參考文獻 |
[1] L. Elden, Matrix Methods in Data Mining and Pattern Recognition. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics, 2007.
[2] N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions,” SIAM Rev., vol. 53, no. 2, pp. 217-288, 2011.
[3] K. Fukunaga, Statistical Pattern Recognition, Acadamic, 1990.
[4] A. Hyvarinen, J Karhunen, and E. Oja, Independent Component Analysis, Wiley Interscience, 2001.
[5] P. N. Belhumeur, J. P. Hespanha, and D. J. Kriegman, “Eigenfaces vs. Fisherfaces: Recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 19, no. 7, pp. 711-720, Jul. 1997.
[6] D. D. Lee and H. S. Seung, “Learning the parts of objects by non-negative matrix factorization”, Nature, vol. 401, no. 6755, pp. 755-791, 1999.
[7] D. D. Lee and H. S. Seung, “Algorithms for non-negative matrix factorization,” in Proc. NIPS, 2000, pp. 556-562.
[8] W. Xu, , X.Liu, and Y. Gong, “Document clustering based on non-negative matrix factorization,” in Proc. Int. ACM Conf. on Research and development in information retrieval (SIGIR), pp. 267-273, 2003.
[9] V. P. Pauca, F. Shahnaz, M. W.Berry, and R. J. Plemmons, “Text mining using non-negative matrix factorizations,” in SDM ’04: Proc. of SIAM Int. Conf. on Data Mining, pp. 452-456, 2004
[10] F. Shahnaz, M. W. Berry, V. P. Pauca, and R. J. Plemmons, “Document clustering using nonnegative matrix factorization,” Inf. Process. Manage. vol. 42, pp. 373-386, 2006.
[11] D. Cai, X. He, X. Wu, and J. Han, “Non-negative matrix factorization on manifold,” in Proc. IEEE Int’l Data Mining (ICDM ’08), pp. 63-72, 2008.
[12] D. Cai, X. F. He, J. W. Han, and T. S. Huang, “Graph regularized non-negative matrix factorization for data representation,” IEEE Trans. Patt. Anal. and Mach. Inte., vol. 33, no. 8, pp. 1548-1560, 2011.
[13] A. Cichocki and A. H. Phan, “Fast local algorithms for large scale nonnegative matrix and tensor factorizations,” IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, vol. E92A, no. 3, pp. 708-721, 2009.
[14] C. Fevotte and J. Idier, “Algorithms for nonnegative matrix factorization with the beta-divergence,” Neural Comput., vol. 23, no. 9, pp. 2421-2456, 2011.
[15] C. Fevotte, N. Bertin, and J. L. Durrieu, “Nonnegative matrix factorization with the Itakura-Saito divergence: with application to music analysis,” Neural Comput., vol. 21, no. 3, pp. 793-830, 2009.
[16] Manh-Quan Bui, Viet-Hang Duong, Seksan Mathulaprangsan, Bach-Tung Pham, Justin Lee, Jia-Jing Wang, “A Survey of Polyphonic Sound Event Detection Based on Non-negative Matrix Factorization”, International Computer Syposium, Dec. Taiwan 2016.
[17] P. Hoyer, “Non-negative sparse coding,” in Proc. IEEE Neural Networks for Signal Processing, pp. 557-565, 2002.
[18] P. Hoyer, “Non-negative matrix factorization with sparseness constraints,” J. Mach. Learn., vol. 5, pp. 1457-1469, 2004.
[19] Z. Yuan and E. Oja, “Projective nonnegative matrix factorization for image compression and feature extraction,” in Proc. 14th Scandinavian Conf. Image Anal., Joensuu, Finland, Jun. 2005, pp. 333-342.
[20] H. Li, T. Adal, W. Wang, D. Emge, and A. Cichocki, “NMF with orthogonality constraints and its application to Raman spectroscopy,” VLSI, vol. 48, pp 83-97, 2007.
[21] N. Guan, D. Tao, Z. Luo, and B. Yuan, “Manifold regularized discriminative nonnegative matrix factorization with fast gradient descent,” IEEE Trans. Image Process., vol 20, no. 7, pp. 2030-2048, 2011.
[22] W. S. Zheng, J. H. Lai, S. Liao, and R. He, “Extracting non-negative basis images using pixel dispersion penalty”, Pattern Recognition, vol. 45, no. 8, pp. 2912–2926, 2012.
