Nonnegative matrix factorization and its applications in pattern recognition
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Matrix factorization is an effective tool for large-scale data processing and analysis. Nonnegative matrix factorization (NMF) method, which decomposes the nonnegative matrix into two nonnegative factor matrices, provides a new way for matrix factorization. NMF is significant in intelligent information processing and pattern recognition. This paper firstly introduces the basic idea of NMF and some new relevant methods. Then we discuss the loss functions and relevant algorithms of NMF in the framework of probabilistic models based on our researches, and the relationship between NMF and information processing of perceptual process. Finally, we make use of NMF to deal with some practical questions of pattern recognition and point out some open problems for NMF.
- Hubert, L. J., Meulman, J. J., Heiser, W. J., Two purposes for matrix factorization: A historical appraisal, SIAM Review, 2000, 42: 68–82. CrossRef
- Duda, R. O., Hart, P. E., Stork, D. G., Pattern Classification, 2nd ed., New York: John Wiley & Sons, 2001.
- Lee, D. D., Seung, H. S., Learning the parts of objects with nonnegative matrix factorization, Nature, 1999, 401: 788–791.
- Paatero, P., Tapper, U., Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values, Environmetrics, 1994, 5: 111–126.
- Lee, D. D., Seung, H. S., Algorithms for nonnegative matrix factorization, Advances in Neural Information Processing Systems 13 (eds. Leen, T., Dietterich, T., Tresp, V.), Cambridge: MIT Press, 2000.
- Sajda, P., Du, S., Parra, L. et al., Recovery of constituent spectra using non-negative matrix factorization, Proc. SPIE, 2003, 5207: 321–331.
- Cichocki, A., Amari, S., Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications, New York: John Wiley & Sons, 2002.
- Liu, W. X., Zheng, N. N., Learning sparse features for classification by mixture models, Pattern Recognition Letters, 2004, 25(2): 155–161.
- Li, S. Z., Hou, X. W., Zhang, H. J. et al., Learning spatially localized, parts-based representation, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2001, 1: 207–212.
- Olshausen, B. A., Field, D. J., Emergence of simple-cell receptive field properties by learning a sparse code for natural images, Nature, 1996, 381: 607–609. CrossRef
- Hoyer, P. O., Non-negative sparse coding, in Proc. Neural Net-works for Signal Processing, 2002, 557-565.
- Hoyer, P. O., Modeling receptive fields with non-negative sparse coding, Neurocomputing, 2003, (52-54): 547-552.
- Liu, W. X., Zheng, N. N., Lu, X. F., Non-negative matrix factorization for visual coding, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003, 3: 293–296.
- Hoyer, P. O., Non-negative matrix factorization with sparseness constraints, Journal of Machine Learning Research, 2004, 5: 1457–1469.
- Guillamet, D., Vitriã, J., Schiele, B., Introducing a weighted non-negative matrix factorization for image classification, Pattern Recognition Letters, 2003, 24(14): 2447–2454. CrossRef
- Paatero, P., Least squares formulation of robust non-negative factor analysis, Chemometrics and Intelligent Laboratory Systems, 1997, 37(1): 23–35. CrossRef
- Welling, M., Weber, M., Positive tensor factorization, Pattern Recognition Letters, 2001, 22(12): 1255–1261. CrossRef
- Wang, Y., Jia, Y., Hu, C. et al., Fisher non-negative matrix factorization for learning local features, Asian Conference on Computer Vision, Korea, January 27-30, 2004.
- Ahn, J. H., Choi, S., Oh, J. H., A multiplicative up-propagation algorithm, in Proc. Interal Conference on Machine Learning, 2004, 17-24.
- Lee, D. D., Seung, H. S., Learning in intelligent embedded systems, in Proceedings of the Embedded Systems Workshop, March 29-31, 1999, Cambridge, Massachusetts, USA. http://hebb.mit.edu/people/ seung/papers/lee_es99.pdf.
- Lee, J. S., Lee, D. D., Choi, S. et al., Non-negative matrix factorization of dynamic images in nuclear medicine, in Proceedings of IEEE Nuclear Science Symposium Conference Record, San Diego, California, November 4-10, 2001, 4: 2027–2030.
- Ramanath, R., Kuehni, R. G., Snyder, W. E. et al., Spectral spaces and color spaces, Color Research and Application, 2004, 29(1): 29–37.
- Kawamoto, T., Hotta, K., Mishima, T. et al., Estimation of single tones from chord sounds using non-negative matrix factorization, Neural Network World, 2000, 3: 429–436.
- Cho, Y. C., Choi, S., Bang, S. Y., Non-negative component parts of sound for classification, in Proc. IEEE Int’l Symp. Signal Processing and Information Technology, Darmstadt, Germany, December 14-17, 2003.
- Novak, M., Mammone, R., Improvement of non-negative matrix factorization based language model using exponential models, IEEE Workshop on Automatic Speech Recognition and Understanding, 2001, 190-193.
- Xu, W., Liu, X., Gong, Y., Document-clustering based on non-negative matrix factorization, Proceedings of SIGIR’03, July 28-August 1, Toronto, CA, 2003, 267-273.
- Seppanen, J. K., Hollmén, J. E., Bingham, E. et al., Nonnegative matrix factorization on gene expression data, Bioinformatics, 2002, poster 49, Bergen, April 2002.
