Abstract
In this paper, a collective neurodynamic optimization approach is proposed to nonnegative tensor factorization. Tensor decompositions are often applied in the data analysis. However, it is often a nonconvex optimization problem, which would cost much time and usually trap into the local minima. To solve this problem, a novel collective neurodynamic optimization approach is proposed by combining recurrent neural networks (RNN) and particle swarm optimization (PSO) algorithm. Each RNN still carries out local search. And then the best solution of each RNN improves through PSO framework. In the end, the global optimal solutions of nonnegative tensor factorization are obtained. Experiments results demonstrate the effectiveness for the nonconvex optimization with constraints.
J. Fan—The work described in the paper was supported by the National Key Research and Development Program of China under project 2016YFC1401007, the Foundation of High Resolution Special Research under 41-Y30B12-9001-14/16, and the National Natural Science Foundation of China under project 61273307.
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References
Chen, Y., Han, D., Qi, L.: New ALS methods with extrapolating search directions and optimal step size for complex-valued tensor decompositions. IEEE Trans. Sig. Process. 59, 5888–5898 (2011)
Cichocki, A., Mandic, D., Lathauwer, L., Zhou, G., Zhao, Q., Caiafa, C.: Tensor decompositions for signal processing applications: from two-way to multiway component analysis. IEEE Sig. Process. Mag. 32, 145–163 (2015)
Dauwels, J., Srinivasan, K., Reddy, M., Cichocki, A.: Near-lossless multichannel EEG compression based on matrix and tensor decompositionss. IEEE J. Biomed. Health Inform. 17, 708–714 (2013)
Kolda, T., Bader, B.: Tensor decompositions and applications. SIAM Rev. 51, 455–500 (2009)
Chen, Y., Hsu, C., Hsu, H., Liao, H.: Simultaneous tensor decomposition and completion using factor priors. IEEE Trans. Pattern Anal. Mach. Intell. 36, 577–591 (2014)
Lee, D., Seung, H.: Algorithms for nonnegative matrix factorization. In: Advances in Neural Information Processing Systems, pp. 556–562 (2000)
Cichocki, A., Zdunek, R., Phan, A., Amari, S.: Nonegative Matrix and Tensor Factorizations: Application to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley, Chichester (2009)
Phan, A., Cichocki, A.: Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification. Neurocomputing 74, 1956–1969 (2011)
Wang, J., Wu, G.: Recurrent neural networks for LU decomposition and Cholesky factorization. Math. Comput. Model. 18, 1–8 (1993)
Xia, Y.S., Wang, J.: A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints. IEEE Trans. Circ. Syst. I Regul. Pap. 51, 1385–1394 (2004)
Yan, Z., Wang, J., Li, G.C.: A collective neurodynamic optimization approach to bound-constrained nonconvex optimization. Neural Netw. 55, 20–29 (2014)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks, pp. 1942–1948 (1995)
Han, M., Fan, J.C., Wang, J.: A dynamic feedforward neural network based on gaussian particle swarm optimization and its application for predictive control. IEEE Trans. Neural Netw. 22, 1457–1468 (2011)
Lathauwer, L.D., Castaing, J., Cardoso, J.F.: Fourth-order cumulantbased blind identification of underdetermined mixtures. IEEE Trans. Sig. Process. 55, 2965–2973 (2007)
Liu, Q.S., Wang, J.: A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming. IEEE Trans. Neural Netw. 19, 558–570 (2008)
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Fan, J., Wang, J. (2017). A Collective Neurodynamic Optimization Approach to Nonnegative Tensor Decomposition. In: Cong, F., Leung, A., Wei, Q. (eds) Advances in Neural Networks - ISNN 2017. ISNN 2017. Lecture Notes in Computer Science(), vol 10262. Springer, Cham. https://doi.org/10.1007/978-3-319-59081-3_25
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DOI: https://doi.org/10.1007/978-3-319-59081-3_25
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