Abstract
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).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
Pan, J., Yang, Q.: Co-localization from labeled and unlabeled data using graph laplacian. In: Proceedings of IJCAI 2007, pp. 2166–2171 (2007)
Roweis, S., Saul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)
Roweis, S.: Em algorithms for pca and spca. In: in Advances in Neural Information Processing Systems, pp. 626–632 (1998)
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)
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)
Tenenbaum, J.B., Silva, V.D., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)
Thrun, S., Burgard, W., Fox, D.: Probabilistic Robotics. MIT Press (2005)
Verbeek, J., Roweis, S.T., Vlassis, N.: Non-linear cca and pca by alignment of local models. In: Procs. of NIPS (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yairi, T. (2012). Co-embedding of Structurally Missing Data by Locally Linear Alignment. In: Tan, PN., Chawla, S., Ho, C.K., Bailey, J. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2012. Lecture Notes in Computer Science(), vol 7302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30220-6_35
Download citation
DOI: https://doi.org/10.1007/978-3-642-30220-6_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30219-0
Online ISBN: 978-3-642-30220-6
eBook Packages: Computer ScienceComputer Science (R0)