Abstract

The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization. A multi-objective optimization problem finds conical combinations of templates that approximate a given data matrix. The templates are chosen so that as far as possible only the initial data set can be represented this way. However, the templates are not required to be nonnegative nor convex combinations of the original data.

中文翻译：

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紧半负矩阵分解

摘要

非负矩阵分解是一种广泛使用的灵活矩阵分解，在生物学，图像和信号处理以及信息检索等领域都有广泛的应用。在这里，我们提出一个相关的矩阵分解。多目标优化问题可以找到近似于给定数据矩阵的模板的圆锥形组合。选择模板，以便尽可能仅以这种方式表示初始数据集。但是，模板不必是原始数据的非负或凸组合。