Skip to main content

Sparse Coding on Multiple Manifold Data

  • Conference paper
Neural Information Processing (ICONIP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8835))

Included in the following conference series:

  • 2401 Accesses

Abstract

Sparse coding has been widely used in computer vision. While capturing high-level semantics, the independent coding process neglects connections between data points. Some recent methods use Laplacian matrix to learn sparse representations with locality preserving on the manifold. Considering data points may lie in or close to multiple low dimensional manifolds embedded in the high dimensional descriptor space, we use sparse representations to code the local similarity between data points on each manifold and embed this topology to sparse coding algorithm. By keeping the locality of manifolds we can preserve the similarity and separability at the same time. Experimental results on several benchmark data sets show our algorithm is effective.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: NIPS, vol. 14, pp. 585–591 (2001)

    Google Scholar 

  2. Donoho, D.L., Grimes, C.: Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. Proceedings of the National Academy of Sciences 100(10), 5591–5596 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Elhamifar, E., Vidal, R.: Sparse manifold clustering and embedding. In: NIPS, pp. 55–63 (2011)

    Google Scholar 

  4. Gao, S., Tsang, I.H., Chia, L.T.: Laplacian sparse coding, hypergraph laplacian sparse coding, and applications. IEEE Transactions on Pattern Analysis and Machine Intelligence 35(1), 92–104 (2013)

    Article  Google Scholar 

  5. Lee, H., Battle, A., Raina, R., Ng, A.Y.: Efficient sparse coding algorithms. Advances in Neural Information Processing Systems 19, 801 (2007)

    Google Scholar 

  6. Liu, B.D., Wang, Y.X., Zhang, Y.J., Shen, B.: Learning dictionary on manifolds for image classification. Pattern Recognition 46(7), 1879–1890 (2013)

    Article  Google Scholar 

  7. Lu, X., Yuan, H., Yan, P., Yuan, Y., Li, X.: Geometry constrained sparse coding for single image super-resolution. In: 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1648–1655. IEEE (2012)

    Google Scholar 

  8. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)

    Article  Google Scholar 

  9. Wang, J., Yang, J., Yu, K., Lv, F., Huang, T., Gong, Y.: Locality-constrained linear coding for image classification. In: 2010 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3360–3367. IEEE (2010)

    Google Scholar 

  10. Yang, J., Yu, K., Gong, Y., Huang, T.: Linear spatial pyramid matching using sparse coding for image classification. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2009, pp. 1794–1801. IEEE (2009)

    Google Scholar 

  11. Zheng, M., Bu, J., Chen, C., Wang, C., Zhang, L., Qiu, G., Cai, D.: Graph regularized sparse coding for image representation. IEEE Transactions on Image Processing 20(5), 1327–1336 (2011)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Zhang, H., Xu, J. (2014). Sparse Coding on Multiple Manifold Data. In: Loo, C.K., Yap, K.S., Wong, K.W., Teoh, A., Huang, K. (eds) Neural Information Processing. ICONIP 2014. Lecture Notes in Computer Science, vol 8835. Springer, Cham. https://doi.org/10.1007/978-3-319-12640-1_62

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-12640-1_62

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12639-5

  • Online ISBN: 978-3-319-12640-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics