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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 林智仁 | |
dc.contributor.author | Chen-Tse Tsai | en |
dc.contributor.author | 蔡鎮澤 | zh_TW |
dc.date.accessioned | 2021-06-13T17:29:30Z | - |
dc.date.available | 2011-07-25 | |
dc.date.copyright | 2011-07-25 | |
dc.date.issued | 2011 | |
dc.date.submitted | 2011-07-12 | |
dc.identifier.citation | J. Barzilai and J. M. Borwein. Two-point step size gradient methods. IMA Journal of Numerical Analysis, 8:141–148, 1988.
R. Bekkerman and M. Scholz. Data weaving: Scaling up the state-of-the-art in data clustering. In Proceedings of CIKM, pages 1083–1092, 2008. D. P. Bertsekas. On the Goldstein-Levitin-Polyak gradient projection method. IEEE Transactions on Automatic Control, 21:174–184, 1976. D. P. Bertsekas. Nonlinear Programming. Athena Scientific, Belmont, MA 02178- 9998, second edition, 1999. E. G. Birgin, J. M. Martínez, and M. Raydan. Nonmonotone spectral projected gradient methods on convex sets. SIAM Journal on Optimization, 10:1196–1211, 2000. S. Bonettini. Inexact block coordinate descent methods with application to non- negative matrix factorization. IMA Journal of Numerical Analysis, 2011. To appear. P. H. Calamai and J. J. Moré. Projected gradient methods for linearly constrained problems. Mathematical Programming, 39:93–116, 1987. Y.-H. Dai and R. Fletcher. Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming. Numerische Mathematik, 100:21–47, 2005. R. Fletcher. On the Barzilai-Borwein method. Optimization and Control with Applications, 96:235–256, 2005. L. Grippo and M. Sciandrone. On the convergence of the block nonlinear Gauss- Seidel method under convex constraints. Operations Research Letters, 26:127–136, 2000. L. Grippo and M. Sciandrone. Nonmonotone globalization techniques for the Barzilai-Borwein gradient method. Computational Optimization and Applications, 23:143–169, 2002. L. Grippo, F. Lampariello, and S. Lucidi. A nonmonotone line search technique for Newton’s method. SIAM Journal on Numerical Analysis, 23:707–716, 1986. L. Han, M. Neumann, and U. Prasad. Alternating projected Barzilai-Borwein methods for nonnegative matrix factorization. Electronic Transactions on Nu- merical Analysis, pages 54–82, 2009. P. O. Hoyer. Non-negative matrix factorization with sparseness constraints. Jour- nal of Machine Learning Research, 5:1457–1469, 2004. J. Kim and H. Park. Toward faster nonnegative matrix factorization: A new algorithm and comparisons. In Eighth IEEE International Conference on Data Mining, pages 353–362. IEEE, 2008. D. D. Lee and H. S. Seung. Learning the parts of objects by non-negative matrix factorization. Nature, 401:788–791, 1999. D. D. Lee and H. S. Seung. Algorithms for non-negative matrix factorization. In T. K. Leen, T. G. Dietterich, and V. Tresp, editors, Advances in Neural Informa- tion Processing Systems 13, pages 556–562. MIT Press, 2001. D. D. Lewis, Y. Yang, T. G. Rose, and F. Li. RCV1: A new benchmark collection for text categorization research. Journal of Machine Learning Research, 5:361– 397, 2004. C.-J. Lin. Projected gradient methods for non-negative matrix factorization. Neural Computation, 19:2756–2779, 2007. URL http://www.csie.ntu.edu.tw/ ~cjlin/papers/pgradnmf.pdf. P. Paatero and U. Tapper. Positive matrix factorization: A non-negative factor model with optimal utilization of error. Environmetrics, 5:111–126, 1994. M. Raydan. The Barzilai and Borwein gradient method for the large scale uncon- strained minimization problem. SIAM Journal on Optimization, 7:26–33, 1997. T. Serafini, G. Zanghirati, and L. Zanni. Gradient projection methods for quadratic programs and applications in training support vector machines. Op- timization Methods and Software, 20:353–378, 2005. R. Zdunek and A. Cichocki. Fast nonnegative matrix factorization algorithms using projected gradient approaches for large-scale problems. Computational In- telligence and Neuroscience, 2008:1–13, 2008. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/39478 | - |
dc.description.abstract | Non-negative matrix factorization (NMF) is a useful dimension reduction tech- nique. Currently, the most effective way to minimize NMF optimization problems is by alternatively solving non-negative least square sub-problems. Some recent stud- ies have shown that projected Barzilai-Borwein methods are very efficient for solving each sub-problem. In this thesis, we study variants of the projected Barzilai-Borwein methods and discuss some useful implementation techniques. We provide an efficient implementation to succeed our popular NMF code via a projected gradient method. | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T17:29:30Z (GMT). No. of bitstreams: 1 ntu-100-R98922028-1.pdf: 1784272 bytes, checksum: 2441a791471daedf880aa78f3ed876f1 (MD5) Previous issue date: 2011 | en |
dc.description.tableofcontents | 口試委員會審定書................................ i
中文摘要...................................... ii ABSTRACT .................................... iii LISTOFFIGURES................................ v LISTOFTABLES................................. vi CHAPTER I.Introduction ............................... 1 II. Projected Gradient and Projected Barzilai-Borwein Methods 4 2.1 Slow Convergence of Projected Gradient Methods . . . . . . . . 5 2.2 Variants of Projected Barzilai-Borwein Methods . . . . . . . . . 6 2.3 The Proposed Procedure ..................... 11 III.Algorithmic and Implementation Issues .............. 13 3.1 Stopping Conditions........................ 13 3.2 Implementation Details ...................... 14 IV.Experiments ............................... 18 4.1 Image Data............................. 20 4.2 Text Data.............................. 24 4.3 The Importanceof α1 ....................... 25 4.4 A ComparisonBetween(2.8)and(2.9). . . . . . . . . . . . . . 26 V.Conclusions................................ 32 BIBLIOGRAPHY................................. 33 | |
dc.language.iso | en | |
dc.title | 投影Barzilai-Borwein法求解非負矩陣分解 | zh_TW |
dc.title | Projected Barzilai-Borwein Methods for Non-negative Matrix Factorization | en |
dc.type | Thesis | |
dc.date.schoolyear | 99-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 林軒田,李育杰 | |
dc.subject.keyword | 非負矩陣分解,Barzilai-Borwein法,梯度下降法, | zh_TW |
dc.subject.keyword | Non-negative matrix factorization,Barzilai-Borwein method,projected gradient method., | en |
dc.relation.page | 34 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2011-07-13 | |
dc.contributor.author-college | 電機資訊學院 | zh_TW |
dc.contributor.author-dept | 資訊工程學研究所 | zh_TW |
顯示於系所單位: | 資訊工程學系 |
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