[23] I. Buciu, N. Nikolaidis, and I. Pitas, “Non-negative matrix factorization in polynomial feature space,” IEEE Trans. Neural Netw., vol. 19, pp. 1090-1100, 2007.
[24] S. Nikitidis, A. Tefas, and I. Pitas, “Projected gradients for subclass discriminant nonnegative subspace learning,” IEEE Trans. Cybern., vol. 44, no. 12, pp. 2806-2819, Dec. 2014.
[25] S. Zafeiriou and M. Petrou, “Nonlinear non-negative component analysis algorithms,” IEEE Trans. Image Process., vol. 19, no. 4, pp.1050-1066, 2009.
[26] B. Scholkopf and A. Smola, Learning with Kernels, Cambridge, MA: MIT Press, 2002.
[27] V. H. Duong, W. C. Hsieh, P. T. Bao, J. C. Wang, “An overview of kernel based nonnegative matrix factorization,” International Conference on Orange Technologies (ICOT), 2014, pp. 227-231.
[28] A. Cichocki, R. Zdunek, and S. Amari, “Csisz´ar’s divergences for non-negative matrix factorization: Family of new algorithms,” In Int. Conf. Independent Component Analysis and Signal Separation, pp. 32-39, 2006.
[29] D. Kong, C. Ding, and H. Huang, “Robust nonnegative matrix factorization using L2,1 norm,” In ACM Int. Conf. Information and Knowledge Management, pp. 673–682, 2011.
[30] R. Sandler and M. Lindenbaum, “Nonnegative matrix factorization with earth mover’s distance metric for image analysis,” IEEE Trans. Pattern Anal. Mach. Intell., 33(8):1590–1602, 2011.
[31] N. Guan, D. Tao, Z. Luo, and J. Shawe-Taylor, “MahNMF: Manhattan non-negative matrix factorization,” 2012, [Online]. Available: http://arxiv.org/abs/1207.3438.
[32] A. Cichocki, S. Cruces, and S. Amari, “Generalized alpha-beta divergences and their application to robust nonnegative matrix factorization,” Entropy, vol. 13, no. 1, pp. 134-170, 2011.
[33] T. Pham, Y.-S. Lee, Y.-B. Lin, T.-C. Tai, and J.-C. Wang, “Single channel source separation using sparse NMF and graph regularization,” in Proc. ASE BigData & SocialInformatics.
[34] V. H. Duong, Y. S. Lee, B. T. Pham, S.Mathulaprangsan, P. T. Bao, J. J. Wang, “Spatial dispersion constrained NMF for monaural source separation”, the 10th International Symposium on Chinese Spoken Language Processing, China 2016.
[35] W. C. Hsieh, C. W. Ho, V. H. Duong, Y. S. Lee, J. C. Wang, “2D semi-NMF of scale-frequency map for environmental sound classification,” Signal and Information Processing Association Annual Summit and Conference (APSIPA), 2014, pp. 1-4.
[36] V. H. Duong, B. T. Pham, P. T. Bao, J. J. Wang, “NMF-based image segmentation”, IEEE International Conference on Consumer Electronics-Taiwan (ICCE-TW), 2016, pp. 1-2.
[37] M. Q. Bui, V. H. Duong, S. Mathulaprangsan, Z Z Hong, B. C. Chen, Z. W. Zhong, J. C. Wang, “NMF/NTF-based methods applied for user-guided audio source separation: An overview”, International Conference on Orange Technologies, Dec. Autralia 2016.
[38] V. H. Duong, M. Q. Bui, J. J. Ding, B. T. Pham, Y. H Li, P. T. Bao, J. C. Wang, “Maximum volume constrained graph nonnegative matrix factorization for facial expression recognition”, IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences, vol.E100-A, no.12, Dec. 2017.
[39] S. Boyd and L. Vandenberghe, Convex optimization, Cambridge University Press, 2004
[40] J. M. Borwein and A. S. Lewis, Convex analysis and nonlinear optimization: Theory and Examples, Springer-Verlag, 2006.
[41] Erwin Kreyszig, Advanced engineering mathematics, International Student Version, John Wiley and Sons, 2011.
[42] B. P. Palka, An introduction to complex function theory, Springer, 1991
[43] M. J. Ablowitz and A. S. Fokas, Complex variables, Cambridge, 2003.
[44] M. Faijul Amin. “Wirtinger calculus based gradient descent and Levenberg-Marquardt learning algorithms in complex-valued neural networks,” Lecture Notes in Computer Science, 2011
[45] A. Hjorunges and D. Gesbert, “Complex-valued matrix differentiation: Techniques and Key Results," IEEE Trans. Signal Process., vol. 55, no. 6, pp. 2740-2746, 2007.