- Brunet, J. P., Tamayo, P., Golub, T. R. et al., Metagenes and molecular pattern discovery using matrix factorization, Proceedings of the National Academy of Sciences, 2004, 101: 4164–4169. CrossRef
- Dai Yingxia et al., System Safety and Intrusion Detection, Beijing: Tsinghua University Publishing Company, 2002.
- Forrest, S., Hofmeyr, S. A., Somayaji, A., Longstaff, T. A., A sense of self for unix processes, Proceedings of IEEE Symposium on Computer Security and Privacy [C], 1996, 120-128.
- Warrender, C., Forrest, S., Pearlmutter, B., Detecting intrusions using system calls: Alternative data models, in Proceedings of IEEE Symposium on Security and Privacy [C], 1999, 133-145.
- Cox, I. J., Kilian, J., Leighton, T. et al., Secure spread spectrum watermarking for multimedia, IEEE Trans. on Image Processing, 1997, 6(12): 1673–1687. CrossRef
- Liu, W. X., Zheng, N. N., Li, X., Nonnegative matrix factorization for EEG signal classification, ISNN, 2004, (2): 470-475.
- Wolpaw, J. R., Birbaumer, N., McFarland, D. J. et al., Brain computer interfaces for communication and control, Clinical Neurophysiology, 2002, 113(6): 767–791. CrossRef
- Keirn, Z. A., Alternative modes of communication between man and machine [D], Masters Thesis, Electrical Engineering, Purdue University, 1988.
- Keirn, Z. A., Aunon, J. I., A new model of communication between man and his surroundings, IEEE Transactions on Biomedical Engineering, 1990, 37: 1209–1214. CrossRef
- Anderson, C. W., Kirby, M., EEG subspace representations and feature selection for brain computer interfaces, in Proceedings of the 1st IEEE Workshop on Computer Vision and Pattern Recognition for Human Computer Interaction, 2003, 475-483.
- Garrett, G., Peterson, D. A., Anderson, C. W. et al., Comparison of linear and nonlinear methods for EEG signal classification, IEEE Transactions on Neural Systems and Rehabilitative Engineering, 2003, 11(2): 141–144.
- Lin Chen, Where does perception come from? Academic Report of the 12th Academicians Conference of Chinese Academy of Sciences. http://www.casad.ac.cn/2005-4/2005418101856.htm
- Zheng Nanning, Cognition and computer vision, Academic Report of Ten Year Anniversary of the National Outstanding Youth Foundation of China, 2004.
- Saito, N., Larson, B. M., Benichou, B., Sparsity vs. statistical independence from a best-basis viewpoint, in Proc. SPIE Wavelet Applications in Signal and Image Processing VIII (eds. Aldroubi, A., Laine, A. F., Unser, M. A.), vol. 4119, 2000, 474–486.
- Saul, L. K., Sha, F., Lee, D. D., Statistical signal processing with nonnegativity constraints, Proceedings of the Eighth European Conference on Speech Communication and Technology, vol. 2, Geneva, Switzerland, 2003, 1001-1004.
- Liu, W. G., Yi, G. L., Existing and New Algorithms for Nonnegative Matrix Factorization. http://www.cs.utexas.edu/users/liuwg/ 383CProject/CS 383C Project.htm.
- Liu, W. X., Zheng, N. N., Li, X., Relative gradient speeding up additive updates for nonnegative matrix factorization, Neurocomputing, 2004, 57: 493–499. CrossRef
- Wild, S. M., Curry, J., Dougherty, A., Improving non-negative matrix factorizations through structured initialization, Pattern Recognition, 2004, 37: 2217–2232. CrossRef
- Donoho, D., Stodden, V., When does non-negative matrix factorization give a correct decomposition into parts? Tech. Report, Department of Statistics, Stanford University, 2003.
- Chu, M., Diele, F., Plemmons, R. et al., Optimality, computation, and interpretations of nonnegative (non-negative) matrix factorizations, Submitted to the SIAM Journal on Matrix Analysis, October 2004.
- Plumbley, M. D., Conditions for non-negative independent component analysis, IEEE Signal Processing Letters, 2002, 9(6): 177–180. CrossRef
- Downs, O. B., MacKay, D., Lee, D. D., The nonnegative Boltzmann machine, in Advances in Neural Information Processing Systems 12 (eds. Solla, S. A., Leen, T. K., Muller, K.-R.), 2000, 428-434.
- Ross, D., Zemel, R., Multiple cause vector quantization, in Advances in Neural Information Processing Systems 15 (eds. Becker, S., Thrun, S., Obermayer, K.), Cambridge: MIT Press, 2003.
- Ge, X. J., Iwata, S., Learning the parts of objects by auto-association, Neural Networks, 2002, 15: 285–295. CrossRef
- Wang Peng, Nonnegative matrix factorization: Wonderful power of math, Computer Education, 2004, 10: 38–40.
- Nonnegative matrix factorization and its applications in pattern recognition
Chinese Science Bulletin
Volume 51, Issue 1 , pp 7-18
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- Science in China Press
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- nonnegative data
- feature extraction
- intrusion detection
- digital watermarking
- EEG signal analysis
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