Abstract
In this paper, we propose new and efficient algorithms for nonnegative Tucker decomposition (NTD): Fast α-NTD algorithm which is much precise and faster than α-NTD [1]; and β-NTD algorithm based on the β divergence. These new algorithms include efficient normalization and initialization steps which help to reduce considerably the running time and increase dramatically the performance. Moreover, the multilevel NTD scheme is also presented, allowing further improvements (almost perfect reconstruction). The performance was also compared to other well-known algorithms (HONMF, HOOI, ALS algorithms) for synthetic and real-world data as well.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kim, Y.D., Cichocki, A., Choi, S.: Nonnegative Tucker Decomposition with Alpha Divergence. In: 2008 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP2008, Nevada (2008)
Tucker, L.R.: Some Mathematical Notes on Three–mode Factor Analysis. Psychometrika 31, 279–311 (1966)
Lathauwer, L.D., Moor, B.D., Vandewalle, J.: A Multilinear Singular Value Decomposition. SIAM J. Matrix Anal. Appl. 21, 1253–1278 (2000)
Mørup, M., Hansen, L.K., Arnfred, S.M.: Algorithms for Sparse Nonnegative Tucker Decompositions. Neural Computation (in print, 2008)
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)
Phan, A.H., Cichocki, A.: Multi-way Nonnegative Tensor Factorization Using Fast Hierarchical Alternating Least Squares Algorithm (HALS). In: 2008 International Symposium on Nonlinear Theory and its Applications, Budapest (2008)
Cichocki, A., Amari, S., Zdunek, R., Kompass, R., Hori, G., He, Z.: Extended SMART Algorithms for Non-Negative Matrix Factorization. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029. Springer, Heidelberg (2006)
Cichocki, A., Zdunek, R., Choi, S., Plemmons, R., Amari, S.: Non-negative Tensor Factorization Using Alpha and Beta Divergences. In: International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2007), pp. 1393–1396. IEEE Press, Honolulu (2007)
Lathauwer, L.D., Moor, B.D., Vandewalle, J.: On the Best Rank-1 and Rank-(R1,R2,...,RN) Approximation of Higher-Order Tensors. SIAM J. Matrix Anal. Appl. 21, 1324–1342 (2000)
Andersson, C.A., Bro, R.: The N-way Toolbox for MATLAB. Chemometrics and Intelligent Laboratory Systems 52, 1–4 (2000)
Bader, B.W., Kolda, T.G.: MATLAB Tensor Toolbox Version 2.2 (2007), http://csmr.ca.sandia.gov/~tgkolda/TensorToolbox/
Wu, Q., Xia, T., Yu, Y.: Hierarchical Tensor Approximation of Multi–Dimensional Images. In: 14th IEEE International Conference on Image Processing, vol. 4, pp. 49–52 (2007)
Cichocki, A., Zdunek, R.: NMFLAB – NTFLAB for Signal and Image Processing. Technical Report, Laboratory for Advanced Brain Signal Processing, BSI, RIKEN (2006), http://www.bsp.brain.riken.jp
The BTF Database Bonn: CEILING Sample, http://btf.cs.uni-bonn.de/download.html
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Phan, A.H., Cichocki, A. (2008). Fast and Efficient Algorithms for Nonnegative Tucker Decomposition. In: Sun, F., Zhang, J., Tan, Y., Cao, J., Yu, W. (eds) Advances in Neural Networks - ISNN 2008. ISNN 2008. Lecture Notes in Computer Science, vol 5264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87734-9_88
Download citation
DOI: https://doi.org/10.1007/978-3-540-87734-9_88
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87733-2
Online ISBN: 978-3-540-87734-9
eBook Packages: Computer ScienceComputer Science (R0)