任意秩非负矩阵分解可行解集的抽样算法
A sampling algorithm to compute the set of feasible solutions for non-negative matrix factorization with an arbitrary rank
摘要：
非负矩阵分解（NMF）是一种从多变量数据中提取特征的有效方法，但一个重要的，有时被忽视的问题是，NMF可能会导致非唯一的解决方案。通常，存在一组可行解（SFS），这使得解释因子分解变得更加困难。这个问题在癌症基因组学中尤其被忽视，其中NMF用于推断癌症演变中存在的突变过程的信息。本文研究了两个突变计数数据的非唯一性程度，并提出了一种新的抽样算法，可以找到SFS。我们的采样算法易于实现，适用于任意秩的NMF。这与NMF秩必须小于或等于四的现有技术相反。对于较低的排名，我们表明，我们的算法执行类似的多边形膨胀算法，开发关系到化学计量学。此外，我们展示了SFS的大小如何对解决方案的外观变化产生很大影响。我们的采样算法是在R软件包\textbf{SFS}（\url{https://github.com/ragnhildlaursen/SFS}）中实现的。
英文摘要：
Non-negative Matrix Factorization (NMF) is a useful method to extract features from multivariate data, but an important and sometimes neglected concern is that NMF can result in non-unique solutions. Often, there exist a Set of Feasible Solutions (SFS), which makes it more difficult to interpret the factorization. This problem is especially ignored in cancer genomics, where NMF is used to infer information about the mutational processes present in the evolution of cancer. In this paper the extent of non-uniqueness is investigated for two mutational counts data, and a new sampling algorithm, that can find the SFS, is introduced. Our sampling algorithm is easy to implement and applies to an arbitrary rank of NMF. This is in contrast to state of the art, where the NMF rank must be smaller than or equal to four. For lower ranks we show that our algorithm performs similarly to the polygon inflation algorithm that is developed in relations to chemometrics. Furthermore, we show how the size of the SFS can have a high influence on the appearing variability of a solution. Our sampling algorithm is implemented in an R package \textbf{SFS} (\url{https://github.com/ragnhildlaursen/SFS}).
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。
