Alternating proximal gradient method for sparse nonnegative Tucker decomposition
Tóm tắt
Từ khóa
Tài liệu tham khảo
Allen, G.I.: Sparse higher-order principal components analysis. In: International conference on artificial intelligence and statistics (AISTATS), pp 27–36 (2012)
Bader, B.W., Kolda, T.G., et al.: Matlab tensor toolbox version 2.5 (2012). http://www.sandia.gov/~tgkolda/TensorToolbox
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183–202 (2009)
Bolte, J., Daniilidis, A., Lewis, A.: The Lojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems. SIAM J. Optim. 17, 1205–1223 (2007)
Carroll, J.D., Chang, J.J.: Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition. Psychometrika 35, 283–319 (1970)
Cichocki, A., Mandic, D., Phan, A.H., Caiafa, C., Zhou, G., Zhao, Q., De Lathauwer, L.: Tensor decompositions for signal processing applications: from two-way to multiway component analysis. arXiv:1403.4462 (2014)
Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley, UK (2009)
Cong, F., Phan, A.H., Zhao, Q., Wu, Q., Ristaniemi, T., Cichocki, A.: Feature extraction by nonnegative tucker decomposition from EEG data including testing and training observations. Neural Inf. Process. 3, 166–173 (2012)
De Lathauwer, L., De Moor, B., Vandewalle, J.: On the best rank-1 and rank- $$(r_1, r_2,\ldots, r_n)$$ ( r 1 , r 2 , … , r n ) approximation of higher-order tensors. SIAM J. Matrix Anal. Appl. 21, 1324–1342 (2000)
Ding, C., Li, T., Jordan, M.: Convex and semi-nonnegative matrix factorizations. Pattern Anal. Mach. Intell. IEEE Trans. 32, 45–55 (2010)
Donoho D., Stodden, V.: When does non-negative matrix factorization give a correct decomposition into parts. Adv. Neural Inf. Process. Syst. 16 (2003)
Friedlander, M.P., Hatz, K.: Computing non-negative tensor factorizations. Optim. Methods Softw. 23, 631–647 (2008)
Harshman, R.A.: Foundations of the parafac procedure: models and conditions for an “explanatory” multimodal factor analysis. UCLA Working Papers Phonetics 16, 1–84 (1970)
Kiers, H.A.L.: Joint orthomax rotation of the core and component matrices resulting from three-mode principal components analysis. J. Classif. 15, 245–263 (1998)
Kim, H., Park, H.: Non-negative matrix factorization based on alternating non-negativity constrained least squares and active set method. SIAM J. Matrix Anal. Appl. 30, 713–730 (2008)
Kim, J., Park, H.: Toward faster nonnegative matrix factorization: a new algorithm and comparisons. In: Data Mining, 2008. ICDM’08. Eighth IEEE International Conference on, IEEE, pp. 353–362 (2008)
Kim, Y.D., Choi, S.: Nonnegative Tucker decomposition. In: Computer Vision and Pattern Recognition, 2007. CVPR’07. IEEE Conference on, IEEE, pp. 1–8 (2007)
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)
Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. Adv. Neural Inf. Process. Syst. 13, 556–562 (2001)
Ling, Q., Xu, Y., Yin, W., Wen, Z.: Decentralized low-rank matrix completion. In: International Conference on Acoustics, Speech, and Signal Processing (ICASSP), SPCOM-P1.4 (2012)
Liu, J., Liu, J., Wonka, P., Ye, J.: Sparse non-negative tensor factorization using columnwise coordinate descent. Pattern Recogn. 45, 649–656 (2011)
Łojasiewicz, S.: Sur la géométrie semi-et sous-analytique. Ann. Inst. Fourier (Grenoble) 43, 1575–1595 (1993)
Mørup, M., Hansen, L.K., Arnfred, S.M.: Algorithms for sparse nonnegative Tucker decompositions. Neural Comput. 20, 2112–2131 (2008)
Paatero, P., Tapper, U.: Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5, 111–126 (1994)
Phan, A.H., Cichocki, A.: Extended hals algorithm for nonnegative tucker decomposition and its applications for multiway analysis and classification. Neurocomputing 74, 1956–1969 (2011)
Phan, A.H., Tichavsky, P., Cichocki, A.: Damped gauss-newton algorithm for nonnegative tucker decomposition. In: Statistical Signal Processing Workshop (SSP), IEEE, pp. 665–668 (2011)
Ramirez, I., Sprechmann, P., Sapiro, G.: Classification and clustering via dictionary learning with structured incoherence and shared features. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3501–3508 (2010)
Schatz, M., Low, T., Geijn, V., Robert, A., Kolda, T.: Exploiting Symmetry in Tensors for High Performance: Multiplication with Symmetric Tensors. arXiv, preprint arXiv:1301.7744 (2013)
Shashua, A., Hazan, T.: Non-negative tensor factorization with applications to statistics and computer vision. In: Proceedings of the 22nd international conference on Machine learning, ACM, pp. 792–799 (2005)
Tucker, L.R.: Some mathematical notes on three-mode factor analysis. Psychometrika 31, 279–311 (1966)
Wen, Z., Yin, W., Zhang, Y.: Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm. Math. Progr. Comput. 4, 333–361 (2012)
Xu, Y., Yin, W.: A block coordinate descent method for regularized multi-convex optimization with applications to nonnegative tensor factorization and completion. SIAM J. Imaging Sci. 6, 1758–1789 (2013)
Xu, Y., Yin, W., Wen, Z., Zhang, Y.: An alternating direction algorithm for matrix completion with nonnegative factors. J. Front. Math. China Special Issue Comput. Math. 7, 365–384 (2011)
Zafeiriou, S.: Discriminant nonnegative tensor factorization algorithms. Neural Netw. IEEE Trans. 20, 217–235 (2009)
Zhang, Q., Wang, H., Plemmons, R.J., Pauca, V.: Tensor methods for hyperspectral data analysis: a space object material identification study. JOSA A 25, 3001–3012 (2008)
Zhang, Y.: An alternating direction algorithm for nonnegative matrix factorization. Rice Technical Report (2010)