NMF and PLSI: equivalence and a hybrid algorithm

ABSTRACT

In this paper, we show that PLSI and NMF optimize the same objective function, although PLSI and NMF are different algorithms as verified by experiments. In addition, we also propose a new hybrid method that runs PLSI and NMF alternatively to achieve better solutions.

REFERENCES

• 1: C. Ding, X. He, and H.D. Simon. On the equivalence of nonnegative matrix factorization and spectral clustering. Proc. SIAM Data Mining Conf, 2005.
• 2: C. Ding, T. Li, and W. Peng. Nonnegative matrix factorization and probabilistic latent semantic indexing: Equivalence, chi-square statistic, and a hybrid method. In AAAI, 2006.
• 3: Eric Gaussier , Cyril Goutte, Relation between PLSA and NMF and implications, Proceedings of the 28th annual international ACM SIGIR conference on Research and development in information retrieval, August 15-19, 2005, Salvador, Brazil [doi>10.1145/1076034.1076148]
• 4: T. Hofmann. Probabilistic latent semantic analysis. In UAI), 1999.
• 5: D.D. Lee and H. S. Seung. Algorithms for non-negative matrix factorization. In T. G. Dietterich and V. Tresp, editors, NIPS 13, 2001.
• 6: Tao Li , Sheng Ma , Mitsunori Ogihara, Document clustering via adaptive subspace iteration, Proceedings of the 27th annual international ACM SIGIR conference on Research and development in information retrieval, July 25-29, 2004, Sheffield, United Kingdom [doi>10.1145/1008992.1009031]

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.6 Learning

Additional Classification:
  I. Computing Methodologies
  I.5 PATTERN RECOGNITION
      I.5.3 Clustering

General Terms:
Algorithms, Experimentation, Theory

Keywords:
NMF, PLSI, chi-square, equivalence