Orthogonal nonnegative matrix t-factorizations for clustering

  • Authors:
  • Chris Ding;Tao Li;Wei Peng;Haesun Park

  • Affiliations:
  • Lawrence Berkeley National Laboratory, Berkeley, CA;Florida International University, Miami, FL;Florida International University, Miami, FL;Georgia Institute of Technology, Atlanta, GA

  • Venue:
  • Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
  • Year:
  • 2006

Quantified Score

Hi-index 0.00

Visualization

Abstract

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