Graph Non-negative Matrix Factorization Based on Self-representation Learning Update for Clustering

Chen Yongheng; Wang Zhenyou; Xu Shengbing

doi:10.12052/gdutxb.250181

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Graph Non-negative Matrix Factorization Based on Self-representation Learning Update for Clustering

更新时间：2026-08-04

- Graph Non-negative Matrix Factorization Based on Self-representation Learning Update for Clustering
- Vol. 43, Issue 4, Pages: 103-114(2026)
- 作者机构：
  
  广东工业大学数学与统计学院,广东,广州,510520
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.250181
  CLC： TP391
- Published：2026
- 稿件说明：
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陈勇亨, 王振友, 徐圣兵. 基于自表示学习更新的图非负矩阵分解聚类[J]. 广东工业大学学报, 2026, 43(4): 103-114.
陈勇亨, 王振友, 徐圣兵. 基于自表示学习更新的图非负矩阵分解聚类[J]. 广东工业大学学报, 2026, 43(4): 103-114. DOI： 10.12052/gdutxb.250181.

DOI： 10.12052/gdutxb.250181

摘要

非负矩阵分解(Non-negative Matrix Factorization，NMF) 是一种基于矩阵分解的降维技术，用于寻找基于潜在特征的线性表示。针对NMF忽略数据局部几何结构的问题，本文提出的图非负矩阵分解(Graph non-negative Matrix Factorization，GNMF)虽然可以较好地改善高维空间中数据之间的几何关系，但其所遵循的图信息，即邻接矩阵是基于可观测空间中原始样本的相关性构建的，无法反映对象间的真实距离关系。针对这个问题，本文将基于自表示的图信息融入到NMF的算法框架中，提出了自表示更新下的图非负矩阵分解(Graph Non-negative Matrix Factorization based on Self-representation Learning Update，GNMFSLU)，该方法利用迭代的方式对图的邻接矩阵进行更新，使得图信息更加接近对象间的真实距离关系，增强了NMF的聚类性能。

Abstract

Non-negative Matrix Factorization (NMF) is a dimensionality reduction technique based on matrix factorization

used to find linear representations based on latent features. Although Graph Nonnegative Matrix Factorization (GNMF)

which is proposed to address the issue of NMF ignoring the local geometric structure of data

can improve the geometric relationship between data in high-dimensional spaces relatively well

the graph information it follows - that is

the adjacency matrix - is constructed based on the distance relationship of the observable space of the original samples and cannot reflect the true distance relationship between objects. To address this issue

we integrate the graph information based on self-representation into the algorithm framework of NMF and propose Graph Non-negative Matrix Factorization based on Self-representation Learning Update (GNMFSLU) . This method updates the adjacency matrix of the graph in each iteration

thereby making the graph information closer to the true distance relationship between objects and enhancing the clustering performance of NMF.

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references

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