---
title: "On Trivial Solution and Scale Transfer Problems in Graph Regularized NMF"
authors:
  - "Quanquan Gu"
  - "Chris H. Q. Ding"
  - "Jiawei Han"
doi: "10.5591/978-1-57735-516-8/IJCAI11-218"
url: "https://ijcai.org/proceedings/2011/218"
pdf: "https://ijcai.org/proceedings/2011/0218.pdf"
venue: "Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence"
year: 2011
pages: "1288-1292"
track: ""
keywords:
---

# On Trivial Solution and Scale Transfer Problems in Graph Regularized NMF

Quanquan Gu, Chris H. Q. Ding, Jiawei Han

*Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence*, pages 1288-1292. DOI: [10.5591/978-1-57735-516-8/IJCAI11-218](https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-218)

## Abstract

Combining graph regularization with nonnegative matrix (tri-)factorization (NMF) has shown great performance improvement compared with traditional nonnegative matrix (tri-)factorization models due to its ability to utilize the geometric structure of the documents and words. In this paper, we show that these models are not well-defined and suffering from trivial solution and scale transfer problems. In order to solve these common problems, we propose two models for graph regularized nonnegative matrix (tri-)factorization, which can be applied for document clustering and co-clustering respectively. In the proposed models, a Normalized Cut-like constraint is imposed on the cluster assignment matrix to make the optimization problem well-defined. We derive a multiplicative updating algorithm for the proposed models, and prove its convergence. Experiments of clustering and co-clustering on benchmark text data sets demonstratethat the proposed models outperform the originalmodels as well as many other state-of-the-art clustering methods.