[46] J. R. Magnus and H. Neudecker, Matrix differntail calculus with application in statistics and econometrics, Essex, England: John Wiley & Sons, Inc., 1988.
[47] D. P. Mandic and V. S. L. Goh. 2009. Complex valued nonlinear adaptive filters: noncircularity, widely linear and neural models. Chichester, U.K. Wiley.
[48] A. van den Bos. 1994. Complex gradient and Hessian. IEEE Proceedings -Vision, Image and Signal Processing 141, 380-382.
[49] Strang, Gilbert, Linear algebra and its applications (4th ed.), Stamford, CT: Cengage Learning, pp. 154-155, 2005.
[50] P. Paatero and U. Tapper, “Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values,” Environ-metrics, vol. 5, pp. 111-126, 1994.
[51] J. Brunet, P. Tamayo, T.R. Golub, and J.P. Mesirov, “Metagenes and molecular pattern discovery using matrix factorization,” National Academy of Sciences, vol. 101, no. 12, pp. 4164-4169, 2004.
[52] Y. Gao and G. Church, “Improving molecular cancer class discovery through sparse non-negative matrix factorization,” Bioinformatics, vol. 21, no. 21, pp. 3970-3975, 2005.
[53] C. H. Cheng, D. S. Huang, L. Zhang, and X. Z. Kong, “Tumor clustering using nonnegative matrix factorization with gene selection,” IEEE Trans. Info. Tech. Biomedicine, vol. 13, no. 4, pp. 599-607, 2009.
[54] T. Virtanen, “Monaural sound source separation by nonnegative matrix factorization with temporal continuity and sparseness criteria,” IEEE Trans. On Audio, Speech, and Language Processing, vol. 15, no. 3, pp. 1066-1074, 2007.
[55] A. Cichocki, R. Zdunek, and S. Amari, “Csisz´ar’s divergences for non-negative matrix factorization: Family of new algorithms,” In Proc. Int’l Conf. Independent Component Analysis and Blind Signal Separation, 2006, pp. 32-39.
[56] A. Cichocki, S. Amari, R. Zdunek, R. Kompass, G. Hori, and Z. He, “Extended smart algorithms for non-negative matrix factorization,” ICAISC, LNCS (LNAI), vol. 4029, pp. 548-562. Springer, Heidelberg (2006).
[57] W. Liu, K. Yuan, and D. Ye, “On alpha-divergence based nonnegative matrix factorization for clustering cancer gene expression dat,” Artif. Intell. Med, vol.44, no. 1, pp.1-5, 2008.
[58] S. Zhang, W. Wang, J. Ford, and F. Makedon “Learning from incomplete ratings using non-negative matrix factorization,” Proc. of SIAM Int. Conf. on Data Mining, pp. 548-552, 2006.
[59] R. Kompass, “A generalized divergence measure for nonnegative matrix factorization,” Neural Comput., vol. 19, no. 3, pp. 780-791, 2007.
[60] B. Fasel and J. Luettin, “Automatic facial expression analysis: a survey,” Pattern Recogn., vol. 36, no. 1, pp. 259-275, 2003.
[61] I. Buciu and I. Pitas, “A new sparse image representation algorithm applied to facial expression recognition,” Proc. MLSP, 2004, pp. 539-548.
[62] R. Zhi, M. Flierl, Q. Ruan, and W. B. Kleijn, “Graph preserving sparse nonnegative matrix factorization with application to facial expression recognition,” IEEE Trans. Syst. Man Cybern., Part B, Cybern., vol. 41, no. 1, pp. 38-52, 2011.
[63] X. W. Chen and T. Huang, “Facial expression recognition: a clustering-based approach,” Pattern Recogn. Lett., vol. 24, no. 9, pp. 1295-1302, 2003.
[64] S. Nikitidis, A. Tefas, N. Nikolaidis, and I. Pitas, “Subclass discriminant nonnegative matrix factorization for facial image analysis,” Pattern Recogn., vol. 45, no. 12, pp. 4080-4091, 2012.
[65] G. Zhou, S. Xie, Z. Yang, J. M. Yang, and Z. He, “Minimum volume constrained nonnegative matrix factorization: enhanced ability of learning parts,” IEEE Trans. Neural Netw., vol. 22, no. 10, pp. 1626-1637, Oct. 2011.
