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On Trivial Solution and Scale Transfer Problems in Graph Regularized NMF

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

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Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence. Pages 1288-1292.

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.

Quanquan Gu, Chris H. Q. Ding, and Jiawei Han. 2011. On Trivial Solution and Scale Transfer Problems in Graph Regularized NMF. In Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI-11. IJCAI, 1288–1292. https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-218
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