## Orthogonal nonnegative matrix tri-factorizations for clustering (2006)

Venue: | In SIGKDD |

Citations: | 66 - 18 self |

### BibTeX

@INPROCEEDINGS{Ding06orthogonalnonnegative,

author = {Chris Ding},

title = {Orthogonal nonnegative matrix tri-factorizations for clustering},

booktitle = {In SIGKDD},

year = {2006},

pages = {126--135},

publisher = {Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

Currently, most research on nonnegative matrix factorization (NMF) focus on 2-factor X = FG T factorization. We provide a systematic analysis of 3-factor X = FSG T NMF. While unconstrained 3-factor NMF is equivalent to unconstrained 2-factor NMF, constrained 3factor NMF brings new features to constrained 2-factor NMF. We study the orthogonality constraint because it leads to rigorous clustering interpretation. We provide new rules for updating F,S,G and prove the convergence of these algorithms. Experiments on 5 datasets and a real world case study are performed to show the capability of bi-orthogonal 3-factor NMF on simultaneously clustering rows and columns of the input data matrix. We provide a new approach of evaluating the quality of clustering on words using class aggregate distribution and multi-peak distribution. We also provide an overview of various NMF extensions and examine their relationships.