[66] T. Liu, M. Gong, and D. Tao, “Large-cone nonnegative matrix factorization,” IEEE Trans. Neural Netw. Learn. Syst., Jun. 2016, doi: 10.1109/TNNLS.2016.2574748.
[67] J. Yang, S. Yang, Y. Fu, X. Li, and T. Huang, “Nonnegative graph embedding,” IEEE CVPR, 2008, pp. 1-8
[68] H. Zhang, Z. J. Zha, Y. Yang, S. Yan, and T. S. Chua, “Robust (semi) nonnegative graph embedding,” IEEE Trans. Image Process., vol. 23, no. 1, pp.2996-3012, 2014.
[69] G. Strang, Linear Algebra and Its Applications, 4th ed., Thomson, Brooks/Cole, Belmont, Ca, 2006.
[70] F. Nie, D. Xu, I. W. H. Tsang, and C. Zhang, “Flexible manifold embedding: a framework for semi-supervised and unsupervised dimension reduction,” IEEE Trans. Image Processing, vol. 19, pp. 1921-1932, 2010.
[71] S. Sun, Z. Hussain, and J. Shawe-Taylor, “Manifold-preserving graph reduction for sparse semi-supervised learning,” Neurocomputing, vol. 124, pp. 13-21, 2014.
[72] S. Dumais, “Using SVMs for text categorization,” Microsoft research, IEEE Intelligent Systems, 1998. www.research.microsoft.com, (Date: 21/ 03/06).
[73] J. Überarbeitung, Text mining in the Life Sciences, 26.9.2004.
http://www.coling.unifreiburg.de/research/projects/TextMining/WhitePaperV20.pdf
[74] C. Lin, “Projected gradient methods for non-negative matrix factorization,” Neural Comput., 19:2756-2779, 2007.
[75] S. Liwicki, G. Tzimiropoulos, S Zafeiriou, and M. Pantic, “Euler principal component analysis,” Int. J. Comput. Vis., vol. 1, pp. 498-518, 2013.
[76] Moskowitz and Martin, A course in complex analysis in one variable, World Scientific Publishing Co., pp. 7 (2002).
[77] D. Cai, X. Wang, and X. He, “Probabilistic dyadic data analysis with local and global consistency,” in Proc. the 26th Ann. Int. Conf. Machine Learning (ICML’09), 2009, pages 105-112.
[78] H. Kim, and H. Park, “Sparse non-negative matrix factorization via alternating nonnegativity constrained least squares for microarray data analysis,” Bioinformatics, vol. 23, no. 12, pp. 1495-1502, 2007.
[79] T. Zhang, B. Fang, Y. Tang, G. He and J. Wen, “Topology preserving non-negative matrix factorization for face recognition,” IEEE Trans. Image Processing, vol. 17, no. 4, pp. 574-584, Apr. 2008.
[80] A. Leonardis and H. Bischof, “Robust recognition using eigenimages,” Comput. Vis. Image Understanding, vol. 78, pp. 99-118, 2000.
[81] H. J. Oh, K.M. Lee, and S. U. Lee, “Occlusion invariant face recognition using selective local nonnegative matrix,” Image Vis. Comput, 2008, doi:10.1016/j.imavis.2008.04.016.
[82] P. N. Belhumeur, J. P. Hespanha, and D. J. Kriegman, “Eigenfaces vs. Fisherfaces: Recognition using class specific linear projection,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 19, no. 7, pp. 711-720, Jul. 1997.
[83] The ORL database of Face.
Website, http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html.
[84] Database by Georgia Institute of Technology.
Website: http://www.anefian.com/research/facereco.html.
[85] Y. Li and A. Ngom, “The non-negative matrix factorization toolbox for biological data mining,” in BMC Source Code for Biology and Medicine, 2013.
[86] N.D. Ho, P. V. Dooren, and V. Blondel, “Weighted nonnegative matrix factorization and face feature extraction,” Image and Vision Computing, 2007.
[87] N. Guan, D. Tao, Z. Luo, and J. Shawe-Taylor. (2012). MahNMF: Manhattan non-negative matrix factorization. [Online]. Available: http://arxiv.org/abs/1207.3438.
[88] Z. Yang, Z. Yuan, and J. Laaksonen, “Projective non-negative matrix factorization with applications to facial image processing,” Int. J. Pattern Recognit. Artif. Intell., vol. 21, no. 8, pp. 1353–1362, Dec. 2007.
