高维图的多重线性代数方法

IF 2.2 2区 数学 Q1 MATHEMATICS, APPLIED Applied Numerical Mathematics Pub Date : 2025-02-01 DOI:10.1016/j.apnum.2023.11.009
Alaeddine Zahir , Khalide Jbilou , Ahmed Ratnani
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引用次数: 0

摘要

在本文中,我们将探讨使用基于多线性代数的方法来处理高维图。多视图集群(MVC)比单视图集群更受欢迎,因为它能够提供更全面的数据洞察。然而,这种方法也提出了挑战,特别是在有效地组合和利用多个视图或特性方面。该领域最近的大部分工作主要集中在张量表示上,而不是将数据视为简单的矩阵。因此,我们将检查和比较这些方法,特别是在两个类别中,即基于图的聚类和基于子空间的聚类。我们将报告使用基准数据集进行的实验,以评估主要聚类方法的性能。
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Multilinear algebra methods for higher-dimensional graphs
In this paper, we will explore the use of multilinear algebra-based methods for higher dimensional graphs. Multi-view clustering (MVC) has gained popularity over the single-view clustering due to its ability to provide more comprehensive insights into the data. However, this approach also presents challenges, particularly in combining and utilizing multiple views or features effectively. Most of recent work in this field focuses mainly on tensor representation instead of treating the data as simple matrices. Accordingly, we will examine and compare these approaches, particularly in two categories, namely graph-based clustering and subspace-based clustering. We will report on experiments conducted using benchmark datasets to evaluate the performance of the main clustering methods.
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来源期刊
Applied Numerical Mathematics
Applied Numerical Mathematics 数学-应用数学
CiteScore
5.60
自引率
7.10%
发文量
225
审稿时长
7.2 months
期刊介绍: The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.
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