Abstract
Projective Nonnegative Matrix Factorization (PNMF) is one of the recent methods for computing low-rank approximations to data matrices. It is advantageous in many practical application domains such as clustering, graph partitioning, and sparse feature extraction. However, up to now a scalable implementation of PNMF for large-scale machine learning problems has been lacking. Here we provide an online algorithm for fast PNMF learning with low memory cost. The new algorithm simply applies multiplicative update rules iteratively on small subsets of the data, with historical data naturally accumulated. Consequently users do not need extra efforts to tune any optimization parameters such as learning rates or the history weight. In addition to scalability and convenience, empirical studies on synthetic and real-world datasets indicate that our online algorithm runs much faster than the existing batch version.
Supported by the Academy of Finland in the project Finnish Center of Excellence in Computational Inference Research (COIN).
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References
Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis. John Wiley (2009)
Ding, C., Li, T., Jordan, M.I.: Convex and semi-nonnegative matrix factorizations. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(1), 45–55 (2010)
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)
Kushner, H.J., Clark, D.S.: Stochastic Approximation Methods for Constrained and Unconstrained Systems. Springer, New York (1978)
Lakshminarayanan, B., Raich, R.: Non-negative matrix factorization for parameter estimation in hidden markov models. In: Proceedings of IEEE International Workshop on Machine Learning for Signal Processing, pp. 89–94 (2010)
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)
Lin, C.J.: Projected gradient methods for non-negative matrix factorization. Neural Computation 19, 2756–2779 (2007)
Liu, C., Yang, H., Fan, J., He, L., Wang, Y.: Distributed nonnegative matrix factorization for web-scale dyadic data analysis on MapReduce. In: Proceedings of 19th International World Wide Web Conference (2010)
Mairal, J., Bach, F., Ponce, J., Sapiro, G.: Online learning for matrix factorization and sparse coding. The Journal of Machine Learning Research 11, 19–60 (2010)
Phillips, P.J., Moon, H., Rizvi, S.A., Rauss, P.J.: The FERET evaluation methodology for face recognition algorithms. IEEE Trans. Pattern Analysis and Machine Intelligence 22, 1090–1104 (2000)
Woodard, D., Flynn, P.: Finger surface as a biometric identifier. Computer Vision and Image Understanding 100(3), 357–384 (2005)
Yang, Z., Oja, E.: Linear and nonlinear projective nonnegative matrix factorization. IEEE Transaction on Neural Networks 21(5), 734–749 (2010)
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)
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Yang, Z., Zhang, H., Oja, E. (2012). Online Projective Nonnegative Matrix Factorization for Large Datasets. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34487-9_35
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DOI: https://doi.org/10.1007/978-3-642-34487-9_35
Publisher Name: Springer, Berlin, Heidelberg
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