[89] Z. Yang and E. Oja, “Linear and nonlinear projective nonnegative matrix factorization,” IEEE Trans. Neur. Network, vol. 21, no. 5, pp. 734-749, 2010.
[90] C. Ding, T. Li, and M. I. Jordan, “Convex and semi-nonnegative matrix factorizations,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 32, no. 1, pp. 45-55, Jan. 2010.
[91] W. Hu, K. Choi, P. Wang, Y. Jiang, and S. Wang, “Convex nonnegative matrix factorization with manifold regularization,” Neural Netw., vol. 63, pp. 94-103, 2015.
[92] J. Barata and M. Hussein, “The Moore–Penrose pseudoinverse: a tutorial review of the theory,” Physics, vol. 42, pp. 146-65, 2012.
[93] B. Fasel and J. Luettin, “Automatic facial expression analysis: a survey,” Pattern Recogn., vol. 36, no. 1, pp. 259-275, 2003.
[94] P. Lucey, J. F. Cohn, T. Kanade, J. Saragih, Z. Ambadar, and I. Matthews, “The extended Cohn–Kanade dataset (CK+): A complete dataset for action unit and emotion-specified expression,” IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. Workshops, pp. 94–101, 2010.
[95] M. Lyons, S. Akamatsu, M. Kamachi, and J. Gyoba, “Coding facial expressions with Gabor wavelets,” Proc. 3rd IEEE Int. Conf. Automatic Face and Gesture Recognition, pp. 200-205, 1998.
[96] Megvii, Face++ Research Toolkit, 2013, http://www.faceplusplus.com
[97] J. Eggert, E. Korner, “Sparse coding and NMF,” the 4th IEEE Int. Joint Conf Neural Networks, 2004, pp. 2529-2533.
[98] M. N. Schmidt, “Speech Separation Using Non-negative Features and Sparse Nonnegative Matrix Factorization Technical Report,” Informatics and Mathematical Modelling, Technical University of Denmark, DTU (2007)
[99] W. Liu, S. Zheng, S. Jia, L. Shen, X. Fu, “Sparse nonnegative matrix factorization with the elastic net,” IEEE International Conference on Bioinformatics and Biomedicine (BIBM), 2010, pp. 265-269.
[100] N. Guan, D. Tao, Z. Luo, B. Yuan, “NeNMF: an optimal gradient method for non-negative matrix factorization,” IEEE Trans. Signal Processing, vol. 60, no.6, pp. 2882-2898, 2012.
[101] V. H. Duong, Y. S. Lee, B. T. Pham, S. Mathulaprangsan, P. T. Bao, and J. C. Wang. “Complex matrix factorization for face recognition,”
Available:https://arxiv.org/ftp/arxiv/papers/1612/1612.02513.pdf
[102] V. H. Duong, Y. S. Lee, J. J. Ding, B. T. Pham, P. T. Bao, and J. C. Wang, “Exemplar-embed complex matrix factorization for facial expression recognition,” IEEE ICASSP, 2017.
[103] D. K. Nguyen, K. Than, and T. B. Ho, “Simplicial nonnegative matrix factorization,” in Proc. Int. Conf. on Research, Innovation and Vision for Future (RIVF), 2013, pp. 47-52.
[104] J. L. Roux, F.Weninger, and J. R. Hershey, “Sparse NMF – half-baked or well done?,” Mitsubishi Electric Research Laboratories Technical Report, 2015.
[105] P. Li, J. Bu, Y. Yang, R. Ji, C. Chen, and D. Cai, “Discriminative orthogonal nonnegative matrix factorization with flexibility for data representation,” Expert Syst. Appl, vol 41, no.4, pp. 1283-1293, 2014
[106] M. Hua, M. K. Lau, J. Pei, and K. Wu, “Continuous K-means monitoring with low reporting cost in sensor networks,” IEEE Trans Knowl. Data Eng., vol. 21, no. 12, pp. 1679-1691, 2009.
[107] S. A. Nene, S. K. Nayar, and H. Murase, “Columbia object image library (COIL-100),” Technical Report CUCS-006-96, Feb. 1996.
[108] W. Xu and Y. Gong, “Document clustering by concept factorization,” in ACM Conf. Research and Development in Information Retrieval, 2004, pp. 202-209.
[109] D. Cai, X. F. He, and J. W. Han, “Locally consistent concept factorization for document clustering,” IEEE Trans Knowl. Data Eng., vol. 23, no. 6, pp. 902-913, 2011. |