Abstract

The previous chapter discussed the use of decision forests for estimating the latent density of unlabeled data. This has led to a forest-based probabilistic generative model which captures efficiently the “intrinsic” structure of the data themselves. The present chapter delves further into the issue of learning the structure of high dimensional data as well as mapping them onto a lower dimensional space, while preserving spatial relationships between data points. This task goes under the name of manifold learning and is closely related to dimensionality reduction and embedding.

Keywords

Manifold Covariance Beach 

References

  1. 22.
    Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput Google Scholar
  2. 23.
    Belkin M, Niyogi P (2008) Towards a theoretical foundation for Laplacian-based manifold methods. J Comput Syst Sci 74(8) Google Scholar
  3. 29.
    Bishop CM, Svensen M, Williams CKI (1998) GTM: the generative topographic mapping. Neural Comput Google Scholar
  4. 58.
    Cayton L (2005) Algorithms for manifold learning. Technical Report CS2008-0923, University of California, San Diego Google Scholar
  5. 61.
    Chapelle O, Schölkopf B, Zien A (2006) Semi-supervised learning. MIT Press, Cambridge Google Scholar
  6. 73.
    Cox TF, Cox MAA (2001) Multidimensional scaling. Chapman and Hall, London Google Scholar
  7. 87.
    De Porte J, Herbst BM, Hereman W, van Der Walt SJ (2008) An introduction to diffusion maps. Techniques Google Scholar
  8. 95.
    Duchateau N, De Craene M, Piella G, Frangi AF (2011) Characterizing pathological deviations from normality using constrained manifold learning. In: Proc medical image computing and computer assisted intervention (MICCAI) Google Scholar
  9. 114.
    Freund Y, Dasgupta S, Kabra M, Verma N (2007) Learning the structure of manifolds using random projections. In: Advances in neural information processing systems (NIPS) Google Scholar
  10. 124.
    Gerber S, Tasdizen T, Joshi S, Whitaker R (2009) On the manifold structure of the space of brain images. In: Proc medical image computing and computer assisted intervention (MICCAI) Google Scholar
  11. 128.
    Geurts P, Ernst D, Wehenkel L (2006) Extremely randomized trees. Mach Learn 36(1) Google Scholar
  12. 142.
    Gray KR, Aljabar P, Heckeman RA, Hammers A, Rueckert D (2011) Random forest-based manifold learning for classification of imaging data in dementia. In: Proc medical image computing and computer assisted intervention (MICCAI) Google Scholar
  13. 149.
    Hamm J, Ye DH, Verma R, Davatzikos C (2010) GRAM: a framework for geodesic registration on anatomical manifolds. Med Image Anal 14(5) Google Scholar
  14. 160.
    Hegde C, Wakin MB, Baraniuk RG (2007) Random projections for manifold learning—proofs and analysis. In: Advances in neural information processing systems (NIPS) Google Scholar
  15. 175.
    Jolliffe IT (1986) Principal component analysis. Springer, Berlin Google Scholar
  16. 194.
    Konukoglu E, Glocker B, Zikic D, Criminisi A (2012) Neighborhood approximation forests. In: Proc medical image computing and computer assisted intervention (MICCAI) Google Scholar
  17. 223.
    Lin Y, Jeon Y (2002) Random forests and adaptive nearest neighbors. J Am Stat Assoc Google Scholar
  18. 236.
    Marée R, Geurts P, Wehenkel L (2007) Content-based image retrieval by indexing random subwindows with randomized trees. In: Proc Asian conf on computer vision (ACCV). LNCS, vol 4844. Springer, Berlin Google Scholar
  19. 262.
    Nadler B, Lafon S, Coifman RR, Kevrekidis IG (2005) Diffusion maps, spectral clustering and eigenfunctions of Fokker-Plank operators. In: Advances in neural information processing systems (NIPS) Google Scholar
  20. 273.
    O’Hara S, Draper BA (2012) Scalable action recognition with a subspace forest. In: Proc IEEE conf computer vision and pattern recognition (CVPR) Google Scholar
  21. 335.
    Shi T, Horvath S (2006) Unsupervised learning with random forest predictors. J Comput Graph Stat 15 Google Scholar
  22. 336.
    Shi J, Malik J (1997) Normalized cuts and image segmentation. In: Proc IEEE conf computer vision and pattern recognition (CVPR), Washington, DC, USA Google Scholar
  23. 367.
    Tenenbaum JB, deSilva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500) Google Scholar
  24. 405.
    Xiong C, Johnson D, Xu R, Corso JJ (2012) Random forests for metric learning with implicit pairwise position dependence. In: Proc of ACM SIGKDD intl conf on knowledge discovery and data mining Google Scholar
  25. 415.
    Zhang Q, Souvenir R, Pless R (2006) On manifold structure of cardiac MRI data: application to segmentation. In: Proc IEEE conf computer vision and pattern recognition (CVPR), Los Alamitos, CA, USA Google Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • A. Criminisi
    • 1
  • J. Shotton
    • 1
  1. 1.Microsoft Research Ltd.CambridgeUK

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