负基质分解的最小二乘方法优于有理函数
Least-squares methods for nonnegative matrix factorization over rational functions
论文作者
论文摘要
非负矩阵分解（NMF）模型被广泛用于恢复线性混合的非负数据。当数据是由连续信号采样的数据时，NMF中的因子可能被限制为非负合理函数的样本，这些函数允许相当通用的模型。使用Rational功能（R-NMF）称之为NMF。我们首先表明，在温和的假设下，R-NMF与NMF不同，这在基本上是独特的分解，这在需要恢复基于盲源分离问题之类的地面真相因子的应用中至关重要。然后，我们提出了解决R-NMF的不同方法：R-Hanls，R-ANLS和R-NLS方法。从我们的测试中，没有什么方法明显优于其他方法，并且在时间和准确性之间应进行权衡。确实，R-Hanls对于大型问题而言是快速准确的，而R-ANLS则更准确，但在时间和内存中都需要更多的资源。 R-NLS非常准确，但仅针对小问题。此外，我们表明，R-NMF在各种任务中的表现都优于NMF，包括恢复半合成连续信号，以及真正的高光谱信号的分类问题。
Nonnegative Matrix Factorization (NMF) models are widely used to recover linearly mixed nonnegative data. When the data is made of samplings of continuous signals, the factors in NMF can be constrained to be samples of nonnegative rational functions, which allow fairly general models; this is referred to as NMF using rational functions (R-NMF). We first show that, under mild assumptions, R-NMF has an essentially unique factorization unlike NMF, which is crucial in applications where ground-truth factors need to be recovered such as blind source separation problems. Then we present different approaches to solve R-NMF: the R-HANLS, R-ANLS and R-NLS methods. From our tests, no method significantly outperforms the others, and a trade-off should be done between time and accuracy. Indeed, R-HANLS is fast and accurate for large problems, while R-ANLS is more accurate, but also more resources demanding, both in time and memory. R-NLS is very accurate but only for small problems. Moreover, we show that R-NMF outperforms NMF in various tasks including the recovery of semi-synthetic continuous signals, and a classification problem of real hyperspectral signals.
