Co-embedding of Structurally Missing Data by Locally Linear Alignment

  • Takehisa Yairi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7302)


This paper proposes a “co-embedding” method to embed the row and column vectors of an observation matrix data whose large portion is structurally missing into low-dimensional latent spaces simultaneously. A remarkable characteristic of this method is that the co-embedding is efficiently obtained via eigendecomposition of a matrix, unlike the conventional methods which require iterative estimation of missing values and suffer from local optima. Besides, we extend the unsupervised co-embedding method to a semi-supervised version, which is reduced to a system of linear equations.In an experimental study, we apply the proposed method to two kinds of tasks – (1) Structure from Motion (SFM) and (2) Simultaneous Localization and Mapping (SLAM).


Dimensionality Reduction Singular Value Decomposition Latent Vector Wireless Device Latent Semantic Indexing 
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  1. 1.
    Okatani, T., Deguchi, K.: On the wiberg algorithm for matrix factorization in the presence of missing components. International Journal of Computer Vision 72(3), 329–337 (2007)CrossRefGoogle Scholar
  2. 2.
    Pan, J., Yang, Q.: Co-localization from labeled and unlabeled data using graph laplacian. In: Proceedings of IJCAI 2007, pp. 2166–2171 (2007)Google Scholar
  3. 3.
    Roweis, S., Saul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)CrossRefGoogle Scholar
  4. 4.
    Roweis, S.: Em algorithms for pca and spca. In: in Advances in Neural Information Processing Systems, pp. 626–632 (1998)Google Scholar
  5. 5.
    Shum, H.Y., Ikeuchi, K., Reddy, R.: Principal component analysis with missing data and its application to polyhedral object modeling. IEEE Trans. Pattern Anal. Mach. Intell. 17(9), 854–867 (1995)CrossRefGoogle Scholar
  6. 6.
    Sindhwani, V., Bucak, S.S., Hu, J., Mojsilovic, A.: One-class matrix completion with lowdensity factorizations. In: Proceedings of the 2010 IEEE International Conference on Data Mining, pp. 1055–1060 (2010)Google Scholar
  7. 7.
    Tenenbaum, J.B., Silva, V.D., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)CrossRefGoogle Scholar
  8. 8.
    Thrun, S., Burgard, W., Fox, D.: Probabilistic Robotics. MIT Press (2005)Google Scholar
  9. 9.
    Verbeek, J., Roweis, S.T., Vlassis, N.: Non-linear cca and pca by alignment of local models. In: Procs. of NIPS (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Takehisa Yairi
    • 1
  1. 1.Research Center for Advanced Science and TechnologyUniversity of TokyoJapan

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