非负矩阵分解问题的进一步限制版本

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-02-03 DOI:10.1016/j.laa.2025.01.040

Yaroslav Shitov

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引用次数: 0

摘要

我们讨论了在Kokol Bukovšek和Šmigoc最近的一篇文章中介绍的SNT-rank和受限SNT-rank的功能。我们从他们的工作中回答了几个问题，并给出了一个不定义限制snt秩的对称非负矩阵的例子。此外，我们证明了一个矩阵的限制snt -秩可以超过它的snt -秩，即使这两个矩阵都被定义。我们利用先前的结果给出了三阶矩阵和欧氏距离矩阵的snt -秩的边界，并确定了snt -秩的算法计算复杂度。

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Further restricted versions of the nonnegative matrix factorization problem

We discuss the functions of SNT-rank and restricted SNT-rank, introduced in a recent article of Kokol Bukovšek and Šmigoc. We answer several questions from their work and give an example of a symmetric nonnegative matrix for which the restricted SNT-rank is not defined. Moreover, we show that the restricted SNT-rank of a matrix can exceed its SNT-rank even if both of them are defined. We use earlier results to give bounds on SNT-ranks of rank-three matrices and Euclidean distance matrices, and we determine the complexity of the algorithmic computation of SNT-ranks.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.