A Two Stage Algorithm for K-Mode Convolutive Nonnegative Tucker Decomposition

  • Qiang Wu
  • Liqing Zhang
  • Andrzej Cichocki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7063)


Higher order tensor model has been seen as a potential mathematical framework to manipulate the multiple factors underlying the observations. In this paper, we propose a flexible two stage algorithm for K-mode Convolutive Nonnegative Tucker Decomposition (K-CNTD) model by an alternating least square procedure. This model can be seen as a convolutive extension of Nonnegative Tucker Decomposition (NTD). Shift-invariant features in different subspaces can be extracted by the K-CNTD algorithm. We impose additional sparseness constraint on the algorithm to find the part-based representations. Extensive simulation results indicate that the K-CNTD algorithm is efficient and provides good performance for a feature extraction task.


Speaker Recognition Tensor Factorization Sparse Constraint Noisy Condition Speaker Modeling 
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  1. 1.
    Cichocki, A., Zdunek, R., Phan, A.H.: Nonnegative matrix and tensor factorizations: applications to exploratory multi-way data analysis and blind source separation. John Wiley and Sons (2009)Google Scholar
  2. 2.
    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)CrossRefzbMATHGoogle Scholar
  3. 3.
    Kroonenberg, P.M., De Leeuw, J.: Principal component analysis of three-mode data by means of alternating least squares algorithms. Psychometrika 45, 69–97 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    De Lathauwer, L., De Moor, B., Vandewalle, J.: A multilinear singular value decomposition. SIAM Journal on Matrix Analysis and Applications 21, 1253–1278 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Harshman, R.A., Hong, S., Lundy, M.E.: Shifted factor analysis Part I: Models and properties. Journal of Chemometrics 17, 363–378 (2003)CrossRefGoogle Scholar
  6. 6.
    Mørup, M., Hansen, L.K., Arnfred, S.M., Lim, L.H., Madsen, K.H.: Shift-invariant multilinear decomposition of neuroimaging data. NeuroImage 42, 1439–1450 (2008)CrossRefGoogle Scholar
  7. 7.
    Mørup, M.: Applications of tensor (multiway array) factorizations and decompositions in data mining. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 1, 24–40 (2011)Google Scholar
  8. 8.
    Smaragdis, P.: Convolutive speech bases and their application to supervised speech separation. IEEE Transactions on Audio, Speech, and Language Processing 15, 1–12 (2007)CrossRefGoogle Scholar
  9. 9.
    Cichocki, A., Phan, A.H.: Fast local algorithms for large scale nonnegative matrix and tensor factorizations. IEICE Transactions on Fundamentals of Electronics 92, 708–721 (2009)CrossRefGoogle Scholar
  10. 10.
    Kim, Y.D., Choi, S.: Nonnegative tucker decomposition. In: CVPR 2007, pp. 1–8 (2007)Google Scholar
  11. 11.
    Wu, Q., Zhang, L.Q., Shi, G.C.: Robust feature extraction for speaker recognition based on constrained nonnegative tensor factorization. Journal of Computer Science and Technology 25, 783–792 (2010)CrossRefGoogle Scholar
  12. 12.
    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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Qiang Wu
    • 1
  • Liqing Zhang
    • 2
  • Andrzej Cichocki
    • 3
  1. 1.School of Information Science and EngineeringShandong UniversityJinanChina
  2. 2.Department of Computer Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina
  3. 3.Laboratory for Advanced Brain Signal ProcessingBSI RIKENWakoshiJapan

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