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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7553))

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Abstract

In the past decade, Probabilistic Latent Semantic Indexing (PLSI) has become an important modeling technique, widely used in clustering or graph partitioning analysis. However, the original PLSI is designed for multinomial data and may not handle other data types. To overcome this restriction, we generalize PLSI to t-exponential family based on a recently proposed information criterion called t-divergence. The t-divergence enjoys more flexibility than KL-divergence in PLSI such that it can accommodate more types of noise in data. To optimize the generalized learning objective, we propose a Majorization-Minimization algorithm which multiplicatively updates the factorizing matrices. The new method is verified in pairwise clustering tasks. Experimental results on real-world datasets show that PLSI with t-divergence can improve clustering performance in purity for certain datasets.

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References

  1. Arora, R., Gupta, M., Kapila, A., Fazel, M.: Clustering by left-stochastic matrix factorization. In: International Conference on Machine Learning (ICML), pp. 761–768 (2011)

    Google Scholar 

  2. Choi, H., Choi, S., Katake, A., Choe, Y.: Learning alpha-integration with partially-labeled data. In: Proc. of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 14–19 (2010)

    Google Scholar 

  3. Cichocki, A., Lee, H., Kim, Y.D., Choi, S.: Non-negative matrix factorization with α-divergence. Pattern Recognition Letters 29, 1433–1440 (2008)

    Article  Google Scholar 

  4. Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis. John Wiley (2009)

    Google Scholar 

  5. Ding, C., Li, T., Peng, W.: On the equivalence between non-negative matrix factorization and probabilistic latent semantic indexing. Computational Statistics and Data Analysis 52(8), 3913–3927 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ding, C., Li, T., Jordan, M.: Convex and semi-nonnegative matrix factorizations. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(1), 45–55 (2010)

    Article  Google Scholar 

  7. Ding, N., Vishwanathan, S.: t-logistic regression. In: Advances in Neural Information Processing Systems, vol. 23, pp. 514–522 (2010)

    Google Scholar 

  8. Ding, N., Vishwanathan, S., Qi, Y.A.: t-divergence based approximate inference. In: Advances in Neural Information Processing Systems, vol. 24, pp. 1494–1502 (2011)

    Google Scholar 

  9. Févotte, C., Bertin, N., Durrieu, J.L.: Nonnegative matrix factorization with the Itakura-Saito divergence: With application to music analysis. Neural Computation 21(3), 793–830 (2009)

    Article  MATH  Google Scholar 

  10. Hofmann, T.: Probabilistic latent semantic indexing. In: Proceedings of the 22nd Annual International Conference on Research and Development in Information Retrieval (SIGIR), pp. 50–57. ACM (1999)

    Google Scholar 

  11. Hunter, D.R., Lange, K.: A tutorial on MM algorithms. The American Statistician 58(1), 30–37 (2004)

    Article  MathSciNet  Google Scholar 

  12. Mollah, M., Sultana, N., Minami, M.: Robust extraction of local structures by the minimum of beta-divergence method. Neural Networks 23, 226–238 (2010)

    Article  Google Scholar 

  13. Yang, Z., Oja, E.: Unified development of multiplicative algorithms for linear and quadratic nonnegative matrix factorization. IEEE Transactions on Neural Networks 22(12), 1878–1891 (2011)

    Article  Google Scholar 

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© 2012 Springer-Verlag Berlin Heidelberg

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Zhang, H., Hao, T., Yang, Z., Oja, E. (2012). Pairwise Clustering with t-PLSI. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds) Artificial Neural Networks and Machine Learning – ICANN 2012. ICANN 2012. Lecture Notes in Computer Science, vol 7553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33266-1_51

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  • DOI: https://doi.org/10.1007/978-3-642-33266-1_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33265-4

  • Online ISBN: 978-3-642-33266-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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